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W orking Model 2D

1. D 1 The Flexbeam Script D 5 Figure D 7 After Running Flexbeam Pin Roller Beam iin aaa The Fixed Free Cantilever Beam The left end of the cantilever beam shown in Figure D 8 is fixed and the right end is free To model a cantilever beam use a square pin to attach the beam to the background or to another body As Figure D 10 indicates Flexbeam replaces the square pin cantilever constraint with a rotational spring whose spring constant is defined by the equation E n 4 L 3n 1 This replacement accommodates the transition from the zero rotation constraint imposed by the square pin at the left end of the first element to the finite rotation at the right end Figure D 8 A Cantilever Beam D 6 Appendix D Scripts Figure D 9 A Cantilever Beam before Flexbeam F Cantilever Beam Notice that in Figure D 10 Flexbeam automatically replaces the square pin at the base of the beam with a rotational spring Figure D 10 A Cantilever Beam after Flexbeam Cantilever Beam Restoring Flexible Bodies to Their Original Rigid Form The script Unflex undoes the alterations that Flexbeam made to the original document To use Unflex on a single beam select one or more of the elements of the beam and run Unflex to restore the beam to its original rigid form If no beams are selected Unflex will ask you whether you wish to simultaneously
2. Objects Selection Working Model Basic Quick Reference Sheet Collection of WMBody objects Item n Bodies Body id name g WMBody lt Collection of M en eel WMConstraint objects N Teen Body Constraints Constraint id name WMConstraint Constrain Collection of Point n ha WMPoint objects Ttem n Points gt Point id name WMPoint Collection of WMInput objects Item n Inputs Input id name g WMinput Collection of baena WMInput objects Item n Outputs Output id name gt WMOutput Column n WMOutputColumn WM Basic objects A Collection of gt WMObject objects tem n y WMObject These objects also have the properties available to WMObject WMCell WMCell objects are properties of WMBody WMConstraint and WMOutputColumn objects see back for more Working Model Basic Objects Shown below are selected properties methods and syntax for Working Model Basic objects Please refer to the manual WMBasic pdf on CD for complete information Methods with return values and all the properties are followed by curly brackets indicating the type of the
3. Vir y f m i collision force as reported in Working Model 2D where t is the animation time step NOTE The measurement of the collision force in Working Model 2D depends on the size of yt whereas the collision impulse f Ar is represented accurately at all times In physical experiments a collision force profile typically resembles a spike shaped bell curve whose support where the function is non zero i e the physical duration of the collision is often much smaller than a typical time step used in numerical simulations see Figure A 4 Physical Collision 8 ___ Force Profile S bell curve 3 g Forces computed 5 numerically rectangles time elapsed Time Steps A 22 Appendix A Technical Information The area underneath the bell curve is called impulse and this quantity is preserved in Working Model 2D correctly regardless of the time step size In Figure A 4 rectangles of various sizes represent the shape of impulse computed in Working Model 2D note that the height peak force varies depending on the time step size because the impulse the area of the rectangles does not change with the step size Because Working Model 2D is a discrete time simulator and because the exact duration of the collision is rarely known even in physical experiments Working Model 2D reports the collision force as the impulse divided by the animation time step The collision force re
4. Figure 7 17 A pendulum with acceleration and velocity vectors The following properties can be represented graphically with vectors e velocity e acceleration total force e gravitational force e electrostatic force e air force e force field e contact force e friction force Displaying Vectors To display one or more vectors 1 Select one or more bodies whose vectors you want to display graphically Figure 7 18 Vector Lengths dialog 7 4 Vectors 243 The Vectors submenu in the Define menu lists the possible vectors that can be displayed for the selected object s If more than one object is selected and the currently displayed vectors for the bodies do not match a will appear next to the vector type signifying that a mixed selection exists 2 Choose the type of vector to display from the Vectors submenu of the Define menu The vectors will be displayed the next time you run the simulation Adjusting the Length of Vectors The length of a displayed vector is based on its magnitude and a scale factor Depending on the properties represented by vectors the vectors may be too long or too short making it difficult or impossible to see their values Working Model 2D provides a tool to adjust the scale factor For example in the SI units system suppose a force vector has magnitude of 10 Newtons and the scale factor is set to 0 1 Then the vector is displayed as 10x 0 1 1 0 or 1 0 me
5. Click OK to save your changes 6 4 Defining World Parameters 207 The following table shows examples of how a number appears depending on which option fixed floating or auto you select Figure 6 18 Numerical formats Number Fixed 1 digit Float 1 digit Auto 1 digit 333 3333 333 3 333 3 Formulas and Units Changing units will affect all the constants and formulas that define the properties of the system For more information on how formulas are converted to match unit changes see Chapter 10 Using Formulas 6 4 Defining World Parameters When you create a new simulation document the initial settings for the world are Figure 6 19 Default f ean potai Air Resistance none Electrostatics none Force Field none Gravity The default setting of gravity is vertical gravity To change the world s gravity 1 Choose Gravity from the World menu 208 Chapter 6 The Workspace Figure 6 20 Gravity dialog Vertical Gravity Planetary Gravity The Gravity dialog appears as shown in Figure 6 20 C C Planetar k i Cancel a 9 807 m s 2 2 Click on the type of gravity you want When None is selected it indicates that gravity is not active Vertical gravity creates a vertical field like that near the surface of the earth Planetary produces gravitational interaction between each pair of objects 3 Enter a value to adjust the magnitude of gravity When adju
6. 2 Select the point and the slot Select two objects by holding down the shift key and clicking on each object in turn 4 19 Slot Joints 161 Figure 4 73 Selecting a point and a straight slot So Select the point and the slot z 3 Click the Join button on the Toolbar Join A slot joint is created The body moves so that the point and slot overlap Figure 4 74 Creating a slot joint by joining a point and a slot New slot joint Cam Mechanism To illustrate how a curved slot joint can be created from primitive elements let s create a component of a cam mechanism as shown in Figure 4 75 below 162 Chapter 4 Constraints Figure 4 75 Simple cam mechanism Create a disk and draw a closed curved slot on it Use the Closed Curved Slot tool Click the first control point on the disk and click several control points finishing the curve with a double click or by pressing the space bar We will make do with an arbitrary slot shape for now Refer to Reshaping a Curved Slot Numerically on page 167 for precise adjustment of the slot geometry Attach a motor on the center of the disk The motor will later drive the mechanism Create a rectangular body a cam follower and attach a point element on one end of the rectangle which will later serve as the pin on the slot Make sure the object is long enough as shown in the figure above Select the slot and hold down the
7. A Linkage Example Figure 5 15 is an example of a mechanism in which moving any piece automatically moves all the others Figure 5 15 A linkage of four rectangles 184 Chapter 5 The Smart Editor Moving any of the pieces causes deformations in the shape of the linkage For instance grabbing and dragging the upper bar causes the deformations shown in Figure 5 16 and Figure 5 17 Figure 5 16 Dragging the upper bar up and to the right Figure 5 17 Dragging the upper bar up and to the left Rotating Bodies C The Rotate tool also uses the Smart Editor to resolve constraints The simple linkage shown in Figure 5 18 has two rectangles and two pin joints Figure 5 18 A linkage of two rectangles and two pin joints Figure 5 19 The dotted line between the pointer and the nearest pivot point 5 3 Understanding the Smart Editor 185 Select the Rotate tool A dotted line will appear between the pointer and the nearest pivot point meaning a point around which one could reasonably rotate an object Joints are used as possible pivot points The center of mass of each object is also used as a possible pivot point See Figure 5 19 Rotate the horizontal rectangle It rotates around the joint connecting it to the vertical rectangle as in Figure 5 20 The Rotate tool will always leave fixed the other body the one that is connecte
8. Running Simulations with Multiple Tracks The default behavior for Working Model 2D is to erase tracks whenever something that may affect the results of the simulation is modified such as modifying an object property or a world setting Disabling the AutoErase Track item in the World menu will inhibit the automatic track erasing and allow simulations with multiple overlapping tracks Selecting Erase Track from the World menu will erase all tracks and refresh all meters and other objects on the Interface layer see below for more details As an example of a multiple track simulation let s look at the effect of elasticity on a simple collision To create the collision model 1 Create a circle 2 Choose Preferences in the World menu Preferences dialog appears 3 Click Allow Velocity Vector Dragging 270 Chapter 8 Running Simulations Figure 8 16 A simple collision model Give the circle an initial downward velocity by selecting it and dragging its velocity vector from the center of the object Create a table by drawing a rectangle and anchoring it in place The model should look similar to the one shown in Figure 8 16 Set the elasticity of the table to 1 You can set the elasticity by opening the Properties window for the table Select the table and choose Properties under the Window menu Control the elasticity of the ball via a Control slider Select the circle object representing the bal
9. The Properties window changes its appearance depending on the type of control you choose 2 If you want to change the title and the color of a control use the Appearance window 236 Figure 7 13 Properties window for controls Sliders Text Box Button Chapter 7 Simulation Interfaces Input 5 Spring 3 Spring Spring 3 Spring Constant Text box Slider Button Data table min Jo500 max 50 000 M Show Text Number of snaps 20 3 Select the control type by clicking on the desired control type Each control type is associated with a different set of properties that you can specify You can specify minimum and maximum values for the slider bars Number of snaps indicate how many discrete values are available in the range of the slider By default a text window is attached to a slider control You can use the text window to enter a precise value within the range even if the value may not coincide with the discrete steps of the slider This text window can be turned on and off by clicking on the Show Text checkbox A text box allows you to enter precise numerical input for the property value Using a button you can quickly select one of the two values specified in min and max boxes A button can act as a toggle switch or as a press and hold button is pressed as long as you hold your mouse button down button Table 7 2 Controls 237 A table control reads its value from a tabl
10. You can also use the geometry of one body to specify that of another Using this feature for instance you can design a four bar linkage in which the length of the crank link is based on a dimension of the coupler link Resizing the coupler link will then automatically resize the crank link based on your specification Working Model provides an automatic snap feature often found in CAD applications As you create bodies and constraints your mouse pointer can snap to certain predefined points on the body geometry allowing precise positioning of objects at their creation You can quickly modify the geometry and position of various objects in Working Model by entering desired properties directly on the screen Simply select the desired object and Working Model will present you with a list of parameters such as width height and position of a body that can be edited on the fly type in the precise values and the modification will take effect immediately Working Model uses Apple events MacOS or DDE Windows to communicate with other applications during a simulation Users can specify physical models of real life mechanical designs and then control them externally through other programs For instance a Microsoft Excel worksheet can be used to model an external control system Working Model can both send data to and receive control signals from the worksheet while a simulation is in progress Furthermore other applications
11. 1 Under the Measure menu choose Time and create a time meter In fact any meter can be used as a variable For now we will just use a Time meter and modify it 2 Double click on the Time meter The Properties window appears 3 Overwrite the field y1 with the formulas shown in Figure 10 9 below If necessary resize the Properties window so you can view the entire text in the formula box This step is where you define the variable In fact you can use any or all of the output fields y1 through y4 to define variables 10 9 Using Meters as Variables in Formulas 343 Figure 10 9 Using a meter field as a variable Dutput 9 Distance Medd Distance Meter Label Equation x frame framef yl distance Ibody 1 p body 10 pl y2 Auto Min Max Overwrite these fields a o o00 f1 000 labelling is optional DET o c00 1 000 You can now refer to the distance quantity by simply typing output 9 y1 or y2 through y4 depending on which field you used as a variable instead of spelling out body 1 p body 10 p For example in order to take the square root distance between the two bodies you can type sqrt output 9 y1 instead of sqrt body 1 p body 10 p If you do not wish to see the meter that holds the formula on your workspace you can hide it Simply remove the checkmark from the item Show in the Appearance window for the meter A 1 APPENDIX A Technical Information
12. NOTE If your display monitor has a resolution of 640 by 480 pixels Working Model 2D only displays the Simple toolbar shown in Figure 2 1 and the Standard toolbar by default The Simple toolbar provides a set of the most commonly used tools To activate other toolbars choose Workspace in the View menu and activate individual toolbars see The View Menu on page 50 34 Chapter 2 Guide to Tools amp Menus Figure 2 1 Simple Toolbar Windows a subset of all tools By clicking and dragging on the border ofa toolbar you can tear it off from its docked position and place it anywhere within the application window Floating toolbars can then be redocked by dragging them to an edge of the window Each toolbar whether floating or docked is available to all open documents Circle Square Rectangle Polygon Curved Body Anchor Point Pin Joint Rigid Joint Slot Joint Spring Damper Spring Damper Force Motor Rope Figure 2 2 Standard Edit and Run Control Toolbars Windows 2 1 The Working Model 2D Toolbars Standard HAE WISE New Open Save Cut Copy Paste Print Help File Operations Clipboard Operations Edit kola 2 9 Arrow Text Zoom Out Rotate Zoom In Run Control Run Stopu Reset Run Stop Reset 35 36 Figure 2 3 Body Join Split and Point Toolbars Windows Chapter 2 Guide to Tools amp Menus Body B Circle O C Square Poly
13. On MacOS systems the Gear tool is hidden in the Pulley pop up palette by default Click and hold on the Pulley tool to bring the Gear tool in view and select it 3 Click and hold the mouse on the first body If attached to a body a gear icon is automatically aligned with the center of mass of the body 4 Drag the mouse to the second body Release the mouse button to create the second gear The second gear icon is automatically aligned with the center of mass of the second body if attached to a body The Coordinates bar display for Gears shows the position of the two endpoints Since the endpoints are always aligned to the Center of Mass the Coordinates bar almost always shows 0 0 initially Editing these values will result in shifting the endpoints of the built in rod for the gear When a gear constraint is defined Working Model 2D creates a pair of external gears or spur gears by default which behave as if they had gear teeth on their outer circumference and were in contact with each other Typically two non overlapping bodies that are close to each other are made into external gears You can define one of the bodies connected with the gear constraint to act as an internal gear a gear that has teeth along the inside of its circumference A typical example may involve two overlapping bodies usually with one completely inside the other where the larger body is defined as the internal gear as shown in Figure 4 3
14. Plastic Rubber 4 0 251 7 Density Wy H 0 3 In Working Model 2D Elasticity refers to the coefficient of restitution considered in collisions To set a body s properties to those of a specific material 1 Bring up the Properties window for the body by double clicking on the body or by selecting it and choosing Properties from the Window menu 2 Choose the desired material from the pop up Material menu Picking a material sets a body s density mass moment elastic and frictional coefficients and charge 72 Chapter 3 Bodies Coordinates bar Figure 3 10 Coordinates bar when two rectangles are selected Properties Window Changing Properties of Multiple Objects Simultaneously You can quickly set many bodies to have the same properties by selecting multiple objects at the same time You can use either the Coordinates bar for quick editing or the Properties window for complete control The Coordinates bar automatically determines what properties are common among the selected objects and displays them accordingly For example all bodies have x and y position as well as orientation The Coordinates bar will display these fields when multiple objects are selected Ifa particular property differs among the selected bodies the Coordinates bar shows the property as blank see Figure 3 10 xl Im yL 5 500 m hl _2 500 m wl __ m al o o00 The above display indicates that the two rectangles have
15. current 1 910 m Constraint 3 Spring Active when M Always If you do not edit this formula the original numeric value will be returned if you delete the control You can create a slider to set the initial velocity of a body before running a simulation Use the slider to adjust the velocity then run the simulation again using the adjusted value For more on formulas see Chapter 10 Using Formulas Creating Controls To create a control for a body or constraint 234 Chapter 7 Simulation Interfaces Figure 7 11 New Control menu rectangle selected Control Position New Control gt Initial Position Initial Position Initial Position Initial H Velocity Initial Y Velocity Initial Velocity Speed and Direction Mass Moment Friction Static Friction Kinetic Friction Elasticity Charge Height Width 1 Select the object whose properties you want to change The properties that you can control are listed on the Control menu You can add a control for each of the properties listed 2 Select the New Control menu item from the Define menu A list of properties that can be controlled appears 3 Choose the desired property A slider with text box control appears You can control the magnitude of the property you chose by dragging the slider Modifying Control Position and Size You can position the control anywhere on the screen by selecting the control and
16. 84 Chapter 3 Bodies Figure 3 20 E ii i Geometry iii New object with two identical e vertices area 6 943 m2 coM x offset 0 000 o Curved body Display in oO Shape coordinates World coordinates Table _ These two vertices have the same x Y coordinates and the polygon has one more vertex 5 Edit the coordinates of the new vertex to create a geometrically distinct point Deleting a Vertex To delete a vertex 1 Click on the object to select it 2 Choose Geometry from the Window menu The Geometry window appears 3 Select the vertex you wish to delete in the Geometry window Figure 3 21 Deleting a vertex How are the Data Represented Copying a Polygon or Curved Body to Another Application 3 4 Body Geometry 85 GSES Geometry 225 E Body 2 Pol w Polygon o Curved body Display in O Shape coordinates World coordinates Table _ x Select this vertex 4 Click on the Delete button The vertex is deleted from the list and the polygon or curved body is reshaped accordingly Copying Polygon or Curved Body Geometry to and from Other Applications Working Model 2D allows you to copy and paste polygon or curved body objects as a collection of vertices You can transfer the coordinates from applications such as a spreadsheet a CNC machining program or even a text editor Geo
17. Graphics Device Options PostScript Paper size C5 Env 6 38 x 9 01 in r 10 O D Legal A4 Executive Com 10 Ens m Layout me Be m Orientation Portrait A C Landscape M Aotsted Paper source AutoSelect Tray z Copies fi Unprintable Area About Restore Defaults omea f e 4 Click OK 8 12 Printing Tracked Frames You can print the progress of motion in your simulations by printing with the tracking feature enabled 1 Create or open a simulation 2 Run the simulation with tracking feature enabled 3 Stop the simulation 4 Choose Print from the File menu The tracked frames of your simulation will be printed 8 13 A Quick Look at the Inner Workings 277 NOTE If you have accumulated tracks from multiple simulation runs Working Model 2D will print only the tracks made in the last simulation 8 13 A Quick Look at the Inner Workings This section provides a brief description of Working Model 2D s approach to simulation The section Useful Simulation Tips on page 280 gives you some ideas to make your simulations efficient fast and accurate Appendix A Technical Information provides more detailed information for interested readers Time Step In Working Model 2D every frame of a simulation represents a certain point in time Ifa new frame is computed every one hundredth of a second the first frame represents the simulation at t
18. Overriding Automatic Attachment Figure 4 16 Constraint with overridden connection Attach to Body Command uppermost bodies lying directly beneath the constraint You can control which bodies are uppermost in front by using Bring To Front and Send To Back in the Object menu You may want to override the automatic attachment when you wish to attach a constraint to a body without having the constraint s endpoint lie within the body s outline Dotted line indicates connection even though endpoint is not within the rectangle s outline To override the automatic connection of a constraint s endpoints to a body 1 Drag the constraint to a position where its endpoints are connected to the desired bodies 2 Hold down the Command MacOS or Control Windows key while dragging either the constraint or one of its endpoints The constraint maintains its current connections while you drag A dotted line appears indicating which body is connected to the constraint if the constraint s endpoint does not lie over the body Alternatively you could modify the endpoint position in the Properties window or Coordinates bar The point coordinates are expressed as an offset from the FOR of the attached body Therefore while a point is attached to a body and positioned within its boundary simply specify the point coordinate so that it is outside the bounds of the body You could also attach multiple points to an arbitrary b
19. The FOR of the slot element will be the FOR of the body Coordinates of the control points will be adjusted accordingly To detach a slot from a body 1 Select the slot element Do not select the body to which the slot is currently attached 164 Chapter 4 Constraints RX RE Gs Bs S Figure 4 76 Properties window with a slot joint or keyed slot joint selected 2 The slot will lose connection with the body although the position of the slot remains unchanged The FOR of the slot will be moved to that of the background i e coordinate origin and the control point coordinates will be Choose Detach from Body in the Object menu adjusted accordingly Slot Joint Properties To modify the properties of a slot joint 1 Select the slot joint and choose Properties from the Window menu Properties Bi Constraint 8 v Stat Joint r Slot Point 6 angle x m u 0150m r Active when oO Always 1 000 Pinned Slot Joint The Slot field of the Properties window describes the slot element of the slot joint The slot element is described by the point at which it is attached to the background or to a body if the slot is on a body and by its rotation for straight slots the angle it forms with the x axis for curved slots the angle is initially 0 For curved slots this attachment point is the first control point created The Point field gives the coordinates of the point
20. To break a rope 1 Select the rope 2 Choose Properties in the Window menu The Properties window appears 114 Chapter 4 Constraints 3 In the Active When field type the desired condition during which the rope is to be active The rope will break when the condition is not satisfied For example you can type time lt 1 0 indicating that the rope is active only while time is less than 1 0 in the current unit system You can also specify a condition such as body 5 a lt 50 which means that the rope will break when body 5 gains acceleration greater than 50 See Turning Constraints On and Off on page 108 for more information 4 5 Springs A spring exerts a force that depends on the distance between its two endpoints A spring applies no force at all when the endpoint distance is equal to the rest length of the spring Creating a Spring To create a spring 1 Select the Spring tool from the Toolbar 2 Position the mouse pointer where you would like to define the first endpoint 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The Coordinates bar shows the coordinates for the two endpoint
21. y and r fields of the vector are all negated body 3 p x value is 10 0 body 3 p x value is 10 0 body 3 p x value is 10 0 In the last case the value of body 3 p is negated as a complete vector plus Takes two vectors and returns a vector which is the sum The vector which is returned will have each of its fields x y r equal to the sum of the corespondent fields of the two vectors being added minus Takes two vectors and returns a vector which is the difference The vector which is returned will have each of its fields x y r equal to the difference of the corespondent fields of the two vectors being added multiply Takes a vector and a number and returns the scalar product The vector which is returned will have each of its fields x y r equal to the product of the number and the corresponding field of the multiplied vector Il magnitude B 6 Functions B 15 Takes a vector and returns a number which is the magnitude of the x and y fields Magnitude is equal to the length of a line drawn from 0 0 to the x y fields of the vector The number returned from the magnitude function is equal to v sqrt v x v x v y v y B 6 Functions Functions take from zero to three arguments and return a number or vector value All functions accept their arguments in the form function argl arg2 There are two kinds of functions available Math functions perform standard
22. 2 Shift select both points Select two objects by holding down the shift key and clicking on each object in turn Select two points gi 3 Click the Join button on the Toolbar A pin joint is created Bodies move so that the points overlap New pin join You can also join a single point to an existing joint to create a joint binding multiple bodies This is very helpful when creating trusses and structures that have several bodies joined at a common point For example to join three bodies with a single pin joint 152 Chapter 4 Constraints Measurable or Optimized Rigid Joints 1 Connect two bodies with a pin joint as explained in the previous sections 2 Attach a point on the third body 3 Select the pin joint and the point Both Join and Split buttons are active at this point If you click Split Working Model 2D will split the pin joint 4 Click the Join button on the Toolbar The three bodies are now connected at a single pin joint For more information on joining elements and splitting constraints see 5 1 Joining Elements and Splitting Constraints Joint Properties Each pin joint or rigid joint consists of two points attached to separate bodies Therefore the Properties window shows the identities and positions of these two points The Properties window of a rigid joint has two radio buttons that specify whether the joint is optimized or measurable An optimiz
23. 2 Choose one of the numbers from the submenu Skipping Frames To skip frames for faster animation 1 Drag down the World menu to Skip Frames without releasing the mouse button A submenu appears just to the right of the pointer 2 Choose the number of frames you wish to skip from the Skip Frames submenu Another way to control the speed of animation is to adjust the Time Step This feature is discussed in Useful Simulation Tips on page 280 of this chapter When you run a simulation for the first time choosing the Skip Frames command does not have any effect Skip Frames only affects simulations that have been run once and are thus stored in the tape player Figure 8 4 Playing in reverse Figure 8 5 Dragging to a specific frame 8 3 Using the Tape Player Controls 253 Playing a Simulation Backwards After you have run a simulation you can play it backwards 1 2 Click the play backward control on the tape player See Figure 8 4 The simulation begins running in reverse You can stop the simulation at any time The simulation will stop by itself when it reaches the first frame Step Backward Click either the play forward or the play backward control to resume animation As the animation runs backward the frame indicator moves to the left while displaying the number of the current frame of animation Moving to a Specific Frame To move quickly to any frame in a recorded simulation
24. 689 4467216 N m 2 Minimally Stiff Cancel C Custom Stiffness Hep Number of Elements to Represent the Flexible Body WARNING Large values of El or n significantly reduce the simulation speed The integration time is proportional to El and proportional to n 2 The first input quantity the structural stiffness is the product of E Young s modulus of elasticity and the area moment of inertia is a geometric property of the cross section of the beam and it is given by the equation I ffy aa where dA is a differential element of area and y is the distance of dA from the centroid axis see Figure D 4 for an example Working Model is unable to calculate 7 because it simulates in the xy plane while the beam cross section lies on the yz plane The second input quantity is n the number of rectangular elements with which to approximate the flexible body A larger value of n produces a more accurate approx imation to the flexible beam However as the warning message in Figure D 3 indi cates the user should be careful to avoid using more elements than necessary Assigning Values for the Rotational Spring Constants Flexbeam replaces the selected rigid rectangular body with a set of smaller rectangular elements attached by rotational springs The spring constants are given by the formulas discussed in the technical paper Determination of Spring Constraints for Modeling Flexible Beams by P
25. All equations are normally evaluated from left to right Precedence is given to operators in the following order operators listed in the same row have equal precedence QO highest precedence A binary operators lowest precedence Operators with the highest precedence are applied first For example the following formula 3 4 2 4 is evaluated as 3 2 4 instead of as 3 2 4 This is because the multiplication operator has a higher precedence than the addition operator Use parentheses to change the order of evaluation or to assure yourself of the order of evaluation if you re not quite sure of the precedence of various operators In the above example you could enter the formula as 3 2 4 to force evaluation of the addition before the multiplication You can nest parentheses as in the formula 3 2 4 10 2 Note on Inequalities B 5 Operators B 13 Be sure to use parentheses and not brackets or braces Although the inequality operators have the same precedences the return value of the formula if 0 lt t lt 1 50 100 is actually equivalent to TE C00 lt b lt 2 50 1 00 since the chain of the binary operators is evaluated from left to right As a result the above formula always returns 50 regardless of the value t since 0 lt f returns 1 or 0 the entire first argument is always 1 or true If you want the effect of return 50 when t is
26. Click once on the rectangle An anchor appears on the rectangle to show that the rectangle is now anchored see Figure 1 31 and will not move when you run the simulation Click Run in the Toolbar The ball bounces a few times and then comes to rest on the rectangle Click Reset in the Toolbar The ball returns to its initial position 28 Chapter 1 A Guided Tour Figure 1 32 Circle and rectangle Figure 1 33 Velocity control Creating Controls You will now create a simulation with an initial velocity control In this simulation the circle will act as a projectile that is fired horizontally from the left You will use a slider control to change the initial velocity of the center of the circle 4 O Drag the circle and rectangle so that your screen resembles Figure 1 32 Select the circle Choose New Control from the Define menu Hold down the mouse button and choose Initial X Velocity from the submenu A new control appears This control specifies the initial velocity of the center of the circle in the x horizontal direction s Circle x Velocity Pick an initial x velocity for the center of the circle by using the slider to raise or lower the value 1 9 A Simple Simulation with Controls and Menu Buttons 29 5 Run the simulation Try to have the ball hit the table by adjusting the initial velocity Reset the simulation to try again Creating Menu Buttons Yo
27. If you are using a LaserWriter printer you ll see the dialog shown in Figure 8 19 LaserWriterPage Setup 2 Of KY Paper US Letter A4 Letter OUS Legal B5 Letter _Tabloid z Cancel Reduce or ino0 Printer Effects A Font Substitution Orientation J Text Smoothing tal EJ Graphics Smoothing amp Faster Bitmap Printing Enlarge The information you see in the Page Setup dialog varies depending on the system and printer you are using The Page Setup command and settings shown here describe page setup for printing to an Apple LaserWriter If you are using a different type of printer the settings and choices you see in the dialog may be different Refer to your MacOS manual for the specific settings to select After you have positioned your simulation within the window at the desired Zoom and location you are ready to print To print the simulation 1 Open a simulation 2 Choose Print from the File menu The Print dialog for your printer appears If you are using a Laser Writer printer you ll see the dialog shown in Figure 8 20 Ifyou are using a different type of printer the settings and choices you see in the dialog will be different Refer to your MacOS manual Figure 8 20 MacOS Print dialog Figure 8 21 Windows Print dialog 3 8 11 Printing a Simulation 275 LaserWriter Design Shop Printer 1 712 print Copies 1 Pages All From To Cover
28. In this situation the Smart Editor moves the three rectangles together Add two new pin joints at the bottom of rectangles B and C as indicated in Figure 1 20 These pin joints will join the rectangles to the background Use the Snap Points if so desired 20 Chapter 1 A Guided Tour Figure 1 20 Pinning the mechanism to the background Figure 1 21 Dragging the mechanism Pin joints between the rectangles and the background 6 Click the Arrow tool This action de selects the Pin Joint tool otherwise further mouse clicks would create more pin joints 7 Drag the rectangle A The joints pivot and the bars now move relative to one another The Smart Editor moves the mechanism while making sure that pin joints do not separate Click here and drag the body Modifying the Linkage Geometry You can use the mouse to modify the linkage geometry e g the lengths of individual links For example to change the size of the left vertical link 1 Click on the left vertical link to select it Figure 1 22 Result of resizing links and pin joint positions 1 8 The Smart Editor 21 Four reshape handles appear at the corners of the rectangle 2 Bring the mouse pointer to one of its top reshape handles and hold down the mouse button Drag the mouse to modify the size of the link If you attached all the pin joints to Snap Points Working Model 2D will automatically modify the attachment to
29. r Gear Ratio lV Automatically Compute r Rod Active M Always M Intemal Gear Body 1 C Body 2 r Gear Force Constraint 1 2 gt Active when M Always E If both bodies are circles the default gear ratio is computed automatically as r r where r and rp are the radii of the first and second disks respectively If at least one of the gear bodies is not a disk say a polygon the default gear ratio is set to 1 0 134 Rod Active Internal Gear Gear Force Chapter 4 Constraints Changing the gear ratio affects the location of the point of contact thereby changing the behavior of bodies connected with gear constraints Please refer to Principle of Simulating Gears on page 131 for more detail You can override the default gear ratio and set it to an arbitrary positive floating point number or use a formula thus allowing more generalized gears For example in Working Model 2D simulations two disks of the same radius can have a gear ratio other than 1 0 By default each pair of gears has a rigid rod constraint between the two centroids A rod constraint maintains a constant distance between two bodies attached at each of its endpoints Therefore a rod keeps the centroids of the two gear bodies apart at its length while allowing each of them to rotate about its endpoints This feature can be useful for example when you are simulating a set of planetary gears You have a control when o
30. reference frame A force that does not rotate with a body has its line of action fixed in the World frame Base Point The Base Point shows the object ID of the endpoint of the force object Pl 4 15 Torque Unlike most other constraints a torque is applied only to one body Creating Torque A torque object attaches to the top body lying under the pointer at the time of the click and applies torque To create a torque P 1 Select the Torque tool from the Toolbar On MacOS systems the Torque tool is hidden in the Force pop up palette by default Click and hold on the Force tool to bring the Torque tool in view and select it 4 15 Torque 143 2 Click on the body which the torque is to be applied Use the Properties window to set the magnitude of the torque Figure 4 52 Sketching a torque Click on the body to apply a torque The attachment position has no significance The Coordinates bar for Torque shows the attachment point x y and the torque magnitude T Figure 4 53 The x y values are in the local coordinate system of the body to which the torque is attached Please be reminded that the torque can be attached anywhere on the body and x y values are irrelevant as far as dynamics are concerned Figure 4 53 Coordinates bar for a torque xL 0267im __yL_ 1e7lm__T_1000 Nm L o e mM l r Point where Torque is attached Torque Magnitude fa Torque Properties A torq
31. 009 MN m 2 C 2 2 Click On or Off to turn electrostatics on or off 3 Enter a value to pick a new value for 1 4 4eo 4 Click OK to save the changes Force Fields You can define forces that act upon each object or each pair of objects by using the Force Field command For example you can model wind forces by applying a horizontal force to all objects that varies randomly with time You can model gravitational systems where the force of gravity behaves in a weird way such as gravity that grows in proportion to the inverse of distance Custom force fields are built upon Working Model 2D formulas which are discussed in Chapter 10 Using Formulas and Appendix B Formula Language Reference Formulas are similar to those found in a computer spreadsheet The primary difference is that spreadsheet formulas refer to other cells in the spreadsheet Working Model 2D formulas refer to the physical parameters of the various objects in the simulation You can click the Sample Force menu in the Force Field dialog box to see examples of the various force fields you can build along with the appropriate formulas that define them Figure 6 23 Force Field dialog 6 4 Defining World Parameters 211 Custom global forces can be applied to each object individually or to each pair of objects Gravitational forces near the earth s surface are a good example of a force field that is applied to each object individually This force is typica
32. 15 shows a rectangle with its name displayed Rectangle Select the Show Center of Mass box to display a body s center of mass The center of mass indicator appears as a black and white disk If you have Track Outline turned on the indicator will also leave its track Center of Mass Symbol ____ If Show Charge is selected then positively charged bodies will have large positive signs in them while negatively charged bodies will have large negative signs in them Initially each circle has a line fixed in it that passes through its geometric center and is parallel to the World frame s x axis The orientation of a circle is defined to be the angle between this line and the x axis of the World frame Select Circle Orientation to display the line that indicates the current orientation of the circle To close the Appearance window click its close box 78 Chapter 3 Bodies Using the Selection Pop up Menu 3 4 Body Geometry Working Model 2D allows you to easily modify geometric parameters of bodies such as e Width and height of a rectangle e Radius of a circle e Position of vertices of a polygon e Position of control points of a curved body To modify the geometry of bodies you can either use the Coordinates bar or the Geometry window The Coordinates bar provides you with quick and easy access for the geometry parameters whereas the Geometry window gives complete control includ
33. 175 A Pinned Slot Joint is composed of a slot and a point A slot joint aligns a point on one body with a slot on a second body A Keyed Slot Joint is composed ofa slot element and a square point element A keyed slot joint aligns a point on one body with a slot on a second body and prevents rotation between the two bodies The Join button combines elements into joints Select both of the elements and then click Join in the toolbar J HEE OE SOROH For examples of how to construct pin and slot joints using the Join button see 4 18 Joints and 4 19 Slot Joints The Split button separates a constraint into its elemental parts Select a joint and click Split in the Toolbar Elements that are split remember that they were once joined so it is easy to take apart pieces of a mechanism and then reassemble them Split and Join can be used with constraints other than pins joints rigid joints and slot joints Controlling Object Motion when Joining When the Join command is issued the Smart Editor uses an optimization algorithm to minimize the distance between the two elements being joined The Smart Editor will move the objects to bring the two elements together as specified while observing other existing constraints Figure 5 3 and 176 Chapter 5 The Smart Editor Figure 5 4 show what happens when two pins on unconstrained rectangles are joined to form a pin joint note that the Smart Editor could h
34. Accuracy dialog This force will tend to push the objects apart You can make sure that objects with 0 elasticity do not rebound by using any of the methods given in the previous section 8 15 Exchanging Files Across Platforms 285 From MacOS to Windows From Windows to MacOS Using Rigid Joints for Robust Collisions Working Model 2D internally sub divides concave polygons into convex regions These convex regions are used in the collision detection algorithm to determine where and in what direction forces are applied between contacting objects In rare cases when concave polygons collide with concave polygons the choice of locations and directions for contact forces is not optimum You can inspect this by selecting one of the polygons and choosing Contact Force from the Vectors menu You can improve the robustness of the contact by building one of the concave polygons from rigidly joined convex polygons and rectangles 8 15 Exchanging Files Across Platforms Working Model 2D files are compatible between the MacOS and Windows versions To read a MacOS file on a Windows computer 1 Make sure the filename abides by Windows naming conventions and has a wm extension A valid name would be exchange wm 2 Transfer the file to your Windows computer You can transfer the files using a floppy disk or over networks 3 Open the file within Working Model 2D on your Windows computer To read a Windows file on a MacOS computer
35. Curved Slot 4 19 Slot Joints 167 Control points can be viewed in either rectangular or polar coordinates Closed curved slots default to polar coordinates Open slots default to rectangular coordinates You can copy and paste the coordinates of the control points to and from the Clipboard which stores the coordinates in the tab delimited text format This feature is useful when you want to export or import numerical data of control point coordinates from other applications in order to define the curved slot precisely see Copying a Curved Slot to and from Other Applications on page 170 for instructions You can of course directly copy and paste curved slots graphically within Working Model 2D just like any other object without using the Copy Paste Table feature Working Model 2D also allows you to copy a finite number of interpolated points in the curved slot to the Clipboard You can specify the number of points to be sampled per one interval between two adjacent control points The Geometry window shows control points in frame of reference FOR coordinates The Properties window of a curved slot displays the coordinates for the slot This point is defined as the frame of reference FOR for the curved slot The FOR of a curved slot is the FOR of the body to which it was attached when the slot was first created If the curved slot was initially created on the background its FOR is the global coordinate origin 0 0 The
36. ENTITIES section Working Model 2D objects are converted in the following fashion e Circles are exported as CIRCLE entities e Rectangles and polygons are exported as closed POLYLINE entities e Lines are exported as LINES e Curved slots are exported as POLYLINEs Open curved slots are exported as open POLYLINEs e All other objects are exported as 2D entities The current numbers and units settings are used when exporting DXF files If you are using a CAD system that uses inches as the unit of measure be sure to set the units of your document to inches before exporting 9 6 Exporting Meter Data to a File 301 To export DXF geometries 1 Create or open a Working Model 2D simulation 2 Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog 3 Set the export type to DXF or DXF animation MacOS only DXF animation will export a file for every requested frame of the simulation 4 Set Export Options as necessary You can choose to export all objects or just those that are selected 5 Click Save MacOS or Export Windows A file is generated with the suffix DXF Open this file in any CAD program that supports the DXF format 9 6 Exporting Meter Data to a File You can export meter data from Working Model 2D in two ways e Use the Export command to export meter data into a new text file e Select one or more meters and then choose Copy Data
37. Geometry windows Showing the Mouse Position x 2 700 m yl 1 900 m ampe eed Showing Object Properties x 1 350 m yl 1 050 m hL_1 100 m wl _4 100 m 0 000 Showing Displacements e g while creating a polygon ax _0 500 m ayl 0 400 m Z 0 640 m h 38 66 The coordinate information shown at the bottom of the document tracks the mouse position to the nearest minor ruler division if Grid Snap is enabled or to the nearest pixel if Grid Snap is disabled When bodies or constraints are selected the Coordinates bar shows the parameters that are most often edited You can edit these values directly in the Coordinates bar and the modification will take effect immediately please see 3 2 Body Properties and 4 3 General Properties of Constraints for details on the usage of the Coordinates bar 202 Chapter 6 The Workspace Showing Displacements Coordinates for Meters and Controls You can select a field using the mouse or the tab key Pressing the tab key allows you to change from one field to the next Pressing the tab key while holding down the shift key allows you to change fields in the reverse order If you start typing on the keyboard immediately after selecting an object Working Model 2D will automatically select the leftmost field on the Coordinates bar as you type When the coordinate values become too long to fit in the edit box you can scroll the text sideways by using t
38. MacOS Users Notes for Windows Users 8 6 Running Scripts 261 5 Continue to run the simulation You still have the data from the initial frames in the file you saved earlier To accommodate a simulation with long history data you can close the application increase the application size see Running Simulations Unattended on page 282 and launch the application again This way the application has more memory allocated You may be able to open the previous file with the saved history and continue the simulation To maximize the memory allocated to Working Model 2D make sure that no other applications are running on your machine After quitting other applications you may be able to continue simulation in Working Model 2D Using the Settings of an Existing Simulation for a New One You can use the current condition of a simulation as the initial condition for a new simulation 1 Drag the frame indicator to the desired starting point 2 Choose Start Here from the World menu The current frame becomes frame zero and the new initial conditions The original initial conditions are lost The simulation is recalculated from this new starting point Save your simulation with a new name before setting new initial conditions if you wish to re use the old initial conditions at some later time 8 6 Running Scripts Working Model 2D allows you to run scripts and tools that are written in the Working Model Basic WM Basic lang
39. MacOS systems holding down the mouse button reveals a pop up menu showing three different output formats On Windows systems each mouse click cycles the meter formats in the order digital graph bar graph and digital again Change the display format to Graph Select V as the only property to be plotted by clicking the buttons on the side of the meter You can click the buttons on the side of the meter to enable or disable the plotting of individual properties Your meter should resemble Figure 1 13 Click these buttons to restrict output to Vy Click Run in the Toolbar 6 1 6 Tracking 15 The meter output is restricted to Vy Click Stop to stop the simulation You can install meters to measure any quantity shown in the Measure menu For more information about meters see 7 1 Meters Displaying Vectors To display the velocity of the projectile as an animated vector 1 2 Select the circle Choose Vectors from the Define menu The Vectors submenu appears Choose Velocity from the Vectors menu From now on a check mark will appear next to Velocity in the Vectors menu indicating that velocity vectors are being displayed Click Run in the Toolbar When you run the simulation a vector appears on the circle showing the velocity of its center of mass Click the Stop button to stop the simulation 1 6 Tracking Tracking shows the path of an object by recording its locat
40. Movie PICT PICT Animation DXF Animation Object Positions Working Model 2D simulations can be saved as industry standard DXF geometry files The DXF format is popular for transferring data between CAD systems DXF files do not contain motion information rather they describe the shape and relative position of objects The data from any meter can be exported as a tab delimited text file You can edit this data with a word processor spreadsheet or graphics application Meter data can also be captured by selecting a meter and then choosing Copy Data from the Edit menu Data from the meter will be copied to the Clipboard You can then paste the data into any application that supports tab delineated text Windows only Video for Windows is an animation data format MacOS only The QuickTime movie format is a standard for animation on MacOS systems Movies exported from Working Model 2D can be played in any application that supports QuickTime You can save a picture of the Working Model 2D workspace as a single PICT file PICT files can be edited in any paint or draw program or pasted directly into documents Sequential PICT files are used by some animation programs in place of QuickTime One PICT file will be generated for each exported frame Sequential DXF geometry files can be saved for each frame of a simulation You can export motion data from Working Model 2D simulations in the form of tab delineated object position
41. Please be reminded that increasing the application memory size of Working Model 2D via Get Info will not give more memory to the scripting engines which attempt to claim memory in addition to the application memory In fact the greater the application memory the less memory becomes available to the scripting engines A 4 Appendix A Technical Information Interested in Fast Playback Video Export Playback A 2 Optimizing Speed Performance MacOS If you are using full page or larger monitors you may find that the animation speed drops below acceptable performance You can increase animation speed by reducing the size of the document window Windows The two main factors that affect performance of Working Model 2D besides the performance of the computer itself are available memory RAM and the size of the document window Lack of sufficient RAM causes frequent disk access and thus negatively affects performance If the amount of physical RAM is insufficient to store Working Model 2D and other applications including Windows the operating system will be constantly forced to swap part of Working Model 2D to disk To avoid this behavior quit other applications so that memory is available to Working Model 2D If you are using full page or larger monitors you may find that the animation speed drops below acceptable performance You can increase animation speed by reducing the size of the document window Section Making
42. Resistance dialog to appear allowing you to control the air resistance within the active simulation Electrostatics causes the Electrostatics dialog to appear allowing you to control electrostatic forces Force Field causes the Force Field dialog to appear allowing you to create your own custom force fields to act upon all of the bodies within the active simulation Run starts your simulation Reset returns a simulation to its initial conditions the first frame Start Here starts your simulation from the current conditions A new set of initial conditions is created based upon the current position and velocity of all objects NOTE You cannot undo Start Here which will erase the simulation history including the previously specified initial conditions Ted Y 1 step Skip Frames presents a submenu which lets you specify various playback rates for your simulations Skipping more frames will allow faster playback of a previously calculated simulation When you open the Skip Frames submenu a checkmark appears to indicate the current skip rate The options available in the submenu are 1 step 2 step 4 step 8 step 16 step and Other The Other dialog lets you choose your own skip rate A skip rate of 1 step will play every frame of your simulation Tracking Tracking presents a submenu which lets you leave a trace of your simulation ails Seige at various time intervals When you open the Tracking submenu a Every 4 frame
43. Script Window Help laj x olea ESE amp 2 KOA 2 9 Runb Stopi Reset Circle X Velocity Xx m y m j e H rf Friday August 02 96 0912 AM Player Mode In Player mode the toolbars are hidden giving more space for the document on the screen The menu set is also reduced All the commands you need to use while running a simulation appear on these menus 264 Figure 8 11 Player mode Chapter 8 Running Simulations 4 Working Model Untitled1 ioj x tb File Edit Run Script Window Help ee Circle x Velocity Friday August 02 96 09 12 AM 74 To run a simulation in Player mode 1 5 Choose Player mode from the Edit menu Notice that you now have a limited set of menus and commands available File Edit and Run Choose Run from the World menu Choose Reset from the World menu Choose Close from the File menu Close the simulation when you finish watching it so that the computer has more memory available for other simulations Choose Edit mode from the Edit menu to return to Edit mode Simulations saved in Player mode are perfect for users who will not be editing the simulation 8 8 Reference Frame 265 8 8 Reference Frame An object remains stationary on the screen when it is selected as the reference frame object while other objects move around it Working Model 2D allows you to choose any object as the current reference frame The defau
44. The Numbers and Units dialog appears Figure 6 16 Numbers and Units Numbers Unit System Fixed Point 3 Digits SI degrees v Floating Point Auto O Wrap Rotation 206 Chapter 6 The Workspace Figure 6 17 Numbers and Units dialog with More Choices selected 5 Select a general unit system from the Unit System menu Unit systems include SI English astronomical atomic and CGS systems Choose how numbers will be displayed by clicking Fixed Point Floating Point or Auto Fixed Point format displays all numbers with a fixed number of digits to the right of the decimal point Floating point format displays all numbers in an exponential format of the form 1 23e4 Auto lets Working Model 2D decide whether to display numbers in fixed or floating point formats Numbers are presented in the best format for quick viewing To fix the units for a particular quantity click on the More Choices box This will allow you to choose the units that a specific quantity will be reported in See Figure 6 17 Numbers and Units Ea Numbers Unit System C Fixed Point SI degrees v C Floating Point 3 Digits ene Auto Fewer Choices Distance Meters x m Force Newtons 7 N Mass Kilograms pa kg Energy Joules Ba Time Seconds 7 s Power watts x Ww Charge Coulombs x C Frequency inone 7 Rotation Degrees x nd Velocity Jnone x Electric Rot Pot Volts Y Velocity inone z
45. This appendix provides you with technical information and describes many of the inner workings of Working Model 2D A 1 Making the Best Use of Available Memory Occasionally Working Model 2D might have insufficient system memory RAM at its disposal and it will warn you accordingly Increasing the Memory Available to Working Model 2D Shown below are several ways to increase the memory available to Working Model 2D Please note that the use of virtual memory has a performance trade off see Optimizing Speed Performance on page A 4 MacOS The MacOS pre allocates memory for an application when it is launched the application will not be launched if the space is not available You can change the memory requirements of Working Model 2D or any MacOS application in the following fashion 1 Quit Working Model 2D Without quitting the application you cannot change the memory requirements The minimum requirement is shown in the Minimum field in the Get Info window for the application A 2 Windows Appendix A Technical Information 2 Select the Working Model 2D icon in the Finder 3 Choose Get Info from the File menu 4 Change the Preferred Size to a larger value in the Memory Requirements box 5 Close the Get Info window The change will not take effect until you close the window The next time you launch Working Model 2D it will attempt to claim as much memory as possible up to the size
46. Timeout 30 000 s Windows Windows only Click the Application button select the application name from the dialog box and click OK Click the Document button Figure 9 16 Apple events link dialog MacOS only Connecting the Inputs Outputs with the Application 9 16 Exchanging Data in Real Time with External Applications 321 On MacOS systems the Apple Event link dialog appears Figure 9 16 On Windows a regular file selection dialog appears Quadra 650 O Aldus Superpaint Eject O Canvas O Excel 5 0 Desktop O FileMaker Pro 2 0 O FrameMaker 4 O HyperCard 2 1 Player O Matlab 4 0 O MS Word 5 1 O Show all files Make Link Send meter output in rows columns Find and select the document to which you wish to link MacOS only Make sure that the application is already running and has the document open then click Make Link Windows only Click OK and the application will be launched automatically if it is not already running The name of the linked file will appear in the Properties window The blank interface object icon will change to the icon of the linked application At this point you have specified the external application and the document with which Working Model 2D will interact You must also specify which individual Controls inputs and Meters outputs in the Working Model 2D document correspond to appropriate elements in the external application For example yo
47. Variable mode Working Model 2D automatically adjusts the integration time step throughout the simulation to optimize the computational performance The integration step may become smaller than the one specified in Animation Step but will never be greater Please see Variable Time Step on page A 9 for more information Simulation Error Tolerances During the course of a simulation Working Model 2D is constantly monitoring various types of potential errors such as e interpenetrating bodies e constraint violations A 18 Appendix A Technical Information Overlap Error Assembly Error Significant Digits At each integration step Working Model 2D checks its computation results to see if the model satisfies the error bounds You can fine tune the following parameters to optimize the simulation results and performance By default Working Model 2D automatically computes an appropriate value for these error criteria for a given model based on the properties of bodies and constraints therein If necessary you can override the default and specify the value on your own it must be greater than zero Keep in mind that as the tolerable error becomes small Working Model 2D may have to spend more computation time to monitor and prevent the errors On the other hand an excessive tolerance may produce inaccurate simulation results Overlap error is used as the upper bound for overlap amount between bodies while Working Model 2D simula
48. a text object To insert new text 1 Click the text object you wish to change 2 Click where you want to insert text 3 Type the text or choose Paste from the Edit menu to paste cut or copied text When you insert text it wraps around to fit within the current margins You can change the size of the text object by dragging one of its handles Changing Text Fonts Sizes and Styles You can choose a font size and style for any text that appears in the workspace To change the text font size or style MacOS 1 Select the text object or object whose name you wish to adjust 2 Choose Font Size or Style from the Object menu 3 Select the desired font size or style from the submenu The changes you make apply to all text in the selected object Windows 1 Select the text object or object whose name you wish to adjust 2 Choose Font from the Object menu 3 Select the desired font size or style from the dialog box The fonts shown in the dialog box are the Windows fonts styles and sizes installed on your computer 248 Chapter 7 Simulation Interfaces The changes you make apply to all text in the selected object Naming Objects To edit or change the name of a body constraint meter or control 1 Select the object whose name you wish to change 2 Choose Appearance from the Window menu 3 Select the current name and type a new one in its place 7 6 Pictures Picture objects are created in Wor
49. amp Menus Joint Tools Joint tools are the collection of Working Model 2D tools to create various types of joints See Chapter 4 Constraints for more information on each joint BY The Pin Joint tool is used to create a pin joint A pin joint allows a single degree of freedom in rotation and no degree of freedom in translation A pair of bodies or a body and the background bound by a pin joint can rotate but cannot translate with respect to each other Bh The Rigid Joint tool is used to create a rigid joint A rigid joint locks two bodies together and allows no degree of freedom The Slot Joint tools are used to create various types of slot joints The Pinned Slot Joint tools constrains a point element on one body to align with a slot element on a second body or the background and allows the first body to rotate about the point element Working Model 2D provides pinned slot joints with vertical horizontal curved and closed curved slots You can change the geometry of the slot after the joint is created Tk S The Keyed Slot Joint tools constrains a point element on one body to align with a slot element on a second body or the background and prohibits the first body from rotating For example a keyed slot joint can constrain the motion of a piston moving in one direction inside a combustion chamber Working Model 2D provides keyed slot joints with vertical and horizontal slots You can change the geometry of the slot af
50. and W Fowler Engineering Dynamics Mechanics Addison Wesley Publishing Company 1995 A 9 Technical References A 27 R E Roberson and R Schwertassek Dynamics of Multibody Systems Springer Verlag 1988 R C Hibbeler Engineering Mechanics Dynamics Macmillan Publishing Co Inc 1983 J L Meriam and L G Kraige Engineering Mechanics Volume 2 Dynamics John Wiley and Sons 1987 David J McGill and Wilton W King Engineering Mechanics an Introduction to Dynamics Brooks Cole Engineering Division 1984 B 1 APPENDIX B Formula Language Reference This appendix describes the Working Model 2D formula language NOTE The formula language is a different system from Working Model Basic WM Basic Although they share similar syntax and numbering schemes they are used for different purposes WM Basic is a language system used to control Working Model 2D while the formula language is a high performance light weight language used by Working Model 2D objects during simulations For more information on WM Basic please refer to the accompanying Working Model Basic User s Manual B 1 About Formulas Formulas follow standard rules of mathematical syntax and strongly resemble the equations used in spreadsheets and programming languages Formulas are composed of identifiers fields operators and functions The following sections discuss each category in detail Formulas can be up to 255 characters in len
51. and try running the simulation with different velocities 1 5 Measuring Properties from a Simulation Working Model 2D allows you to measure many physical properties including velocity acceleration and energy by using meters and vectors Meters and vectors provide visual representations of quantities you want to measure Meters can display information in the form of e numbers digital e graphs plot or e level indicators bar graph Vectors represent the properties of velocity acceleration and force as visual arrows The direction of the arrow indicates the direction of the vector and the arrow s length corresponds to the vector s magnitude In the following exercises you will measure a projectile s velocity and display it in various ways First you will display it as a digital meter Then you will change that meter to a graph Finally you will display the velocity of the projectile as an animated vector 12 Chapter 1 A Guided Tour Creating a Velocity Meter To create a digital meter that measures the velocity of the projectile s center of mass follow these steps Reset 1 Click Reset in the Toolbar 2 Draw a circle in the lower left hand corner of the workspace if one is not already there Select the circle Your screen should resemble Figure 1 10 When the circle is selected four small dots and the velocity arrow appear If your screen does not resemble Figure 1 10 repeat the steps of the previ
52. are editing the constraint coordinates numerically you can use not only numeric values but also geometry based formulas which specify constraint positions with respect to the geometry of bodies Using Object Snap When Object Snap is active an endpoint of a constraint automatically attaches to the closest snap point of a body or to the closest point element when you release the mouse button The attachment occurs only if the snap symbol marked as an X appears see below This Object Snap feature helps you position the constraints precisely right from the start For example you can easily position a motor to the geometric center of a circle As the mouse pointer hovers across the screen the closest snap point is shown with an X shaped symbol Figure 4 10 is an example where a motor is about to be attached to the center of a circle Figure 4 10 Attaching a motor with Object Snap Fal Only by dragging the motor near the midpoint the motor attaches to it y by aragging P automatically 102 Chapter 4 Constraints Figure 4 11 Snap Points for bodies The object snap feature can be turned on or off at any time To toggle the object snap mode 1 Choose Object Snap in the View menu Object Snap is already active if a checkmark is visible beside the menu item Each type of body has a specific set of snap points shown in Figure 4 11 Curved bodies have only one snap point at the frame of reference FOR To use snap po
53. body has a velocity of 0 in the x direction and 10 in the y direction the body has a velocity that is in the direction of 90 or 4 2 on the coordinate plane The formula angle body 3 v would return the value of 4 2 Takes a number and returns the inverse cosine of the number Values are returned in the range 0 4 Takes a number and returns the inverse sine of the number Values are returned in the range 4 2 4 2 Takes a number and returns the inverse tangent of the number Values are returned in the range 4 2 4 2 Takes two numbers and returns the inverse tangent of y x This function is useful because unlike the atan function it can generate an angle in the correct quadrant Values are returned in the range 1 4 1 4 Takes a number and returns the smallest integer no smaller than the number Takes a number and returns the cosine of the number Takes a number and returns the exponential of the number e raised to the value of the number Takes a number and returns the largest integer no larger than the number B 18 if X y 2 In x log x mag v max x y Appendix B Formula Language Reference Takes three numbers If the value of the first number x is not equal to 0 then returns the value of the second number y Otherwise returns the value of the third number z Example if time gt 1 20 0 returns the value 20 if time is greater than 1 otherwise returns the value 0
54. by using the Vector Display dialog choose Vector Display in the Define menu The V and V coordinates in the Properties window specify the initial velocity of a body The V coordinate indicates the initial angular velocity of the object about its center of mass This value can only be set using the Properties window When you have a body subject to constraints such as pin joint rigid joint etc you should make sure that the initial velocities you specify are consistent with those constraints See Avoiding Inconsistent Initial Velocities on page 281 for more details You can also use Control objects in Working Model 2D to set the initial position of a body For more information see 7 2 Controls Elasticity and Friction Elasticity and Friction control how two objects behave when they come into contact with each other Elasticity in Working Model 2D corresponds to the coefficient of restitution used in simulating collisions In mechanics or physics the coefficient of restitution is really a property of a collision and not of a body The coefficient of restitution is equal to the ratio of the relative velocities of the colliding objects immediately before and after the collision Friction Density 3 2 Body Properties 69 For example if the coefficient of restitution is 0 0 the difference in velocities of the two bodies after a collision will be zero i e they will stick together An elasticity of 1 0
55. can send scripting commands using WM Basic to Working Model As long as the external application supports a few basic features of DDE and or Apple events it can send commands to or invoke an entire program in Working Model Although Working Model provides a vast array of math functions you can implement still more advanced functions in another application and link them to a Working Model simulation XX Exporting Static Animated Data Input and Output Devices Complete Set of Menu Buttons Text Tool Moving Graphics Custom Global Forces Extensive Graphical Features Multiple Reference Frames Working Model exchanges geometries with most popular CAD programs through the DXF file format Numerical simulation data can be exported as meter data to a file Working Model also supports standard PICT and QuickTime movie formats on MacOS systems and Video for Windows AVI files export on Windows systems Working Model is a natural choice as a tool for creating animated images of unprecedented realism since it models interactions between moving objects according to real world dynamics with high accuracy On MacOS systems you can export animated data as frame sequences in a variety of standard file formats including MacroMind Three D Wavefront and DXF animation allowing a seamless integration of Working Model files with animation programs Real time input devices include sliders buttons and text fields Real time
56. can use a spring damper to simulate a McPherson strut a combination of a shock absorber with a coiled spring wrapped around it Creating a Spring Damper To create a spring damper 1 Select the Spring Damper tool from the Toolbar On MacOS systems the Spring Damper tool is hidden in the Spring pop up palette by default Click and hold on the Spring tool to bring the Spring Damper tool in view and select it 2 Position the mouse pointer where you would like to define the first endpoint 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The Coordinates bar shows the coordinates for the two endpoints of the damped spring and its rest length for the spring component as shown in Figure 4 28 Both coordinate values are given in local coordinates of the body to which each point is attached x 4 500 m y 2 200 m x 1 600 m y 0 100 m 1L 2 285 m First Point Second Point Spring Rest Length Spring Damper Properties The individual spring and the damper components each have a constant that describes their behavior 120 Chapter 4 Constraints Figure 4 29 Properties window for a spring damper Prope
57. connect two bodies or a body and the background the endpoints of the spring are the attachment points The Spring Damper tool creates a combination spring and damper For example a spring damper simulates a McPherson strut a combination of a shock absorber with a coiled spring wrapped around it Like dampers and springs spring dampers can be attached between a body and the background or between two bodies the endpoints of a spring damper are the attachment points On MacOS systems the Spring Rotational Spring and Spring Damper tools are accessed through the Spring pop up palette The Gear tool connects any two bodies with a gear constraint Click on two objects to define a pair of gears By default Working Model 2D defines gear constraints to be external spur gears You can define internal gears one of the gears is inside the other by choosing the option from the Properties window The gear icon on one of the bodies changes to a gear showing internal teeth See Gear Properties on page 133 for details The Pulley tool creates a pulleys connected by a rope Define each pulley with a single click Double click to signal the last pulley Any pulley within a link can be attached to either the background or to a body Since Working Model 2D approximates pulleys as thread holes through which a rope is routed they are massless and dimensionless 46 Chapter 2 Guide to Tools amp Menus On MacOS systems the G
58. connects to the body and permits frictionless rotation Properties Window As with all other objects in the Working Model 2D workspace you can double click on any constraint to display the Properties window which is used to adjust or define the constraint s parameters You can also display the Properties window for any constraint by selecting the constraint and choosing Properties from the Window menu Constraint Components and Selection Pop up Figure 4 2 Selection pop up showing a pin joint s association with other objects 4 3 General Properties of Constraints 93 The Properties window displays a variety of parameters depending on the type of constraint selected Please refer to individual sections on each constraint later in this chapter for details The Properties window can assist you tremendously in finding connections between constraints point elements and bodies For example e Given a constraint you can determine to which body or bodies it is attached and which point elements are part of the constraint e Given a point element you can determine to which body the point is attached and to which constraint the point belongs e Given a body you can find out which point elements are attached to it To determine the connections between constraints point elements and bodies 1 Select an object for which you want to find out the connections and associations In this case start out with a pin joi
59. create and manipulate objects Then you learned how to run sample simulations and create simple ones yourself You saw that creating a simple simulation consists of drawing objects setting their initial velocities and then running the simulation with the click of a button You used the Smart Editor to create and edit a complex linkage of bodies You also learned how to display meters and vectors for measuring physical quantities how to track objects how to add simple controls to adjust data input during a simulation and how to create menu buttons 2 1 The Working Model 2D Toolbars 33 CHAPTER 2 Guide to Tools amp Menus In this chapter you will learn about the main tools and menus of Working Model 2D 2 1 The Working Model 2D Toolbars Working Model 2D features a set of tools that are easily accessed through the use of toolbars allowing you to build a simulation model by selecting tools to draw the components as if you were using a drawing program The toolbars are designed differently on Windows and MacOS systems so that they conform to standard interface guidelines on each platform Both designs provide access to an identical set of tools Windows Toolbars On Windows systems Working Model 2D provides a set of dockable floating toolbars shown in Figure 2 2 Figure 2 3 and Figure 2 4 When you first launch the program the toolbars are in their docked positions on the top and left edges of the application window
60. default Click and hold on the Spring tool to bring the Rotational Spring tool in view and select it 2 Position the mouse pointer at where you want to create the spring and click once The Coordinates bar shows the coordinates for the Base Point point element on the bottom layer and the Top Point point element on the top layer as well as the rest rotation Figure 4 30 Both coordinate values are given in reference to the body to which each point is attached r 45 000 y 0 200 m x 0 250 m yl 3 750 m x 1 000 m l 1 l Base Point Top Point Rotation Rotational Spring Properties To change the properties of a rotational spring 1 Select the rotational spring and choose Properties from the Window menu 122 Chapter 4 Constraints Figure 4 31 Properties window with rotational spring selected Rotational Spring Type Rotational Spring Constant Rotational Damper Constant f Constraint 3 RotS pring x RotSprini Torque K for 75 N m rotation 0 000 i current 0 000 i c 0 000 N s m r Base Point Point 1 r Point Point 2 r Active when VV Always M You can create rotational springs that exert torques proportional to the square cube or inverse square of their rotations as they are wound up Use the pop up menu next to Torque in the Properties window to change the rotational spring type A rotational spring with a la
61. dragging it You can also position the control using the Coordinates bar When a control is selected the Coordinates bar displays the x y coordinates of the control in pixel coordinates on the Working Model 2D document The origin 0 0 of the pixel coordinates are set at the top left corner of the document window see Figure 7 4 The x axis extends to the right whereas the y axis extends downward note that the y axis of pixel coordinates runs Figure 7 12 Pixel coordinates for controls Modifying Control Size 7 2 Controls 235 opposite from the physical coordinates employed in Working Model 2D simulations The position of the control is given in terms of the selection handle shown at the top left corner You can directly modify the x y values in the Coordinates bar Untitled 1 lolx units in pixels 0 0 150 200 150 ic Control Coordinates bar shows x y pixel coordinates x 200 000 y 150 000 D n 9 You can modify the control size by selecting the control and dragging one of the selection handles small black squares shown at the corners Types of Controls and Properties After creating a slider bar you can change the type of the control to be a text box or a button or you can use an external file to feed the data into the control To change the properties of a control 1 Double click on the control or select the control and then choose Properties from the Window menu
62. first endpoint Figure 4 55 Coordinates bar for an actuator 4 16 Actuators 145 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The actual length of an actuator must always be positive That is you must make sure that the distance between the endpoints of the actuator does not become zero Otherwise the simulation result becomes indeterminate The Coordinates bar shows the coordinates for the two endpoints of the actuator and its length as shown in Figure 4 55 Both coordinate values are given in reference to the body to which each point is attached x 0 700 m x _1 300 m yl 0 150 m First Point Second Point Actuator Properties To change the properties of an actuator 1 Select the actuator and choose Properties from the Window menu The Properties window appears as shown in Figure 4 56 146 Chapter 4 Constraints Figure 4 56 Properties window with an actuator gt Constaini 3 Actuator Z selected 7 Actuator ype Force bal value 1 000 N Active when VV Always m 2 Choose the type and property appropriate for your simulation You can enter equations in the value field
63. from the Edit menu Doing so copies the data onto the Clipboard You can then paste the data into another application To export meter information to a data file 1 Create or open a simulation Create meters to measure the properties you wish to export 2 Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog 302 Chapter 9 Importing and Exporting Files and Data 3 Set the export type to Meter Data 4 Set Export Options as necessary see below 5 Click Save MacOS or Export Windows Meter data is exported as a tab delineated text file You can open the exported file with any word processor or spreadsheet program Meter data is stored in columns with each row representing a new simulation frame The numerical format of meter data is taken from the current settings in the Numbers and Units dialog box A document with a single position meter would produce the following file Data From Untitled 1 at 8 32 20 PM 2 4 93 Position of Rectangle 2 t x Y rot 0 000 1 250 3 000 0 000 0 020 1365 2 884 0 000 0 040 1 480 2 772 0 000 0 060 T4595 2 664 0 000 0 080 1 710 S2999 0 000 0 100 1 825 2 459 0 000 0 120 1 940 2 362 0 000 0 140 2 055 2 270 0 000 0 160 2 170 2 181 0 000 0 180 2 285 2 097 0 000 0 200 2 400 2 016 0 000 Please refer to Comparing Results of Multiple Simulations on page 230 for the file format of the meter data taken from
64. gear bodies are automatically given a Do Not Collide designation You cannot make gear bodies collide unless you remove the gear constraint between them e For non circular gear bodies the default gear ratio is 1 0 During the simulation Working Model 2D is only responsible for maintaining the rotation angular velocity and angular acceleration of the bodies in accordance with a given gear ratio Working Model 2D does not take into account the geometries of the bodies Figure 4 42 Properties window for a gear Gear Ratio 4 11 Gears 133 If one of the bodies is designated as an internal gear the gear ratio cannot be 1 0 unless the centers of mass of the gear bodies coincide Otherwise the point of contact would be located at infinity and the simulation will become indeterministic consider the case where a b 1 0 in the lower right drawing in Figure 4 41 A warning dialog appears when the gear ratio for an internal gear is explicitly assigned as 1 0 A formula definition of gear ratio cannot be evaluated until run time so you must make sure that the formula does not return 1 0 for an internal gear ratio during the simulation Gear Properties To define or change the properties of a gear constraint 1 Click on the rod connecting the gears or box select it and choose Properties from the Window menu Alternately you can double click on the line rod connecting the pair of gears fr Constraint 11 Gear Gear
65. information on how to use these features see Chapter 5 The Smart Editor You can rotate more than one object at a time with the Rotate tool To rotate two or more objects 1 Select the objects you wish to rotate Click the objects with the Rotate tool or with the Arrow tool Hold down the shift key to extend the selection 2 Select the Rotate tool 3 Drag on one of the objects or in the white space between objects The selected objects will rotate around the point indicated by the dotted line In some circumstances you may wish to rotate the selection around a point that is not closest to the pointer You can do this with the Option MacOS or Control Windows key 1 Select the objects you wish to rotate Use shift select or box select if you wish to rotate multiple objects 2 Select the Rotate tool 3 Move the pointer on top of the point which the object is meant to be rotated about Observe that a small circle appears around the point 4 When a small circle is visible around the point hold down the Option MacOS or Control Windows key Move the mouse and observe that a dashed line segment appears between the point and the mouse pointer 218 Chapter 6 The Workspace Figure 6 25 Rotating around a point element While holding down the Option or Control key the line will remain connected to the point and will not snap to other nearby points In Figure 6 25 below the user moved the pointer over the point
66. is 15 meaning 15 frames per second will be displayed The Video for Windows mechanism automatically adjusts each frame to meet the demand set by Playback Rate Exceedingly high values will result in degraded animation and therefore are not recommended Suppose you set the parameters as follows e Export every n frames 5 Bitmap Depth 8 e Frame Multiplier 4 e Playback Rate 10 and exported 80 frames Then the exported AVI file will have 80 frames 5 export every 5 frames 16 frames It will take 16 frames x 4 multiplier 10 frames s 6 4 sec to play back the entire AVI file Modifying Video Compression Options Working Model 2D provides default values for the image compression options that are sufficient for most purposes If you wish to customize the image quality and storage requirements Working Model 2D provides access to the advanced options built into Video for Windows To set the compression option parameters 1 Choose Export from the File menu 2 Set the export type to Video for Windows 3 Click the button Options 4 Click More Choices Figure 9 9 Video Compression dialog 9 9 Exporting Object Motion Paths or Keyframes MacOS only The Video Compression dialog appears Figure 9 9 309 For more information on the options in the Video Compression dialog please refer to the documentation on Video for Windows provided by Microsoft Corporation Video Compress
67. it will bring up a file selection dialog to allow the user to locate the file This will happen every time the Open menu button is pressed so it is best to store all related files in the same directory 2 Open the first document 3 Choose Menu Button from the Control menu A dialog box appears asking you to choose the command you want this button to execute 4 Choose the file that should be opened when the Open bution is pressed When you click the Open button inside the current simulation the simulation closes The simulation you selected when creating the Open button will open 7 4 Vectors You can graphically represent kinematic velocity and acceleration and kinetic force properties by displaying vectors Vectors can be placed on points and bodies Select the endpoint of a constraint to display force vectors for forces produced by the constraint l Vector display for torques is not supported in Working Model 2D 242 Chapter 7 Simulation Interfaces Vectors that designate velocity and acceleration are always drawn pointing out from a body s center of mass Vectors that display force quantities can be drawn either pointing from a body s center or pointing in to a body s center Vectors that display the forces encountered when bodies contact one another can be displayed at the point of contact or at the mass center of each body Figure 7 17 shows a body with active velocity and acceleration vectors
68. joint or You can also join a point element and a slot element to form a slot joint For more information see Chapter 5 The Smart Editor The Join button also re combines elements that have been separated using the Split button The Split button separates a joint into its component elements In this sense the Split button reverses an action performed by the Join button For example if you select a pin joint and click the Split button the joint is split into two point elements See Chapter 5 The Smart Editor for more information Point and Slot Tools The Point tool is used to create a point element A point element attaches to a body or to the background and serves as a basis for creating joint constraints For example you can attach two point elements on separate bodies and combine the two elements to form a pin joint Two bodies connected by a pin joint can rotate freely with respect to each other See Chapter 5 The Smart Editor for more information The Square Point tool is used to create a square point element Like a point element a square point attaches to a body or to the background For example you can attach two square points on separate bodies and combine the two elements to form a rigid joint which locks the two bodies together See Chapter 5 The Smart Editor for more information Figure 2 6 A slot joint example ae i 2 1 The Working Model 2D Toolbars 43 The Slot Element tools
69. keep the attachment in its position relative to the end of the vertical link If the point was not attached to a Snap Point no adjustments will be made Figure 1 22 provides a comparison between the two cases After the left vertical link was extended Pin Joint attached without Pin Joint attached with Object Snap Object Snap The difference comes from one of the Working Model 2D features called point based parametrics In short the Object Snap feature is linked with an automatic specification of point positions based on the geometry of the bodies involved in the joint attachment You can turn this feature on or off using the Preferences dialog in the World menu Please see 8 4 Preferences for more information Joining and Splitting The Smart Editor can automatically assemble or disassemble a mechanism You can temporarily split pin joints leaving a separate point on each body These points can be edited individually and then the pin joint can be re assembled with the Join command 1 Restore the mechanism to its original form 22 Chapter 1 A Guided Tour La Figure 1 23 Selecting a pin joint Splite Your screen should resemble Figure 1 23 Ifyou have only reshaped the mechanism once you can select Undo from the Edit menu Otherwise use the resize handles to reshape the mechanism until it resembles its original form 2 Click the Arrow tool in the Toolbar 3 Click the pin joint p t
70. labeled as such The chapters and appendices in this guide are described below e Chapter 1 A Guided Tour discusses creating and running simulations e Chapter 2 Guide to Tools amp Menus describes each tool and menu e Chapter 3 Bodies explains how to create and modify bodies e Chapter 4 Constraints explains how to create and modify constraints that govern interactions among bodies e Chapter 5 The Smart Editor explains how to use the Smart Editor to create and modify complex assemblies of bodies and constraints e Chapter 6 The Workspace describes various Workspace options e Chapter 7 Simulation Interfaces describes various controls and meters that you can use in simulations e Chapter 8 Running Simulations explains how to run and replay simulations how to track objects and how to print simulations e Chapter 9 Importing and Exporting Files and Data explains how Working Model can interact with other applications e Chapter 10 Using Formulas explains how to use formulas e Appendix A Technical Information provides basic information on how Working Model works e Appendix B Formula Language Reference explains the Working Model formula language e Appendix C Useful Tips and Shortcuts provides a list of keyboard command equivalents and shortcuts e Appendix D Scripts CHAPTER 1 A Guided Tour In this chapter you will lear
71. mathematical operations Simulation functions return information from Working Model 2D simulations B 16 Appendix B Formula Language Reference List of Functions Name Inputs Output abs number number and number number 1 or 0 angle vector number acos number number asin number number atan number number atan2 number number number ceil number number cos number number exp number number floor number number if number number number number in number number log number number mag vector number max number number number min number number number mod number number number not number 1 or 0 or number number 1 or 0 pi ZA pow number number number rand number sign number 1 or 1 sin number number sqr number number vector number sqrt number number tan number number vector number number vector abs x Takes a number and returns the absolute value of the number Example abs body 3 p x returns the absolute value of body 3 s x position and x y angle v acos x asin x atan x atan2 y x ceil x cos x exp x floor x B 6 Functions B 17 Logical AND operation Takes two numbers and returns the value 1 if both numbers are not 0 Otherwise returns the value 0 Example and time gt 1 body 2 v y gt 10 returns the value 1 if time is greater than 1 and body 2 s y velocity is greater than 10 Takes a vector and returns the angle the vector makes with the coordinate plane For example if a
72. mechanism where the size of body 1 depends on the size of body 3 Suppose you want the width and height of body 1 to be half of the width and height of body 3 respectively You would then specify the width and height fields of body 1 as World Coordinates Shape Coordinates 3 4 Body Geometry 81 Width body 3 width 2 Height body 3 height 2 Resizing body 3 will now automatically change the size of body 1 NOTE When a formula expression is used to specify the Geometry of a body the formula is only evaluated at the first frame at t 0 The result of evaluation will be used for the remainder of the simulation For example if a function cos f is used to specify the width of a rectangle then the rectangle will maintain a width cos 0 1 0 for the remainder of the simulation regardless of the value of t or cos Coordinates for Polygons and Curved Bodies Polygon vertices and curved body control points are shown as a table in the Geometry window Their coordinates can be displayed either in shape coordinates or in world coordinates World coordinates show the actual position of a vertex in the workspace as global coordinates For polygon and curved body objects World coordinates are always given in rectangular Cartesian coordinates Shape coordinates show the position of each vertex with respect to the object s FOR see Frame of Reference FOR on page 67 as local coord
73. moving apart will bounce back with the same kinetic energy due to the rope tension On the other hand a rope with a coefficient of 0 is completely inelastic the kinetic energy of attached bodies will be completely absorbed by the rope as it becomes taut Slack rope Figure 4 23 Resizing a rope while maintaining its length Simulating a Breaking Rope 4 4 Ropes 113 You can first create a taut rope then specify the length to be longer than the current length The rope will be slack while the endpoints of the rope will remain stationary In order to modify the distance between the two endpoints without modifying the length of the rope 1 Move the endpoints of the rope until it is of the desired length The rope s length is automatically set to be the distance between the two endpoints 2 Move either endpoint of the rope while holding down the Option MacOS or Control Windows key The rope becomes taut or slack depending on how you move the endpoint Hold Control key Windows or Option key MacOS and drag endpoint The rope will maintain its length You can simulate a rope that breaks in the middle of the simulation In Working Model 2D you only need to turn off the rope The inactive rope is displayed as a dotted line and exerts no force You need to determine when the rope is supposed to be broken For example you may want to turn off the rope at time gt 1 0
74. multiple simulations Figure 9 6 Meter Data export options Include Header Include x axis 9 6 Exporting Meter Data to a File 303 Export Meter Data Default suffix Data Export every oR frames every 0 010 s MacOS Export data from every meter OD selected meters only amp Include header amp Include x axis Export Meter Data x Default suffix DTA Windows Export every frames Cancel every Export data from every meter selected meters only T Include header T Include x axis This option includes the file name date meter name and column names before all numerical data This option will help in referring to specific columns of data When this option is turned off only numerical data is exported This option includes the x axis data of each meter as a column Meters generally have time as the x axis default You can specify another variable such as the frame number and make it the independent variable Copying and Pasting Data from Meters To copy simulation data directly to the Clipboard 1 Create or open a simulation 2 Add meters to measure object parameters 3 Run the simulation for the time duration that you want to collect data 304 Chapter 9 Importing and Exporting Files and Data 4 Select one or more meters 5 Choose Copy Data from the Edit menu Your data is now in the Clipboard You can paste this data into other applications Reading Meter Data B
75. of the current document e World menu settings including the ones in the Preferences dialog e View menu settings and e Vector Length Display settings under the Define menu 8 5 Recording a Simulation Recording a simulation can take up a great deal of memory Depending on how many objects meters and vectors are activated a single frame of animation can use up several thousand bytes of memory Working Model 2D automatically uses all available memory to store large simulations Memory Requirements of a Recording If your simulation has used up all available memory that is the tape player is full you will see the following dialog box Figure 8 8 The tape player is full Keep running and write over the beginning of the tape If the tape player memory is full you can continue running your simulation in several ways e Close other Working Model 2D documents to make more memory available to the tape player e Make more memory available to Working Model 2D see Increasing the Memory Available to Working Model 2D on page A 1 Let the tape player loop and continue running the simulation 260 Chapter 8 Running Simulations Overwriting the Existing Frames Splitting into Multiple Files e Increase the time step of the simulation resulting in more spacing between frames An increase in the space between frames allows you to record the simulation for a longer time in the tape player When do
76. of the location and distribution of contact loads than is available in a rigid body analysis As a result contact and collision loads are ignored Coordinate System Assignment In calculating and presenting the shear force and bending moment diagrams this script employs the coordinate system assigned to the rectangle by Working Model Figure D 14 illustrates how this coordinate is assigned to a beam The diagrams display the shear force and bending moment versus the rectangle s x coordinate shown below The script calculates the bending moment value along the line y 0 which passes through the geometric center of the beam Coordinate System be 2 a ag P i p i A r et t 1 i E 1 i Bending Shear i Moment Force t f t N f bs r a ar Sign Convention Y yA Forces and moments shown are acting in positive direction D 2 The Shear Force and Bending Moment Script D 11 Figure D 15 Definition of the Area Moment of Inertia Sign Convention The bottom half of Figure D 14 shows an exploded view of the beam element B The shear force and bending moment are the internal loads which hold the beam together and ensure the rigid connection between the element B and the remainder of the beam or the two elements A and C Figure D 14 also shows the sign convention for positive shear force and bending moment As explained in the figure e The shear force is positive when element A
77. of three numbers a b and cas min min a b c Takes two numbers and returns the remainder when the first value is divided by the second Logical NOT operation Takes a number and returns the value 0 if the number is not 0 Otherwise returns the value 1 Logical OR operation Takes two numbers and returns the value if at least one of the numbers is not 0 Returns 0 if and only if both numbers are 0 Example or time gt 1 body 2 v r gt 10 returns the value 1 if time is greater than 1 or body 2 s angular velocity is greater than 10 Takes two numbers and returns the value of x raised to the power of y i e returns x Returns the value of 1 4 Returns a random value between 0 and 1 B 20 Appendix B Formula Language Reference sign x Takes a number and returns the value 1 if the number is greater than or equal to zero Otherwise returns the value 1 sin x Takes a number and returns the sine of the number sqr x Takes a number or a vector If the input is a number returns the square x x of the number If the input is a vector returns the sum of the x field squared and the y field squared sqrt x Takes a number and returns the square root of the number tan x Takes a number and returns the tangent of the number vector x y Takes two numbers and returns a vector composed of the two numbers The first number x becomes the x field of the vector The second number becomes the y field of t
78. ofan error is a small fraction of the overall displacement of the probe which probably extends to millions of miles However suppose you are interested in the orientation of the probe while it travels in space Further assume that the error must stay within 1 Working Model 2D evaluates an angular error by converting it to the arc length drawn by the body with the given angle In our case a 20 foot body swings 1 to draw the arc length of Z feet 1 degrees Fapltadians deg 0 175 feet Summary A 6 Simulation Accuracy Dialog and Simulation Parameters A 13 The body dimension of 20 feet is divided by two to obtain the rotation radius assuming the body rotates about its center of mass Then the Absolute Acceptable Error of 1 mile is too large you need to tighten it to about 2 inches Y 0 175 feet Meanwhile you can leave the Relative Acceptable Error to about 10 to maintain the positional error of 1 mile Since the overall tolerance has become tighter because of the small absolute error computing the simulation will take longer than estimating the position alone Shown below are general rules of thumb in fine tuning the acceptable errors e You should almost always keep the Relative Acceptable Error low by choosing a large value at least 4 for Significant Digits in the Accuracy dialog e You may need to control the Absolute Acceptable Error defined as Integrator Error in the Accuracy dialog depen
79. or meter object without changing its window size or position for example sliding a control bar Certain actions require redrawing of the interface layer and will erase tracks even if AutoErase Track is disabled Such actions include but are not limited to e changing the position of a control object creating a new meter object e manually changing meter scales autoscale is disabled when the AutoErase is disabled and e zooming the window The recommended usage of multiple tracks is as follows 272 Chapter 8 Running Simulations Build your simulation model Enable AutoErase and run the model for the range of parameters with which you are trying to experiment By so doing the meters will automatically scale themselves to accommodate the range of measurements Disable AutoErase then run multiple experiments making variations with the parameters of the objects in the model Now you can examine the graphical results of multiple simulations 8 10 Saving a Simulation When you save a simulation file Working Model 2D automatically saves any tape history associated with the simulation The saved simulation runs faster when played because the computer does not have to perform calculations To save your simulation and tape history 1 Choose Save from the File menu The Save As dialog appears as shown in Figure 8 18 if this is the first time you are saving the simulation If you have already saved your simu
80. output devices include graphs digital displays and bar displays You can create buttons to execute Working Model menu commands including Run Reset and Quit Buttons can simplify pre made simulations for the first time user they can also be used to create Working Model documents in which one document leads to the next with the click of a button You can annotate simulations directly on the workspace using any font size or style of text available on your computer You can paste pictures created with a paint or draw program directly on the workspace or link them to objects For example you can create a circular object and attach a picture of a baseball to it By supplying an equation you can simulate planetary gravity as well as earth gravity electrostatic forces air resistance proportional to velocity or velocity squared or your own custom global forces For example you can create magnetic fields wind and electron gun fields You can show and hide objects fill objects with patterns and colors display the electrostatic charge of objects or choose the thickness of an object s outline show object names and display vectors You can view simulations using any body or point as the frame of reference Complete Control of Units Complete Formula Language Menu less Player Documents Custom Tracking Object Layering Vector Displays Save Time History Pause Control What is Working Model 2D xxi You ca
81. perfectly elastic means that the difference in velocities after the collision will be the same as before except that they are in the opposite direction See A 7 Simulating Collisions for more information In Working Model 2D each body is assigned an elasticity constant The coefficient of restitution in a collision is defined as the lower value of the constants given to the two bodies involved in the collision Thus if one body has an elasticity of 0 2 and another body has an elasticity of 0 8 the resulting collision will occur with a coefficient of restitution of 0 2 You can change the coefficient of elasticity of one or more bodies by entering a value directly into the Properties window Working Model 2D correctly models both static and kinetic Coulomb friction Static friction occurs when two objects are in contact and are not moving relative to each other Kinetic friction occurs when the objects are in contact and are moving relative to each other A friction coefficient represents a property of interaction between two objects In Working Model 2D each body is assigned a static and kinetic friction constant The coefficients of static and kinetic friction between two objects are defined by taking the lower value for each coefficient given for the interacting objects Thus the coefficient of kinetic friction between an object with a value of 0 05 and another object with a value of 0 3 would be 0 05 You can change th
82. physical property in a Working Model 2D simulation you can also customize meters to measure display or evaluate arithmetic and mathematical expressions using the versatile formula language available in Working Model 2D What Can Be Measured with Meters When you select a set of objects Working Model 2D automatically presents a menu of quantities that are available for measurement in the Measure menu Therefore to see which properties can be measured for any object simply select the object and then look at the Measure pull down menu The menu shows the measurable quantities of the particular object Figure 7 1 shows an example when a body is selected Please note that the Measure menu is simply a selected set of readily available meters and that meters can measure quantities that are more complex or not readily available in the Measure menu You can easily customize any meter by using simple formula expressions to describe the values you wish to measure For example to measure the energy of two objects you can simply change the default formula on one of your meters to measure the desired quantity Please see 10 5 Customizing Meters for more information Figure 7 1 Measure menu when one body is selected 7 1 Meters 223 Time Position Velocity Acceleration PAA vvv Center of Mass Position gt Center of Mass Velocity Center of Mass Acceleration gt Ad Momentum Angular Momentum Total Force Tota
83. pointer to the other corner of that rectangle Working Model 2D will display a dotted rectangle to indicate the selected area When you release the mouse button all objects enclosed by the rectangle are selected All other objects are de selected If you hold down the Shift key while dragging the selection rectangle the selection state of all enclosed objects is toggled Objects that were previously not selected become selected objects that were previously selected become de selected You can select all objects in a simulation even the ones that are off screen with one command choose Select All from the Edit menu All objects become selected To deselect all objects click on the workspace in a place where there are no objects Showing All Hidden Objects To show all hidden objects 1 Choose Select All from the Edit menu All objects are selected including those that are hidden 2 Choose Appearance from the Window menu The Appearance window appears 3 Click to set the checkmark next to Show All objects will be affected and as a result will now be shown Cutting Copying Pasting and Clearing Selected objects can be erased put into temporary storage or taken out of one simulation and placed in another simulation 214 Clipboard Cut Copy Paste Chapter 6 The Workspace When an object is copied all of its attributes for example its initial velocity and display characteristics such as vectors are pr
84. press the a key again and click on the anchored body This will remove the anchor two anchors on the same body cancel each other When joining two square points to form a rigid joint you may notice that one or both bodies rotate The rotation occurs because the Smart Editor aligns the orientations of the two square points when making the rigid joint For example suppose two perfectly horizontal rectangular objects each contain a square point one of which is rotated 30 with respect to the rectangle it is in If you join these two square points the two rectangles will be connected with a relative angle of 30 between them because the Smart Editor aligned the orientations of the two square points If you subsequently change the rotation of one of the points the bodies will rotate with respect to each other 178 Chapter 5 The Smart Editor Figure 5 7 Two pinned rectangles Figure 5 8 Dragging two pinned rectangles 5 2 Dragging and Rotating Joined Bodies The Smart Editor is an interactive tool Hands on use is the best way to learn its power and capabilities The Working Model 2D Tutorial and Chapter 1 A Guided Tour of this User s Manual provide examples to help you learn to use the Smart Editor What follows is a demonstration of the ideas and techniques involved in using the Smart Editor You can read through the following section or if you wish try the concepts on your computer as you follow along The sect
85. radius orientation Moving the Circle to Starting Position To position the circle for the start of the simulation 1 Select the Arrow tool if it is not already selected 1 4 Setting Up a Simple Simulation 9 2 Position the pointer inside the circle 3 Hold the mouse button and drag the circle to the lower left corner of the screen as shown in Figure 1 7 Figure 1 7 untitled Dragging the circle Press and hold down the mouse button here drag to here and release the mouse button Alternatively you can use the Coordinates bar to specify a precise initial position Simply type the desired numbers into x and y fields of the Coordinates bar see Figure 1 6 Specifying Initial Velocity To specify the initial velocity of the center of the circle 1 Click the circle to select it Four square dots appear around the circle 2 Choose Preferences from the World menu The Preferences dialog appears see Figure 1 8 You can use this dialog to modify preferences and save them for all new documents 3 Check the item titled Allow velocity vector dragging Click OK A new round dot appears at the center of the circle 10 Chapter 1 A Guided Tour Figure 1 8 Preferences dialog Edit objects as 0 Click here and make sure the Objects checkmark appears T I Allow velocity vector dragging I Calculate initial conditions
86. restore all the beams in your document Name Convention For Beam Elements within the D 1 The Flexbeam Script Working Model Document Unflex identifies the bodies modified by Flexbeam by examining the name of each body in the workspace Flexbeam assigns a name to each of the rectangular elements of the following form name flexbeam 3 digit number 3 digit number The first 3 digit number refers to the identification number of the flexible body The second 3 digit number expresses the identification number of a particular element in a particular flexible body The fourth element of the second flexible body therefore would have the name flexbeam002004 Sample Scripts and Documents Flexbeam includes the following sample scripts and documents Type Filename Description Sample Scripts flexbeam wbs The Script which creates flexible representations of beams unflex wbs The script which undoes the effect of Flexbeam flexbeam hlp The help file for Flexbeam Documents bridge wm Truck driving over a flexible bridge fixfree wm Accuracy of a fixed free cantilever beam fixroll wm Accuracy of a fixed roller beam pinroll wm Accuracy of a pinned roller beam References The spring constants provided by Flexbeam are determined by the formulas in Determination of Spring Constants for Modeling Flexible Beams by Paul Mitiguy and Arun Banerjee The effectiveness of this formulation is discussed in MSC Software s tech
87. shift key to select the point on the cam follower Click Join Note that the cam follower is now attached to the slot Adjust the cam follower so that it is horizontal at roughly the same y position of the driving motor Attaching a Slot to a Body Detaching a Slot from a Body 4 19 Slot Joints 163 You can drag the follower and or use the Properties window of the follower to type in the y coordinates and rotation to adjust the position and orientation precisely Use a horizontal keyed slot to attach the end of the cam follower to the background Click Run Observe how the cam follower moves as the cam rotates Attaching and Detaching a Slot Element You can freely attach a slot element to or detach it from a body For example if you have a closed slot element attached to the background e g converted from a DXF file you can attach the slot element to a circular body to create acam To attach a slot to a body 1 3 Move the slot element to the desired position on or near the body Working Model 2D will not alter the position of the slot or the body when attaching them together You need to position the slot to the desired position on the body first You can change the color or pattern of the body to transparent so that you can see the slot element when it is covered by the object Select both the body and the slot element Use shift select or box select Choose Attach to Body from the Object menu
88. showing control point coordinates Notes on Interpolations Worksheet 152 987 169 616 77 828 29 820 100 187 158 682 2 Copy the selected data to the Clipboard using the Copy function of that application 3 Switch to Working Model 2D and create an initial curved slot Choose Geometry from the Window menu The control points of this initial slot are not important as they will be overwritten with the new data that is pasted in the next step 4 In the Geometry window select whether you want the data to be interpreted as Cartesian or Polar coordinates by clicking on the appropriate radio button 5 Similarly select whether you want the interpolated curve to be open or closed 6 Click the Paste button in the Geometry window The data points are automatically interpreted as control points for the curved slot To construct a smooth curve through a series of control points Working Model 2D uses a third order B spline interpolation one of the most commonly used interpolation methods However since different CAD CAM packages often interpolate control points with different methods the generated curve the result of the interpolation may appear slightly different from one package to another even though the control points are identical Thus when you use Copy Table to export a curved slot you designed on Working Model 2D another CAD package may interpret the control points in its own way and display another cur
89. simulation The bottom of any constraint object s Properties window contains a field titled Active When This field is set to Always by default meaning that the constraint is always active throughout the simulation Figure 4 18 Active When field J Constraint 20 Damped Damped Spring poo nm K 50 000 N m length 2 800 m current 2 800 m r Damper K fi 000 N s m Active When Field Active when Remove the checkmark from the I Always ln Always box and edit the field Jtime lt 5 0 There are two ways to control when a constraint will be active 1 Enter a formula directly into the Active When field in the constraint Properties window The constraint is active whenever the value or formula in the Active When field is greater than zero For a complete description of the Working Model 2D formula language consult Chapter 10 Using Formulas Alternatively 1 Select a constraint and then choose New Control from the Define menu 2 Select On Off from the submenu that appears next to New Control A new control will be created that allows you to turn the constraint on and off For more information on controls see 7 2 Controls Constraint Length Constraint Velocity Figure 4 19 Constraint velocity and force in the positive direction Constraint Forces Constraint Rotation 4 3 General Properties of Constraints 109 Polarity Definitions Constraint length is the sepa
90. snap to the nearest point about which objects can be rotated Pressing the r key will automatically select the Rotate tool The Text tool is used to enter text directly onto the simulation workspace The Zoom In tool increases the magnification of the workspace by a factor of two 2x The new view is centered on the area around the pointer Holding down the shift key will toggle this tool to the Zoom Out tool The Zoom Out tool decreases the magnification of the workspace by a factor of two 1 2x Holding down the shift key will toggle this tool to the Zoom In tool aojo A B 2 1 The Working Model 2D Toolbars 41 On MacOS systems the Zoom In and Zoom Out tools are accessed through the Zoom pop up palette Run Controls The Run button starts a simulation On MacOS systems the Run button changes into the Stop button when a simulation is in progress The Stop button stops a simulation in progress On MacOS systems the Stop button changes into the Run button when a simulation is not running The Reset button is used to bring a simulation back to its initial conditions the first frame Body Tools The Circle tool is used to create circular bodies The Square tool is used to create square bodies The Rectangle tool is used to create rectangular bodies On MacOS systems the Square and Rectangle tools are accessed through the Rectangle Square pop up palette The Polygon tool is used to create polygons other
91. text ASCII data input To transfer curved slot data from Working Model 2D to another application 1 Select the curved slot and choose Geometry from the Window menu The Geometry window appears and shows the control points Choose the coordinate system to represent the data points Cartesian and Polar coordinates are available If you want the interpolated points to be exported click the Interpolated checkbox and specify how many interpolated points are to be exported between each pair of adjacent control points Click the Copy button in the Geometry window The table of point coordinates are copied to the Clipboard For this step do not use the Copy in the Edit menu which only copies a single number selected Switch to the target application and use Paste from its Edit menu to paste the data points Each row of data represents a pair of point coordinates separated by a tab To transfer curved slot data from another application to Working Model 2D 1 Select the table of points in another application Ideally the data should be tabulated in the two column format where each row represents a pair of point coordinates delimited by a tab Otherwise Working Model 2D assumes a list of numbers to be sequential pairs of point coordinates Figure 3 22 below shows a sample Microsoft Excel worksheet holding coordinate pairs for six control points 172 Chapter 4 Constraints Figure 4 81 Sample Excel spreadsheet
92. the length field is blank indicating that the springs share the same spring constant and have different lengths If you modify a property of a mixed selection in the Properties window all the selected constraints will have the same value For example if you typed 2 0 in the length field in the Properties window as shown in Figure 4 5 then the two springs would both have 2 0 meters as their rest length Showing and Hiding Constraints You can show or hide constraints selectively using the Appearance window All constraints function whether they are hidden or shown Below are some reasons why you might want to hide constraints e Hiding slot elements to avoid a long slot cutting across your simulation screen e Hiding a spring damper suspension mechanism in an automobile to make the model look more realistic To show or hide constraints 1 Select the constraint you wish to show or hide 2 Choose Appearance in the Window menu The Appearance window appears 3 Click on the Show checkbox as appropriate Figure 4 6 Assigning Names to Constraints You can assign custom names to constraints to identify individual points and constraints quickly You can also display names within the simulation window near the center of each constraint To assign a custom name to a constraint 1 Select the constraint you wish to name 2 Choose Appearance in the Window menu Figure 4 6 Appearance window Linear Constraints Rotat
93. the same y coordinates height and orientation To set the properties of more than one body at the same time 1 Select all the bodies with properties you wish to change You can select multiple objects using shift select selecting one object after another while holding down the shift key 2 Enter the new value in the appropriate field of the Coordinates bar All of the selected bodies will have their properties modified at the same time The Properties window automatically shows the common parameters in its fields If a particular property differs among the selected bodies the Properties window shows the property as blank see Figure 2 7 To set the properties of more than one body at the same time 1 Select all the bodies with properties you wish to change Figure 3 11 Properties window with more than one body selected Using the Selection Pop up Menu 3 2 Body Properties 73 You can select multiple objects using shift select selecting one object after another while holding down the shift key The selection pop up shows mixed selection When you open the selection pop up the relevant items are shown with a minus sign next to the object ID Figure 2 7 The selected bodies perti have different x and y LE coordinates Body 1 Rectangle T Body 2 Polygon Body 10 Circle i o 000 Constraint 6 Spring Constraint 9 Pin Joi
94. to create actuators that behave like drivers For more information on using equations see Chapter 10 Using Formulas Force A force actuator exerts a force between its endpoints Length A length actuator exerts the force necessary to keep the endpoints at a specified distance You cannot specify length less than or equal to 0 If you specify the length as a numeric constant the actuator will be modified to the specified length immediately The Smart Editor see Chapter 5 The Smart Editor will automatically modify the rest of the model to accommodate the specification If you used a formula expression to specify the length the formula will be immediately evaluated as t 0 and the actuator length will be modified accordingly Again the Smart Editor will automatically modify the rest of the model to accommodate the specification Velocity A velocity actuator exerts whatever force is necessary to maintain the relative velocity between the endpoints as specified Acceleration al Figure 4 57 Coordinates bar for a motor 4 17 Motors 147 An acceleration actuator exerts the force necessary to maintain the relative acceleration between the endpoints as specified NOTE When you use a function to specify the actuator force length velocity or acceleration make sure that the function does not result in the actuator length less than or equal to 0 in the duration of the simulation 4 17 Motors A motor is composed of two
95. used in a position meter 10 6 Specifying Body Path by Position 337 HO Properties Output 4 P v Fosition of Circle 3 Label Equation time Body 3 p x Body 3 p y Bodyl3 p r Auto Min Max xX 1 000 v1 K 1 000 1 000 2 1 000 1 000 v2 1 000 A meter that measures the position of a body contains the following three formulas body 1 p x body 1 p y body 1 p r These formulas refer to the configuration of the object in terms of its position x y and rotation r You can create custom meters by replacing the default formulas with your own formulas The title and appearance of a meter can also be altered using the Appearance window Further any meter field can be used in another formula description See Using Meters as Variables in Formulas on page 342 for examples 10 6 Specifying Body Path by Position Typically the simulation calculations of Working Model 2D automatically governs the motion of objects in your simulation model at run time Input controls as described in Chapter 6 The Workspace are only effective in defining initial positions of bodies 338 Chapter 10 Using Formulas But suppose you wish to move a body in your model according to some predefined trajectory that can be described using formulas You can use the Anchor tool to fix the body thereby releasing it from the physical interactions computed by Working Model 2D and assign arbitrary formulas to
96. variable n differs depending on the ID number assigned to the pin joint in your model The expression constraintforce n refers to the force vector acting on the body on the top layer For example suppose a pin joint constraint 5 consists of point 3 and point 4 Then the force meter for constraint 5 measures the force acting at point 3 Again the components are broken into global x and y coordinate axes Figure 4 66 Concept for joint force meters 4 19 Slot Joints 155 Point 3 Two points form a pin joint constraint 5 Rectangle on Top Layer Rectangle on Bottom Layer The meter created for constraint 5 will measure the vector constraintforce 5 which is equivalent to the vector point 3 force You can measure the force acting on the bottom point by replacing the force meter fields with point 4 force x point 4 force y point 4 force for x y components and the magnitude respectively Please refer to Point Fields on page B 7 for more information 4 19 Slot Joints Slot joints align a point on one body with a slot on another or on the background A slot can be either straight or curved Creating a Straight Slot Joint You can create a straight slot joint by either e using one of the straight Slot Joint tools from the Toolbar or e joining a straight slot element with a point or a square point element to create pinned or keyed slot joints respectively F
97. with a 680x0 processor You must have a PowerPC based computer to use the Script Editor in the MacOS version of Working Model 2D List of Scripts Tools The list provides quick access to available scripts The list can be modified see Adding Scripts and Tools to the Working Model 2D Menu on page 262 for instructions The Window Menu The Window menu provides three utility windows to specify precise values for an object s properties The fields that appear in a utility window depend on the type of object that is selected Each utility window features a selection pop up menu at the top The selection pop up menu shows the ID such as body 3 and name e g Rectangle of the object currently selected The name can be customized using the Appearance window For more information on how to use these windows see Chapter 3 Bodies and Chapter 4 Constraints 56 Chapter 2 Guide to Tools amp Menus Figure 2 7 Properties window Figure 2 8 Appearance window The Properties window Figure 2 7 provides direct access to the physical properties of the currently selected object Different fields will appear depending on the type of object that is selected The properties of several selected objects can be changed at the same time select multiple objects and modify the desired properties in the window fr Body 1 Rectangle z Rectangle x fA 400 m y 0 550 m Jo co0 i VE pooo m s Vy Joco mis v joo
98. 0 m point element DC nD Pla Local Coordinates Global Coordinates When the coordinates are given with geometry based expressions such as 0 0 0 0 and body 3 width global coordinates are not available for editing x body 1 m y 0 0 Im hua CODD Keo Es 1 d Local Coordinates NOTE Ifthe position of the endpoint is defined by a formula see Using Geometry based Formulas Point based Parametrics on page 104 its global coordinates are not available in the Coordinates bar You can enter numerical values or formulas in the Coordinates bar The modification takes effect immediately even if formulas are entered Individual sections later in this chapter discuss which parameters can be edited using the Coordinates bar for each constraint Using Geometry based Working Model 2D features geometry and constraint based parametrics Formulas Point based You can use these formulas to define positions of objects via symbols rather Parametrics than numerical values For example Figure 4 14 shows how point positions on rectangles and a circle can be expressed using parametric formulas Figure 4 14 Examples of geometry formulas body 1 body 1 width 2 body 1 height 2 body 2 height attached to body 1 G k body 2 width D body 2 body 3 radius lt body 2 width 2 body 2 height 2 attached to body 2 body 2 width 4 0 0 0 0 body
99. 00 N m t 0 050 s frame 1 x 2 05 Min 1 01e 01 N m t 1 450 s frame 29 x 2 05 e Shear Max 1 40e 01 N t 0 050 s frame 1 x 2 05 Min 1 44e 01 N t 1 800 s frame 36 x 2 05 The Export button provides for the export of the shear force and bending moment data of the current time frame to a data file With the gt and lt buttons you can step forward and backward to any frame of interest This may be used for example to record the profile associated with the maximum bending moment The script automatically names the file according to the format Shear dta The triple pound sign symbolizes the numeric characters between 001 and 999 and reflects the order in which this file was written For example the first profile exported is written to the file Shear001 dta The files are written in the directory in which Working Model resides e g C Program Files Working Model Figure D 14 Coordinate System and Sign Convention Appendix D Scripts Unit Systems see previous Flexbeam script Contact and Collision Forces Not Included This script creates the shear force and bending moment diagrams by identifying the kinematic state of the beam and the magnitude direction and point of application of the external loads applied to it Working Model is designed primarily for rigid body dynamic analysis The construction of the shear force and bending moment diagrams requires a more detailed description
100. 1 Transfer the file to your MacOS computer 2 Open the file within Working Model 2D on the MacOS computer If you wish to modify the original file so that double clicking the file would launch the application you can either e open the file within Working Model 2D and save it again 286 Chapter 8 Running Simulations Figure 8 24 Converting file type using ResEdit e let an automated program such as PC Exchange handle the file type conversions or e manually modify the file resource type using applications such as ResEdit To modify the file type using ResEdit 1 Transfer the file to your MacOS computer 2 Launch ResEdit and open the Working Model 2D file 3 select Get Info from the File menu and enter the following information see Figure 8 24 for a sample Type FzzX Creator wmK SSS Info for WM Test File File wm Test File O Locked 7 File Type Type FzzH__ Creator Information O File Locked C Resources Locked File In Use Yes O Printer Driver MultiFinder Compatible File Protected No Created Mon Jan 2 1995 Time 3 23 32 PM Modified Mon Jan 2 1995 Time 3 23 33 PM Size 286 bytes in resource fork 5488 bytes in data fork Finder Flags 7 8 6 0 4 Has BNDL INoINITs Label _None vj O Shared iJ Inited O Invisible O Stationery O Alias O Use Custom Icon The character is option r 4 Quit ResEdit making sure to save your ch
101. 10 1 Units in Formulas 327 How Working Model 2D Handles Unit Conversions A constant is defined as a literal number such as 3 12 Everything else is considered a formula including expressions that evaluate to constants such as 3 2 When the unit system is changed Working Model 2D updates the values of all constants For example entering a value of 10 ina position field measured in meters and then changing the distance units to centimeters will cause the value to be automatically changed to 1000 cm Note that this change preserves the physical quantity of length in agreement with Rule 2 When the unit system is changed all the factors in the formula are multiplied by the proper conversion constants Suppose the current unit system is feet pounds seconds and you entered a length of an actuator as follows Length time 5 in feet At time 1 0 the length would be 6 0 feet If you use the Numbers and Units dialog to change the unit system in inches the equation will automatically be converted to Length 12 time 5 in inches Note that the physical quantity is preserved before and after the unit system is changed without the conversion factor 12 the length would have been 6 0 inches at t 1 0 although you would have expected it to be 6 0 feet 72 0 inches Furthermore if the time units were changed from seconds to minutes the equation would become Length 12 time 60 5 in inches because t
102. 3 radius 2 Figure 4 15 How geometry formulas preserve constraint attachment Automatic Constraint Attachment 4 3 General Properties of Constraints 105 To modify the position of constraint endpoints via parametric formula 1 Select the constraint endpoint whose position you would like to modify 2 Choose Properties in the Window menu Properties window appears 3 Type the desired geometry based formula in the position fields Alternatively you could type the formulas directly into the Coordinates bar however you may find the fields a bit too short to enter long expressions Geometry formulas not only help you position constraints endpoints precisely but also make these endpoint attachment immune to resize and reshape As shown in Figure 4 15 you can stretch a rectangle and the spring endpoint stays attached to the midpoint of one of its sides boas 5 a Attached at body 3 width 2 body 3 height 2 J Reshape the Rectangle nao and the attachment remains at the specified location R Please refer to Appendix B Formula Language Reference for a complete listing of formula language expressions Controlling Constraint Attachment Constraints automatically connect to bodies that lie beneath them For a linear constraint each of the endpoints connects to the topmost body lying beneath it For a rotational constraint the two endpoints connect to the two 106 Chapter 4 Constraints
103. 3D polygons we strongly recommend that you choose a perspective of your 3D model in the CAD program that best illustrates the object before exporting it to the DXF file to be sent to Working Model 2D e LINEs are imported as lines However in Working Model 2D lines do not have any physical properties the sole reason of their existence in Working Model 2D is to facilitate the interface with CAD packages You can resize and move lines in Working Model 2D but they have no effect on simulations Once lines are imported the user needs to convert them to either polygons or to curved slots See Converting Lines into Physical Objects on page 296 for more information e POINTs are imported as Point objects in Working Model 2D Initially all points are attached to the background See Attaching Points and Slots to Bodies on page 297 to reconstruct your model Working Model 2D automatically assigns units to the numbers in DXF files based on the current unit system defined in the Numbers amp Units dialog box For example if you are importing a DXF file drawn in inches be sure to set the length units in Working Model 2D to inches before importing Figure 9 2 Import dialog 9 4 Importing CAD Geometries as DXF files 295 Importing a DXF File To import a DXF geometry file into Working Model 2D 1 2 Make sure your unit system is consistent with the target DXF file Choose Import from the File menu The Import dialog
104. 400 m wi3400 m 0 000 You can also create a rectangle or a square in the following fashion 1 Click the Rectangle or the Square tool to select it 2 Position the pointer in a blank area of the background 3 Click once and drag the mouse Note that the rectangle or the square is drawn diagonally following your mouse movement 4 When the body reaches the desired size click the mouse button again You do not need to change any options or preferences to use this alternate drawing method Working Model 2D intelligently identifies your actions on the mouse and switches drawing methods You can quickly edit the position orientation and dimensions width and height of the rectangle or square you just created as follows Figure 3 4 Coordinates bar display for a rectangle 3 1 Creating Bodies 61 Select the rectangle or square if it is not already selected Ifyou have just drawn the object it is selected already Click the field you would like to edit in the Coordinates bar and type the number desired see Figure 3 4 for available parameters Press the Enter or Return key The object will immediately reflect the changes entered X position y position height width orientation 2300 m y 0200 m h1400 m w 3400 m aloo S L A m e A H 3 2 Body Properties 3 3 Body Appearance and 3 4 Body Geometry will further discuss modifiable parameters of bodies Also please
105. 8 Figure 4 38 An internal gear Chain drive mechanism Figure 4 39 Chain drive mechanism using internal gears 4 11 Gears 129 external gear internal gear Working Model 2D defines external gears by default even if two bodies are clearly overlapping To create an internal gear 1 2 Create and select a gear constraint Open the Properties window and click on the Internal Gear checkbox One of the gear icons will turn into an internal gear icon indicating that the gear will behave as if it had internal teeth Click on the appropriate radio button in the Properties window to indicate which gear you want to be internal with teeth on the inside of its circumference You can use an internal gear to simulate a chain drive mechanism as well As with spur gears you can specify the gear ratio see Gear Properties on page 133 for details An example of a chain mechanism is shown in Figure 4 39 body 2 driving gear diameter 1 0 meter body 1 driven gear diameter 2 0 meters 130 Chapter 4 Constraints Figure 4 40 Properties window for gears to simulate a chain drive To create a chain drive mechanism like the one above Create two disks that are slightly separated as shown in Figure 4 39 Connect the two disks with a gear constraint Attach a pin joint or motor to the disks as appropriate For example attach a motor to the center of one of the disks and attach a
106. A checkmark appears next to the Grid command when the grid is displayed To hide the grid choose Grid again The checkmark next to it disappears Figure 6 10 Grid lines and grid snap Grid lines at gt major divisions N a 2000 3 000 i Grid snap at every division Aligning Objects to the Grid You can align objects to the grid by using Grid Snap Grid snaps occur at the smaller marks on the rulers as shown in Figure 6 10 When grid snap is on regardless of whether the grid is visible it affects tools by causing tool movements to align to grid points 1 Choose Grid Snap from the View menu Figure 6 11 Coordinates bar and its functions Showing Mouse Position Editing Object Parameters 6 2 Viewing Options 201 Grid Snap is on if you see a checkmark by the submenu item titled Grid Snap Aligning Objects to Bodies The Object Snap command is extremely useful when you wish to attach constraints to a vertex the center or a midpoint of a body Please see Positioning Constraints Precisely on page 101 for complete information Displaying the Coordinates Bar The Coordinates bar Figure 6 11 is a versatile tool designed to help you build models quickly The bar continuously displays the mouse position as you hover the mouse object parameters as you select objects and displacements as you drag objects Furthermore you can use it to edit object parameters without opening the Properties or
107. C Show name Frame Oo E o Track center of mass o Show center of mass o Track connect o Show charge amp Track outline You can change the appearance of an object such as its color or fill pattern by changing the information in the Appearance window Figure 6 28 Geometry Window Figure 6 29 Geometry window for a polygon CHAPTER 7 6 6 Using Windows to Change Object Properties 221 To display the Appearance window for one or more objects select the objects and then choose Appearance from the Window menu All utility windows show data for the current selection Changing the data in the windows changes the data for the currently selected object or objects The Geometry window Figure 6 29 contains information mostly relevant to bodies You can modify dimensions of bodies using the Geometry window For polygons and curved slots the Geometry window displays a versatile table for editing vertices and control points Body 2 Pol v r Display in O Shape coordinates World coordinates r Table x Simulation Interfaces In this chapter you will find instructions to e Attach pictures to objects e Change font sizes styles and colors 222 Chapter 7 Simulation Interfaces e Create input controls e Create menu buttons e Display data for analysis 7 1 Meters Meters allow you to extract numerical and graphical data from your simulation Not only can you measure almost any
108. Cell Radius WMCel1 VX VY VR WMCell VertexCount Integer Width WMCel1 WMConstraint Kind String ActiveWhen WMCel1 AddVertex n x y AppendPoint x y CurrentLength Double DamperK WMCel11 DeleteVertex n Elasticity WMCel1 K WMCe11 Kind WMCe11 Length WMCel1 WMPoint Body WMBody Constraint WMConstraint PX PY PR WMCel1l WMinput Format String Min Max Double Value Double WMOutput Format String Column n WMOutputColumn WMOutputColumn Label String Cell WMCe11 WMObject X Integer Y Integer Width Integer Height Integer ID Integer Kind String Name String WMCell Formula String Value Double M DYNAMIC O Design Simulation V Technologies Interactive Physics Students and educators in high schools and colleges around the world use Interactive Physics to investigate and experiment with concepts in physics Working Model 2D University students educators and professional engineers use Working Model 2D to understand how mechanical systems work and perform without building physical models gSStIGNER Dynamic Designer z Professional Engineers use i Dynamic Designer Motion to 2 build virtual prototypes of their Ve mechanical designs in order to j validate performance and function from within their CAD system
109. FOR for the slot remains fixed when the slot is reshaped either graphically or by editing one of the control points in the Geometry window so that the coordinates of other control points remain unchanged As a slot is moved or dragged the FOR is moved along In this way the control points shown as offsets from the FOR remain unchanged as a slot is moved Reshaping a Curved Slot Numerically You can accurately modify the shape of curved slots by specifying coordinates for each control point To enter the coordinate values use the Geometry window If you want to reshape a curved slot graphically please see Reshaping a Curved Slot on page 158 for mouse driven reshaping 168 Chapter 4 Constraints Using the Geometry Window The Geometry window can be used to add or delete control points you can even copy a coordinates table to and from the Clipboard for exchange of precise geometric data with other applications You can use the Geometry window to modify the positions of individual control points You can also add and delete control points Also please see Copying a Curved Slot to and from Other Applications on page 170 for instructions to export or import geometry table to and from other applications To reshape a curved slot 1 Click the slot to select it 2 Choose Geometry from the Window menu The Geometry window appears as in Figure 4 77 3 Enter new values for the control point locations The slot will chan
110. Jp 2 AA az I PON Bulysom www workingmodel com Information in this document is subject to change without notice and does not represent a license contract agreement or commitment to the purchaser licensor reseller distributor or any other party The software described in this document is furnished under a license agreement or non disclosure agreement The software may be used or copied only in accordance with the terms of the agreement It is against the law to copy the software on any medium except as specifically allowed in the license or non disclosure agreement No part of this manual may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying and recording for any purpose without express written permission of Design Simulation Technologies Inc Copyright Design Simulation Technologies Inc 2006 2010 All rights reserved Portions 2000 2005 MSC Software Corporation Portions 1992 1995 Summit Software Company Interactive Physics Interactive Physics II Interactive Physics Player Smart Editor Working Model Working Model Basic and WM Basic are trademarks of MSC Software Corporation Apple Macintosh Mac Apple Guide and QuickTime are registered trademarks of Apple Computer Incorporated Microsoft Windows and WinHelp are registered trademarks of Microsoft Corporation MATLAB is a registered trademark of the MathWorks Incorporated AutoCAD is a registered t
111. O Extrude i 000 Extrude Figure 9 14 Import dialog 9 14 Importing Lincages Files MacOS only 317 Click an x in the box next to Extrude to create three dimensional objects in the obj files You can also choose the extrusion depth To maintain a balanced geometry propotions among the objects try to choose an extrusion depth that is comparable to the width of the smallest object 9 14 Importing Lincages Files MacOS only Working Model 2D directly imports files from the motion synthesis package Lincages Working Model 2D directly imports files from the Lincages motion synthesis application Each link is translated to be a polygon The driving joint is translated as a motor All other joints are translated to be pin joints To import Lincages geometries into Working Model 2D 1 Create a new Working Model 2D simulation 2 Choose Import from the File menu The Import dialog box appears see Figure 9 14 S DEMONSTRATIONS vj WM_MPW Desktop DHF eater aisawaaiie Show eater aisawaaiie TEXT documents 3 Choose Lincages as the type of file you wish to import 4 Select the file you wish to import 5 Click Import The imported objects are placed directly on the workspace 318 Overview Overview Chapter 9 Importing and Exporting Files and Data 9 15 Controlling Working Model 2D from Another Application Working Model 2D can function as a DDE server Windows or as
112. ONSs and POLYLINEs composed of 3 or more vertices are imported as closed two dimensional straight edged polygons POLYLINEs composed of only 2 vertices are ignored e Open POLYLINEs in the DXF file are translated into closed polygon bodies e POLYLINEs splined or curve fit are translated into straight edged polygons Ifyou wish to import polygons with curved circumferences we recommend that you approximate the curved portion with a many faceted straight edged POLYLINE in the CAD program before exporting it to the DXF file ARCs are imported as sets of continuous line segments to approximate the curve Once ARCs are imported as lines the user needs to convert them to either polygons or to curved slots See Converting Lines into Physical Objects on page 296 for more information SPLINEs are saved in DXF format with the original vertices control points and spline fit vertices In essence splines are recorded as a fine grain POLYLINE or a polygon of many vertices Your CAD programs may let you decide how many fit points will be computed per spline AutoCAD for example allows you to control this number with the SPLINESEGS command Working Model 2D will import all these vertices and convert the overall object into a polygon e 3D POLYLINEs are read in but Working Model 2D ignores the third coordinate of each vertex As a result Working Model 2D effectively imports a 2D projection of your 3D model If you wish to import
113. Page No First Page Last Page Paper Source Paper Cassette Manual Feed Print Black amp White Color Grayscale Destination Printer PostScript File Click OK Windows Printing After you have positioned your simulation within the window at the desired Zoom and location you are ready to print To print the simulation 1 2 3 Create or open a simulation Choose Print from the File menu The Print dialog for your printer appears It will indicate the default printer settings and allow you to select a different printer which pages to print the number of copies to print whether to direct the output to a file instead of the printer and whether to collate copies Print 21x m Printer Name Sales Printer o Properties Status Ready Type HP Laserdet 4 4M Plus PS Where serverl sales Comment Sales Printer T Print to file gt Print range Copies All Number of copies fi Pages fon Cf to Selection UBB T Collate Cancel Select any other Print options by clicking the Properties button 276 Chapter 8 Running Simulations Figure 8 22 Windows Print Properties dialog In the Properties dialog you can select options pertaining to paper handling graphic printing PostScript printing if available and other printer specific options by clicking on the appropriate folder tab at the top HP Laserjet 4 4M PostScript Properties 21x Paper
114. Slot Friction script allows you to model friction in your slot joints Before running the script create and select a slot joint Run the script to create the applied forces that are programmed to model friction in the slot An input control is created for you to assign the friction coefficient D 11 The Slot Damping Script The Slot Damping script allows you to model damping in your slot joints Before running the script create and select a slot joint Run the script to create the applied forces that are programmed to model damping in the slot An input control is created for you to assign the damping coefficient The units for the damping coefficient are consistent with those currently assigned to your simulation For example if you currently have selected force to be represented in lbf and velocity in feet second then the damping coefficient has units of lbf second foot Working Model Basic Example To determine the name of the body associated with the first point of a constraint named Shock Spring QUICK REFERENCE SHEET MsgBox WM ActiveDocument Constraint Shock Spring Point 1 Body Name This chart shows selected relations between WM Basic objects For complete information refer to the manual WMBasic pdf on CD Methods such as Body n Point n return individual WMApplication Documents Collection of Constant WM WMDocument objects ActiveDocument WMDocument
115. Three or more points Pin Create and or select the point s where you would like to add a constraint Run the script and specify the desired constraint D 5 The Document Model Script This script enables you to completely document a model Running this script produces a text file that lists information e g units properties bodies constraints integration settings etc that describes the model D 6 The Zoom to Extent Script Zoom to Extent adjusts the zoom so you can view your entire model in the simulation window Simply select this script from the menu to run it D 7 The Measure Between Points Script Running this script creates a meter that measures the distance between the two selected points The distance is displayed once you run or re run your model D 8 The Flip Polygon Script Flip Polygon allows you to flip a polygon into a mirror image position Before running this script create and select a polygon Run the script then specify whether you want to flip the polygon horizontally or vertically D 9 The Pin Friction Script This script allows you to simulate friction on pin joints Before running the script create and select a pin joint Run the script to create two input controls one for the effective pin radius and the other for the coefficient of friction in the joint Adjust the values and run your model to simulate the friction D 10 The Slot Friction Script D 15 D 10 The Slot Friction Script The
116. To activate tracking 1 Setup or open a simulation 2 Choose Track from the World menu 3 Select how often you wish to track from the Track submenu Objects will be tracked the next time you run a simulation To control which individual components of each object are tracked 1 Select the object whose individual tracking behavior you want to define 2 Choose Appearance from the Window menu The Appearance window appears Figure 8 15 Tracking options in the Appearance window 8 9 Tracking 269 Ap Bodyl3Hircle v Color Pattern Circle 3 Show Show name m Track connect Frame amp Track outline Show charge amp oO Fill w go Track center of mass o Show center of mass m amp Show circle orientation 3 Click on the desired tracking options You can choose to track the outline and or the center of mass point You can also connect the center of mass point tracks with a line by selecting Track connect Tracking Only Selected Objects Since bodies have the Track Outline check box selected by default in the Appearance window activating Tracking will show tracks for all bodies If you want to track only one or more objects after activating Tracking select all constraints and bodies and deselect all tracking options shown in the Appearance window Then select just the bodies and constraints you want to track and check the tracking options you want to be enabled for those objects
117. Tools Use one of the Zoom tools to increase or decrease magnification of the objects in the world 2 E To use the Zoom tools 1 Select the Zoom tool with a positive sign to increase magnification Zoom In Select the tool with a negative sign to decrease magnification Zoom Out The pointer changes to a magnifying glass On MacOS systems the Zoom Out tool is hidden in the Zoom pop up palette by default Click and hold on the Zoom In tool to bring the Zoom Out tool in view and select it 6 2 Viewing Options 195 2 Click on the area you want to zoom in or out The objects on the screen become larger when you Zoom In and smaller when you Zoom Out The new window after changing the magnification will be arranged so that where you clicked the Zoom tool becomes the center of the screen see Figure 6 4 Figure 6 4 E Untitled 1 Zooming before Figure 6 5 and after But the zoom tool stays where it was on the screen 196 Chapter 6 The Workspace Using the View Size Dialog Figure 6 6 View Size dialog Each time you use the Zoom In tool the magnification increases by a factor of two 2x Each time you use the Zoom Out tool the magnification decreases by a factor of two 1 2x The workspace scale in the View Size dialog indicates the size of the workspace in relation to objects in rea
118. Typically the first argument of an if function is a relation such as x gt y or a logical operation such as and a b You can write nested if statements by recursively using other if functions as its own arguments For example shown below is a somewhat naive C code segment which returns the maximum of three numbers a b and c if a gt b if a gt c return a else return c else if b gt c return b else return c In the formula language of Working Model 2D the above segment can be translated into a single line as follows if a gt b if a gt c a c if b gt c b c Takes a number and returns the natural logarithm of the number Takes a number and returns the base 10 logarithm of the number Takes a vector and returns the magnitude of the vector Result is the same as v Takes two numbers and returns the larger of the two numbers Example min x y mod x y not x or x y pow x y pi rand B 6 Functions B 19 max body 1 a x body 2 a x returns the larger x acceleration of either body 1 or body 2 If you wish to find the maximum of three numbers a b andc you could recursively use the max functions as follows max max a b c Takes two numbers and returns the smaller of the two Example min body 1 v x body 2 v x returns the smaller x velocity of either body 1 or body 2 Asin the max function you could find the minimum
119. Vx field The center of mass will start at V 0 and accelerate to the right during the simulation To make the center of mass move with a constant velocity type 5 0 in a velocity field Putting the number in parentheses will force the velocity to be a formula NOTE Ifthe anchored body has a formula in any of its velocity fields Working Model 2D treats the anchor as a velocity constraint and the position fields even if they contain formulas will be applied only at the first frame 10 8 Defining Frames of Reference Working Model 2D can animate your simulation in a non standard frame of reference For example you might want the animation to track a moving object which would otherwise leave the screen at some point Figure 10 6 shows a simulation of a square tumbling down a wedge shaped platform The reference frame is the background By default Working Model 2D uses the background as the frame of reference 340 Chapter 10 Using Formulas Figure 10 6 A block tumbling down a wedge After selecting the square as the frame of reference that is view the simulation from the mass center of the square and the square s orientation the animation would appear as in Figure 10 7 Note that the anchored wedge appears to rotate during the simulation Figure 10 7 Simulation from the block s reference frame E Figure 10 8 again shows the same simulation But this time the simulation is vi
120. Your Simulation Run Faster on page 280 also provides useful tips on how to optimize the simulation speed Please recall that Working Model 2D saves a simulation history in memory as it calculates each frame If no part of the model is changed Working Model 2D does not need to spend time computing the simulation again Therefore if you are interested in demonstrating the simulation result to an audience you can run the simulation up to the desired number of frames simply save the simulation result with the history the option is available in the Save As dialog box re open the simulation later and simply play it back You can also save the animated simulation results in a run time animation format The MacOS version of Working Model 2D supports QuickTime export whereas the Windows version is capable of exporting Video for Windows files These data formats are optimized for rendering smooth Overview Analytical Method A 3 Numerical Methods A 5 animation and their playback rate can be considerably higher than that of Working Model 2D Furthermore the recipients of these files need not have a copy of Working Model 2D to view the animated results For more details please see Chapter 9 Importing and Exporting Files and Data A 3 Numerical Methods Working Model 2D solves problems using a variety of sophisticated numerical methods A problem is time discretized so that Working Model 2D computes motion and forces
121. a circular pin which allows the beam to rotate Figure D 17 shows that the difference between the two analyses is substantial Figure D 17 also highlights that in the dynamic analysis the peak bending moment occurs in the middle of the beam which is consistent with the notion that a falling smoke stack breaks into two pieces before hitting the ground D 3 The Optimize Script D 13 Figure D 17 Analysis of Static and Dynamic Sa ee hblad Beams Force in Newtons Moment in Newton Meters 15 44547 48 65324 Static Beam Shear Force Bending Moment x Force in Newtons Moment in Newton Meters Dynamic Beam D 3 The Optimize Script This script will adjust a user specified parameter to minimize a user specified cost When invoked choose the Optimization Demo option to see some example uses for this script The script needs e An input parameter to vary named PO A meter named COST that measures the cost function to minimize To inform Working Model of the length of your simulation run add a pause control If you need to stop the optimization at any time use Ctrl C D 4 The Create Constraint Script Create Constraint allows you to create constraints between points The type of constraint that you can create depends on the number of points selected Appendix D Scripts A One point Force Torque B Two Points Actuator Damper Pin Rod Rope Separator Spring Spring Damper C
122. acOS applications Any paint draw or graphics application will open or import PICT files Prior to QuickTime many applications stored animation sequences as a series ofindividual PICT files These PICT files are numbered sequentially with the suffix PICT 0001 PICT 0002 Ifyou wish to create a series of screen shots you can use the PICT animation export to automatically generate a number of PICT files To export PICT or PICT animation 1 2 Create or open a Working Model 2D simulation Choose Export from the File menu Figure 9 11 PICT export options Default Suffix Export Increment Starting File Number 9 11 Exporting PICT and PICT Animation MacOS only 313 The Export dialog box appears see Figure 9 1 for general information on the Export dialog 3 Set the export type to PICT 4 Set Export Options as necessary You can set the starting frame number of a PICT animation sequence in the Export Options 5 Click OK Export PICT MA Default suffix PICT Be Export every 1 ranes every 0 010 s Starting file number E Sequential PICT files will be stored with names such as Car PICT 0001 Car PICT 0002 Car PICT 0003 Leave the suffix as PICT if you are exporting sequential PICT files and your animation package requires naming of this type You can skip simulation frames when exporting sequential PICT files by choosing an export increment greater than 1 Change t
123. ack to Control Objects You can use the output data of the meter object as an input to control other objects Control objects can read an external data the section Types of Controls and Properties on page 235 provides specific instructions NOTE While the output data is recorded after each frame is computed using that data as an input will specify the controlled values at the beginning of each frame before it is computed 9 7 Exporting QuickTime Movies MacOS only QuickTime is the standard animation data format used on MacOS systems QuickTime files contain sequential images that can be played back as movies in many applications Complex Working Model 2D simulations will play back more quickly as QuickTime movies To export QuickTime movies 1 Create or open a simulation 2 Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog 3 Set the export type to QuickTime Movie 4 Set Export Options as necessary see below 5 Click Save Figure 9 7 QuickTime Movie export options Export Increment Playback Rate 9 7 Exporting QuickTime Movies MacOS only 305 Export QuickTime Movie Default suffix Export every mE frames every 0 010 s Playback rate cok frames per second QuickTime Export provides the following parameters You can skip simulation frames when exporting QuickTime movies by choosing an export incremen
124. aining their current position in the workspace You may find this command useful in importing DXF files See Chapter 9 Importing and Exporting Files and Data for details Detach from Body detaches a set of points and or slots from the body to which they are currently attached The detached points and slots are immediately attached to the background RITE Convert to Lines Convert Objects presents a submenu with the following options Convert to Polygon Convert to Curved Slot Convert to Lines converts selected polygons into line segments Convert to Polygon converts selected line segments into a polygon Convert to Curved Slot converts selected line segments into a curved slot The endpoints of the line segments are converted into the control points of the curve 54 Chapter 2 Guide to Tools amp Menus Vectors No Vectors Vector Display Vector Lengths New Menu Button New Control New Application Interface Measure Time Position Velocity Acceleration P U A Center of Mass Position Center of Mass Velocity Center of Mass Acceleration Momentum Angular Momentum Total Force Total Torque Gravity Force Electrostatic Force fiir Force Force Field Kinetic Energy Gravity Potential vrvrvy ee The Define Menu Vectors presents a submenu which allows you to display vectors for the properties of a selected object Any combination of the listed vectors can be selected and the
125. an Apple event server MacOS In short Working Model 2D acts as a server and another application such as Microsoft Excel sends requests to it as a client Working Model 2D is also capable of issuing OLE commands All requests and commands are written in Working Model Basic WM Basic a scripting language system embedded in Working Model 2D This document only provides a brief overview of the communication feature Please refer to the accompanying Working Model Basic User s Manual for complete information 9 16 Exchanging Data in Real Time with External Applications Working Model 2D can exchange data in real time with external applications using Apple Events on MacOS systems or Dynamic Data Exchange DDE on Windows systems In short Working Model 2D serves as a client to tap into the capabilities available in other application such as Excel which acts as a server Working Model 2D sends and receives data to and from another application once every animation time step Such links allow you to create a complex control system in another application and drive a Working Model 2D simulation with it You can also implement complex functions in other applications which may not be supported directly in Working Model 2D For example you can implement a look up table in Microsoft Excel for the horsepower curve of a motor An exercise in the accompanied Working Model 2D Tutorial uses this external link feature We encourage you to try th
126. and constraints in the following situations e When an object is dragged or rotated the Smart Editor dynamically updates the workspace A moving picture of your mechanism follows the pointer as you drag or rotate When the Join command is invoked the Smart Editor verifies that no constraint is being violated Because the Join command can cause bodies to move around in the workspace the Smart Editor moves objects as necessary to satisfy constraints e When a new coordinate position or geometry dimension such as the width of a rectangle or a length of a rod is entered into the Properties window As in the case of Join it is necessary to verify that the new position and geometry are consistent with existing constraints There is one major exception to the rules the select all drag exception e Ifevery constraint attached to a selected body is also selected then dragging the body will disable the Smart Editor For instance since the pin joint at the left of the rectangle is not selected dragging the rectangle causes it to pivot around that joint as in Figure 5 23 188 Chapter 5 The Smart Editor Figure 5 23 Dragging a rectangle without selecting the joint attached to it Figure 5 24 Dragging a rectangle after selecting the joint attached to it If you now select the pin joint and drag again the rectangle will be dragged rather than rotated Using the Smart Editor with Ropes A rope ob
127. and then held down the Option MacOS or Control Windows key while moving the pointer over the object s to be rotated The body will rotate with this point fixed to the background 5 While holding down the Option MacOS or Control Windows key move the mouse pointer to one of the objects you wish to rotate 6 Click and hold down the mouse button and drag the objects as if you were rotating them The selected objects will rotate with the selected point remains fixed The motions of rotating bodies are subject to constraints attached to them See Chapter 5 The Smart Editor for more details Moving an Object to Front or Back Each object on the physical layer can be moved in front of or behind other objects on the physical layer To move one object in front of another Figure 6 26 Moving a rectangle to front of a circle Properties Window 6 6 Using Windows to Change Object Properties 219 1 Select an object 2 Choose Move To Front from the Object menu to move the selected object in front of all the other objects in that layer Figure 6 26 shows a selected rectangle before and after using Move To Front Before After 3 Choose Send To Back from the Object menu to move the selected object behind all other objects in that layer 6 6 Using Windows to Change Object Properties When you want to change an object s properties or parameters you can always start by selecting
128. anges The file is now ready to be opened by Working Model 2D The file now bears the Working Model 2D document icon Translation Issues Although files are fully compatible on both platforms there are some differences in the system environments that might affect the translation of files 9 1 Available Export Import Options 287 Colors In general the colors available on the two platforms will not have a one to one mapping so Working Model 2D will do its best to find the closest color available on the current platform This might result in different colors being used for a given simulation The user can obviously modify the colors at any time Sometimes transparency information is lost on pictures translated from PICT MacOS to metafiles Windows Fonts Fonts also do not always have a one to one mapping The default font is used for all fonts in a document that do not map to a font currently installed on the system CHAPTER 9 Importing and Exporting Files and Data This chapter contains information on how to Import and export DXF CAD geometries e Export meter data e Export movies and animations e Import Lincages files MacOS only e Establish real time links using Apple Events MacOS or DDE Windows 9 1 Available Export Import Options Export Working Model 2D can export data in various formats 288 Chapter 9 Importing and Exporting Files and Data DXF Meter Data Video for Windows QuickTime
129. are equal When you first create a rope it has no slack i e it is stretched taut between the two endpoints When you move an endpoint the rope remains taut and its length is automatically updated You can also set the length numerically in the Properties window or Coordinates bar for the rope If you specify the length as a numeric constant the rope will be modified to the specified length immediately If the specified length is longer than the current length the rope will become slack If the specified length is shorter than the current length the rope will immediately shorten and the Smart Editor see Chapter 5 The Smart Editor will automatically modify the rest of the model to accommodate the specification If you used a formula expression to specify the length the formula will be immediately evaluated as t 0 and the rope length will be modified accordingly Again the Smart Editor will automatically modify the rest of the model to accommodate the specification Rope constraints apply tension and absorb energy when they move from a slack configuration to their full length The coefficient of elasticity for a rope determines how much energy will be preserved during this transition The coefficient of elasticity determines the difference between the relative velocities of attached bodies before and after a rope reaches full length A coefficient of 1 0 results in a completely elastic rope i e attached bodies which are
130. are used in conjunction with the point elements to form slot joints For example you can attach a slot element to the back ground attach a point element to a body and join the two elements to form a slot joint The slot joint allows the body to slide and rotate along the joint see Figure 2 6 The body can slide or rotate along the slot joint Working Model 2D provides the slot element tools in several predefined orientations and geometries as shown below You can use the Properties window to modify the geometry of the slot elements after you create them The Horizontal Slot tool is used to create a slot element oriented horizontally The Vertical Slot tool is used to create a slot element oriented vertically The Curved Slot tool is used to create a open curved slot element from a series of smoothly interpolated splined control points Define each control point with a single click and double click the final point Pressing the spacebar will also complete a curved slot by marking the last defined point as the final control point The Closed Curved Slot tool is used to create a closed curved slot element from a series of splined control points Define each control point of the curve with a single click Double click to signal the final point or press the spacebar to close the slot On MacOS systems the Slot Element tools are accessed through the Slot pop up palette 44 Chapter 2 Guide to Tools
131. as shown in Figure 4 34 Background attachments Body attachment To create a pulley system 1 Select the Pulley tool in the Toolbar 2 Position the pointer in an empty area of the screen The pointer changes from an arrow to a crosshair indicating that you can start drawing 3 Click once to set the starting point 126 Figure 4 35 Coordinates bar for a pulley system P Chapter 4 Constraints 4 Click again to create the first joint of the pulley Each time you click you will create a new segment of the rope along with the tiny hole that acts as a joint 5 Double click on the last point or press any key to complete the pulley The Coordinates bar shows the coordinates for the first and last points created Figure 4 35 as well as the total length of the rope in the pulley system Both coordinate values are given in reference to the body to which each point is attached x _ 3 400 m y 1 300 m x _1 800 m y _2 400 m 1 _3 464 m J l First Point Last Point Length Pulley System Properties To change the properties of a pulley system 1 Select the pulley system and choose Properties from the Window menu Figure 4 36 Properties window with pulley system selected Length Constraint 1 Pulley Sys 7 Pulley System length 6 308 m current 6 308 m elasticity Jo c00 Active when MV Always This is the actual length of the pulley sys
132. asurement Units formats include SI Metric English Astronomical and CGS 52 Chapter 2 Guide to Tools amp Menus Join Split 3 Mowe To Front F Send To Back 6 v Collide Do Not Collide Font Size Style vvv Attach Picture Attach to Body B gt Convert Objects View Size causes the View Size dialog box to appear allowing you to set the simulation view and scale to any value Background Color allows you to select the color of the background in the Working Model 2D window New Reference Frame allows you to attach a reference frame to any selected body Simulations can be viewed from any previously created reference frame Delete Reference Frame presents a submenu that includes all reference frames except Home Selecting a submenu item will delete that frame of reference List of Reference Frames The name of each defined reference frame is appended to this menu you can select any reference frame by choosing its name or by using the keyboard shortcut NOTE The Home reference frame is predefined and will always be on the list of reference frames The Object Menu Join combines two selected elements points and slots to form a joint Split separates a joint or other constraint into its component elements Move To Front puts the selected object s in front of all other objects Send To Back puts the selected object s behind all other objects Collide will make the selected ob
133. ata 5 Specify which columns you would like to use as time and data reference Setting 0 as the time column indicates that Working Model 2D will read data row by row for every animation frame see Animation Step on page A 16 for details You must specify a positive number for the data column you cannot specify 0 as the data column 238 Chapter 7 Simulation Interfaces Figure 7 14 Table data and simulation time steps As shown in Figure 7 14 discrete data values provided from a column in the table file are interpolated into a continuous linear function from which Working Model 2D reads a data value at each time step data value time tl t2 values given in data column of file t1 simulation t2 time given in time column of file The numbers on the time column in the table file must be sorted in increasing order otherwise the simulation behavior may not be accurate If the input file has a time column you should not make the Animation step in the Accuracy dialog greater than the time step given in the input file in order to ensure smooth animation When you save your Working Model 2D simulation with or without recording the saved document includes the table data Therefore when you re open the simulation document at a later time Working Model 2D does not need to have access to the table file If you choose Start Here in the World menu Working Model 2D will use the same table data ass
134. atic is no longer filled To use the automatic time step click in the radio button next to Automatic The value for the step chosen by Working Model 2D appears in the dialog 3 Click OK Simulation Accuracy Working Model 2D provides you with complete control of the numerical algorithms used in creating simulations For convenience these choices have been condensed into two general accuracy modes Fast Objects may overlap Relatively constant calculation time per frame Inelastic collisions may rebound Minimal warnings given for high velocities and accelerations e Accurate Prevents objects from grossly overlapping Inelastic collisions are solved correctly Friction is solved exactly You can also create custom accuracy modes by choosing other combinations of parameters For more about controlling simulation parameters see Appendix A Technical Information To select a accuracy mode 1 Reset the simulation Inaccurate Integration Initial Body Overlap 8 13 A Quick Look at the Inner Workings 279 2 Choose Accuracy from the World menu The Simulation Accuracy dialog appears Figure 8 23 3 Click the desired accuracy mode Warnings and Countermeasures Working Model 2D pauses a simulation and provides warnings when a given model undergoes configurations that may prove physically infeasible or lead to unstable simulations You can override these warnings at run time or turn them off from the beginning in t
135. ation For example the commands can initialize data before you start a simulation Commands typed in the Execute box will be executed at every frame of the Working Model 2D simulation As an example you can use Excel to implement a feedback system which changes the magnitude of the torque of a motor based on its rotational speed 1 Create an Excel spreadsheet and write a function that describes the feedback control 2 Make sure a motor in your model has a meter for the rotational speed and a control for the torque The meter and control serve as the input and the output for the control system respectively 3 In Working Model 2D create an External Application Interface by choosing New Application Interface in the Define menu Choose the Excel document See Setting up an Application Interface on page 320 for an explanation of how to define the interface 4 Select the motor s control from the lists of inputs shown in the Properties window of the interface 5 Type the appropriate Excel cell in the Variable fields of the input Make sure the cell contains the desired control function in Excel 9 16 Exchanging Data in Real Time with External Applications 325 6 Select the motor s meter from the lists of outputs shown in the Properties window Type the appropriate cell in the variable field Make sure that the cell is used as the input in the Excel function 7 Run your simulation At every frame velocity
136. attach a spring endpoint to the second vertex of a polygon suppose it is body 3 by specifying the endpoint coordinate as X body 3 vertex 2 x y body 3 vertex 2 y This way the endpoint will always remain on the second vertex even when the size and the shape of the polygon is modified Please refer to Using Geometry based Formulas Point based Parametrics on page 104 for instructions Also Body Fields on page B 6 provides references for syntax Customizing Motors and Actuators To make a sinusoidal driver draw an actuator and select the type of actuator as length A default value for the length appears for example 2 00 An actuator with a constant length acts as a rod 334 Chapter 10 Using Formulas Figure 10 4 Force Field dialog An actuator can be turned into a sinusoidal driver by replacing the constant value of 2 00 with a formula Entering the formula Sin time 2 0 in place of 2 00 will create a sinusoidal driver that changes in length from 1 00 to 3 00 meters every 2 4 seconds Also see Actuator Properties on page 145 for detailed discussion on length actuators 10 4 Defining Force Fields The force field feature of Working Model 2D allows you to model many types of force fields that affect individual objects as well as pairs of objects Formulas entered in the Force Field dialog are applied as forces and torques to all objects To apply a force of 5 N in th
137. aul Mitiguy and Arun Banerjee D 4 Figure D 5 A Pinned Roller Beam Figure D 6 Before Running Flexbeam Appendix D Scripts For all springs other than those which model cantilever supports the value of k is given by where L is the length of the smaller rectangular element Beam Constraints The constraints one can impose on a beam are termed fixed pinned roller and free The fixed constraint confines a point on the beam to no translational movement in any direction and it restricts the beam from rotating about that point The pinned constraint imposes the same translational confinement but allows the body to rotate The roller constraint confines a point to translational movement in only one direction The roller can have either a fixed or a pinned attachment which would determine whether or not rotation of the beam about that point could occur The free constraint which really is no constraint at all allows a point to move in any direction and there are no restrictions to the rotation of the body about that point In the rest of this sec tion the construction of two of the more standard beam types is discussed The Pinned Roller Beam The left end of the pinned roller beam shown in Figure D 5 is pinned and the right end is attached to a pin roller To model the pinned roller beam use the circular pin for the pinned constraint and the slot joint to represent the end attached to the roller Pin Roller Beam
138. automatically IV Prevent editing except at initial conditions MV Change cursor to stop sign during Run I Loop when tape player is full IV Automatic point equations on Object Snap Save Current Settinas Cancel 4 Position the pointer on the center dot in the circle and drag away from it to specify the projectile s initial velocity see Figure 1 9 While dragging try to match the arrow shown in Figure 1 9 5 Release the mouse button at the desired initial velocity The arrow represents the initial velocity of the projectile s center of mass Figure 1 9 Specifying an initial velocity for the Yy nE Position the mouse pointer projectile s center of mass to the center of the circle and drag the vector 6 Drag the tip of the arrow to adjust the velocity vector Run i Stopil Reset 1 5 Measuring Properties from a Simulation 11 Running the Simulation You are now ready to run your simulation To run the simulation 1 Click Run in the Toolbar Watch your first simulation run Because normal earth gravity is on by default in a new document the circle moves with the trajectory of a typical projectile 2 Click the Stop button in the Toolbar to stop the simulation Alternatively you can click once on the background to stop the simulation 3 Click Reset in the Toolbar to reset the simulation to initial conditions 4 Go back to step 3 under Specifying Initial Velocity
139. ave moved either rectangle the choice was purely arbitrary Figure 5 3 Two unconstrained rectangles Figure 5 4 Joining two unconstrained rectangles Figure 5 5 and Figure 5 6 show what happens when you join two rectangles that are only free to rotate about a pin joint but cannot translate Figure 5 5 Two constrained rectangles o o Ee a Pin Joints Figure 5 6 Joining two constrained rectangles Rotation between Rigidly Joined Bodies 5 1 Joining Elements and Splitting Constraints 177 a Controlling the Movement of Objects To join objects while keeping one or more in place simply lock the objects you do not want to move using anchors When editing complex mechanisms with the mouse or when joining it is sometimes useful to lock down certain parts of the mechanism temporarily If no part of a mechanism is joined to the background dragging any component in the mechanism will move the whole mechanism and joining will move any object to achieve assembly You can use the Anchor tool to lock objects in place This will ensure that only the unanchored objects are moved by the mouse or by the Join tool Use the a key and the space bar to quickly select the anchor and arrow tools while editing After pressing the a key you can anchor a certain part of a mechanism then press the space bar to change to the Arrow tool and drag the mechanism When done
140. beam Unit Systems Flexbeam works with the SI and English unit systems only Flexbeam automatically selects the mass and distance units to be consistent with the current force unit If the user selects the force unit to be Newtons the script selects meters for the distance unit and kilograms for the mass unit If the user selects the force unit to be pounds the script selects inches for the distance unit and pounds mass for the mass unit If the user selects another unit for force dynes for example the user is notified that this system of units is unavailable and the program terminates Running Flexbeam To use Flexbeam 1 Select the rectangular body within your Working Model document which is to be modeled as a flexible beam 2 Choose Flexbeam from the Script menu 3 Enter the values for the structural stiffness of the beam E and the number of elements n with which to model the beam The structural stiffness can be chosen through either the highly stiff minimally stiff or custom option The highly stiff and minimally stiff options provide a specified deflection for a load based on the weight of the beam The highly stiff option speci fies roughly a 3 deflection while the minimally stiff option specifies roughly a 10 deflection D 1 The Flexbeam Script Figure D 3 Dialog Provided by Flexbeam Figure D 4 Centroid Axis Flexible Body Information x r Structural Stiffness Highly Stiff El
141. between 0 and 1 or else return 100 you should type if and 0 lt t t lt 1 50 100 Please refer to List of Functions on page B 16 for detailed discussions on each function Vector Operators The following operators will work on vectors Operator Input s Output negate vector vector plus vector vector vector minus vector vector vector multiply number vector vector magnitude vector number These operators require that their input types match those listed in the previous chart Vector operators are useful for simplifying formulas To display a meter showing the distance between two bodies you would enter the following formula body 3 p body 2 p c6 99 This formula contains two vector operators First the to subtract the two positions of the bodies operator was used B 14 Appendix B Formula Language Reference body 3 p body 2 p result is a vector The chart above indicates that the minus operator can be used on two vectors and that the result is a vector The result can then be used with the magnitude operator to produce a number The following table shows some of possibly common mistakes and corrections Incorrect Correct body 2 lal lbody 2 al lbody 2 l a lbody 2 al lbody 2 a x abs body 2 a x body 2 a x body 2 v Unify both operands to vectors or numbers negate Takes a vector quantity and returns the negative of the quantity The x
142. box appears see Figure 9 2 Import 21x Import from a72 z El c prez Es 9 Scripts mo Import type DxF dsf z Cancel Choose DXF as the type of file you wish to import Select the file you wish to import Click Open MacOS or Import Windows The imported objects are placed directly on the workspace The import process may take some time depending on the size of the DXF file You can observe the import process in a progress dialog Important Notes on Importing DXF Files DXF files created from complex CAD drawing can be extremely large especially since they are ASCII not binary files Importing large DXF files into Working Model 2D can take a long time you will see a progress dialog to help you judge how far along the process is Furthermore importing DXF files containing hundreds of objects will significantly decrease the speed of Working Model 2D since it will have to keep track of a very large number of objects 296 Chapter 9 Importing and Exporting Files and Data Lines to Polygon Conversion We strongly recommend that you only export the physical objects that you want to simulate from your CAD drawing Importing a CAD drawing with extraneous lines and objects into Working Model 2D will be slow and time consuming The best approach is to edit your drawing in the CAD program before you export it as a DXF file so that only the objects and constraint attachment points that will be relevant to your si
143. chniques The engine allows the construction of a complex system and can compute its dynamics under a variety of constraints and forces In addition to user imposed constraints such as springs pulleys or joints the engine has the capability to simulate world level interactions such as collisions gravity air resistance and electrostatics Every aspect of a simulation from the integration time step and technique to the coefficients of friction and restitution can be adjusted by the user Working Model has an embedded scripting system called Working Model Basic WM Basic is a programming language that closely resembles Microsoft Visual Basic and gives full access to Working Model s functions xviii Smart Editor For example you can write scripts to create modify and join bodies and constraints You can run iterative simulations overnight and export the data files for future review You can design custom dialog boxes to create a new simulation environment You can even run scripts provided by third party vendors and add them to Working Model s menu To run a script select the script s menu and then the desired script Information various useful scripts is found in Appendix D Please refer to the Working Model Basic User s Manual for instructions and language reference NOTE On MacOS systems the Script Editor requires a PowerPC processor Users running Working Model on 680x0 based computers will be able to run scr
144. city for more information 3 3 Body Appearance The Appearance window controls the appearance of an object Selection Pop up Menu Name Field Body 8 Rectan Rectangle w name Color Pattern Fit T Track center of mass J Show center of mass LJ I Track connect I Show charge Frome V Track outline _ Show circle orientation To display the Appearance window 1 Select the body whose appearance you wish to change 2 Choose Appearance from the Window menu The Appearance window for that object appears Figure 3 13 Alternately if the Appearance window is already visible you can simply select the object whose appearance you would like to modify from the selection pop up menu at the top of the utility window Figure 3 13 The menu will show the list of ID numbers and the names of all objects in the document You can change and assign meaningful names by typing into the name field located directly below the selection pop up to help searching through the list To change the color and fill pattern for an object s interior and outline click on the pop up menus next to Fill and Frame in the body Appearance window 76 Chapter 3 Bodies Fill Frame Track Center of Mass Track Connect Track Outline Figure 3 14 Example of Track Center of Mass Track Connect and Track Outline Show Show Name The center of a body can be transparent a solid color or a pattern
145. corresponding vectors will be drawn and dynamically updated during the course of a Working Model 2D simulation For example the menu shown at left displays the vectors available for a body No Vectors prevents any vectors from being drawn for a selected body Vector Display presents the Vector Display dialog in which you can change vector colors and styles Vector Lengths presents the Vector Lengths dialog in which you can globally change the length of velocity force and acceleration vectors New Menu Button presents the New Menu Button dialog in which you can create buttons that perform menu commands New Control presents a submenu of object properties that can be interactively controlled through graphical data entry tools The properties that appear in this menu depend on what kind of object is selected By default New Control creates a slider bar as a data entry tool Working Model 2D allows more versatile input tools such as text button and external file input See 7 2 Controls for details New Application Interface allows Working Model 2D to link its data output to other application programs Two examples of applications are MATLAB Windows only and Excel See 9 16 Exchanging Data in Real Time with External Applications for details The Measure Menu Time creates a meter that measures time during a simulation List of other properties The Measure menu lists the measurable properties for any
146. cument do not have a physical equivalent and consequently they have to be converted to appropriate Working Model 2D objects such as polygons or curved slots You can perform these conversions within Working Model 2D see Converting Lines into Physical Objects on page 296 Incorporating DXF Files into Working Model 2D Typically you incorporate a CAD drawing into Working Model 2D in the following order DXF Conversion Rules in Working Model 2D 9 4 Importing CAD Geometries as DXF files 293 1 From your CAD program save the drawing as a DXF file Please refer to Important Notes on Importing DXF Files on page 295 for preparation of your drawing 2 Import the file into Working Model 2D Please read on for instructions 3 If necessary convert selected lines to form polygons curved slots and other Working Model 2D objects See Converting Lines into Physical Objects on page 296 4 Attach individual points to appropriate bodies see Attaching Points and Slots to Bodies on page 297 Construct joints and other constraints as necessary 5 Assign desired properties such as body to objects Verify collision specifications between bodies See 3 6 Controlling Collisions among Bodies 6 Run your simulation Note that a DXF file contains a drawing whereas objects treated in Working Model 2D are components of a physical model Therefore Working Model 2D enforces a set of conversion rules when importi
147. currently active document under anew name Print causes the Print dialog to appear allowing you to print your simulations Page Setup MacOS only presents a dialog that specifies printing options such as paper size and orientation The specific options available depend on the printer currently selected Show Page Breaks MacOS only if active places page break marker lines on the workspace to assist you in designing the layout when you want a hard copy of a simulation A checkmark appears before the menu item when it is active Import presents a dialog for importing external files into the workspace See Chapter 9 Importing and Exporting Files and Data for the types of files that may be imported 48 Chapter 2 Guide to Tools amp Menus I Undo Drag Cut 3H Copy C Paste EaU Clear Select All A Duplicate 3D Reshape Y Player Mode Gravity Air Resistance Electrostatics Force Field Run ER Reset T Start Here 38H Skip Frames gt Tracking gt AutoErase Track Erase Track E Retain Meter Values Erase Meter Values Accuracy Pause Control Preferences Export presents a dialog for exporting Working Model 2D data See Chapter 9 Importing and Exporting Files and Data for the formats in which data may be exported Exit Windows or Quit MacOS exits Working Model 2D List of Recently Opened Documents Up to four files that were most recent
148. d The above examples reveal that the objects in the model are associated as shown in the diagram Figure 4 4 4 3 General Properties of Constraints 95 Figure 4 4 Associations among objects in Figure 4 2 Object Names in the Selection Pop up Selecting Multiple Objects Figure 4 5 Properties window with more than one spring selected Not shown in Properties window All constraints have a default name when first created but you can assign arbitrary names to each of them or to any Working Model 2D object The custom names appear in the Selection pop up helping you find the desired object s quickly To assign custom names to constraints please see Assigning Names to Constraints on page 96 If you selected multiple objects the Selection pop up in the Properties window shows mixed selection as the item name To find out which objects are selected simply click the pop up selection Figure 4 5 The selected bodies will be listed with a minus sign on the left Properties ix mixed selection Sprin Force fk M x K 50 000 N m Properties E3 mixed selection x Selection Pop up length m current m Selected Constraints Springs r Active when M Always E 96 Chapter 4 Constraints The Properties window only shows properties that are the same across all selected constraints For example Figure 4 5 shows that the spring constant is 50 but
149. d to the selected body at the pivot point If the pivot point is connected to the background then the rotation is relative to the background 186 Chapter 5 The Smart Editor Figure 5 20 Rotating the horizontal rectangle 3 Try to rotate the vertical rectangle Bring the pointer close to the bottom pin joint A dotted line appears between the bottom pin joint and the pointer as in Figure 5 21 Figure 5 21 Preparing to rotate the vertical rectangle 4 Drag the vertical rectangle The entire assembly rotates about the bottom pin joint as shown in Figure 5 22 Figure 5 22 Rotating the vertical rectangle Fixing a Base Point Select All Drag 5 3 Understanding the Smart Editor 187 The Smart Editor takes care of all constraints while these rotations are occurring It makes sure that the new configuration is consistent with existing constraints It is possible to fix a base point for a rotation rather than using the nearest pivot If you move near to a pivot point then hold down the Option MacOS or Control Windows key while moving the mouse the editor will not keep proposing new pivot points but will instead use the one you selected the one nearest the pointer when you pressed Option or Control See Rotating Objects on page 216 for instructions When is the Smart Editor Used The Smart Editor is automatically used to resolve conflicts between user commands
150. d will rotate around the object Figure 8 12 and Figure 8 13 show the same collision from two reference frames the Home can be chosen in the Workspace menu reference frame and the reference frame of the darker circle Friction was turned off during this simulation so that the collision is elastic and the reference frames do not rotate 266 Chapter 8 Running Simulations Figure 8 12 Reference frames a collision eee N O 2 Figure 8 13 The same collision from the reference frame of the dark circle 8500 3 EN To create a new reference frame 1 Select an object body or point If you do not select an object you will create a new reference frame for the background 2 Choose New Reference Frame from the View menu The New Reference Frame dialog appears as in Figure 8 14 Figure 8 14 New Reference Frame dialog 8 8 Reference Frame 267 New Reference Frame x Name Circle VV Show eye Cmos I Show X Y axes 3 Type a name for the new reference frame You can also choose to display a reference frame eye x and y axes or both The eye and axes appear at the center of the origin of the reference frame 4 Click OK The new reference frame becomes the current reference frame and is appended to the bottom of the View menu To choose between various reference frames pick the desired reference frame from the bottom of the View menu You can create reference frames by using the Working Model 2D
151. data will be sent to the spreadsheet whose macro will calculate the desired torque The torque is returned to the Working Model 2D simulation as a motor input through the control 326 Chapter 10 Using Formulas CHAPTER 10 Using Formulas This chapter describes how to use formulas to customize e Input controls e Meters Bodies e Global forces e Frames of reference Working Model 2D allows you to enter formulas in most places where you would typically enter a number Formulas enable you to build custom forces and constraints and to dynamically control the behavior of objects Formulas also serve as the underlying mechanism that links input controls to the simulation Formulas control the data displayed by meters and output devices For a complete listing of the Working Model 2D formula language consult Appendix B Formula Language Reference 10 1 Units in Formulas Working Model 2D automatically keeps track of the unit system associated with formulas according to the following two ground rules Rule 1 All formulas and constants are associated with units consistent with the current settings in the Numbers and Units dialog Rule 2 If you change the settings in the dialog Working Model 2D automatically multiplies all constants and formulas by the proper unit conversion factors in order to ensure that the simulation behaves the same way before and after the change Constants Formulas Effects on Meters
152. dependent of the constraints connected to it apply the Split command to each of the constraints For more information about moving objects see Chapter 5 The Smart Editor Rotating Objects The Rotate tool allows you to rotate selected objects while keeping a point of the object fixed to the background The point chosen to be rotated about may be any point in the workspace e g a pin joint or a center of mass The Rotate tool can be used to select objects for rotation as well as for the actual rotation operation After you select the object s you wish to rotate a line will snap from the pointer to the closest point on the workspace This is the point which will be fixed to the background during the rotation To rotate an object 1 Select the Rotate tool 2 Click the object you wish to rotate The object becomes selected A line jumps from the pointer to the center of the selected object indicating that the object will rotate about this point The body will rotate with this point fixed to the background Rotating Multiple Objects Fixing a Base Point for a Rotation 6 5 Modifying Objects 217 3 Drag the object to rotate it You can also rotate a body by changing the rotation angle in the Properties window for the selected body As in the case of moving objects rotating an object that is connected to other objects by constraints may cause these other objects to move as well For more
153. ding on the magnitude of the solution you are interested in The following section provides more information on how to control simulation parameters A 6 Simulation Accuracy Dialog and Simulation Parameters There are two ways of using the Simulation Accuracy dialog can be opened by choosing Accuracy in the World menu For most purposes you can simply choose Fast or Accurate modes of simulation and let Working Model 2D automatically choose a time step and other simulation parameters for your problem For those interested in intimately controlling the simulation speed and accuracy more simulation variables are available when the More Choices button is clicked A 14 Appendix A Technical Information Figure A 3 Simulation Accur acy dialog with Animation Step r Integrator Error More Choices selected C Fast Automatic Automatic OK r jp 050 20 000 is mere Fewer Choices Integrato _ r Integration Step f Euler approximate fast Fixed Inte tep 0050 KuttaMerson accurate Variable Steps per frame Automati Overlap Error P SmE 0 008 mM Wamings I Inaccurate integration c Assembly Error r Sulomdtie I Initial body overlap 8 400e 004 I Redundant constraints mere _ G Automatic Inconsistent constraints Significant Digits Fast Accurate These buttons default the simulation parameters as follows Warn inaccurate integration Wa
154. dle will become highlighted 3 Select Cut from the Edit menu or press the delete key The vertex will disappear 3 2 Body Properties 66 Chapter 3 Bodies Properties Window Figure 3 9 Properties window for a body Coordinates Bar Each object in the Working Model 2D workspace behaves according to its defined characteristics and properties The properties of an object can be changed in one of the two ways e changing values in the Properties window e changing values in the Coordinates bar The Properties window Figure 3 9 provides you with full access to the available properties of bodies Information regarding geometry and appearance can be accessed through the Geometry window see 3 4 Body Geometry and the Appearance window see 3 3 Body Appearance Rectangle F400 m y 0550 m apoo Ve poo m s vp foo m s yofooo0 s material Standard mass 3 420 kg stat fric Jo300 kin fric Jo300 elastic ps charge 1 000e 004 C density 1 000 kg m 2 Planar moment E kg m 2 Selection Pop up Menu To open the Properties window 1 Either 1 double click on a body to view its Properties window or 2 select the body and then choose Properties from the Window menu You can shift from one body to another by simply clicking on different bodies or choosing the object from the list in the selection pop up Menu shown in Figure 3 9 The Coordinates bar at the bottom of the document window shows
155. drag the frame indicator left or right Drag the Frame Indicator 0D E Em 0 Drag to arbitrary frame positions You can also click any portion of the gray region on the tape player controls to immediately move the frame indicator to that location 254 Chapter 8 Running Simulations Replaying the Simulation To continue the simulation beyond the current recording drag the frame indicator as far to the right as it will go and then click the play forward control Working Model 2D now continues the simulation If you click the play forward control during any frame in a recorded simulation Working Model 2D will display the recorded frames until it reaches the end of the recorded simulation then it will resume computing additional frames Speeding up Playback When you run a simulation for the first time Working Model 2D not only draws the animation on the screen but also calculates the motion whose results are to be displayed in the animation For most simulations this calculation does not noticeably slow down the animation since Working Model 2D quickly calculates the motion For complicated simulations particularly simulations with many objects touching each other at the same time the animation may be slow the first time you run the simulation You can speed up the animation by playing the simulation again or by using the Skip feature The Skip feature increases animation speed by removing animati
156. e amp Units Be Be ae C JO o Axes amp Connect points To change the colors of lines on a graph 1 Select the meter 2 Choose Appearance from the Window menu 3 Select the desired color for each parameter by clicking in the color pop up menu 230 Chapter 7 Simulation Interfaces Retain Meter Values Erase Meter Values Recording Meter Data to a File Comparing Results of Multiple Simulations You can compare the results of multiple simulations by activating Retain Meter Values in the World menu If Retain Meter Values is active Working Model 2D saves simulation histories in its memory for each run The meter objects retain their data allowing you to compare the graphical results of multiple simulations By default Retain Meter Values is inactive When Retain Meter Values is enabled histories are erased only when Erase Meter Values is selected from the World menu The Erase Meter Values command tells Working Model 2D to discard the meter data from all the past simulations except the very last one For example if you have a graph meter open and have recorded data from multiple simulation runs selecting Erase Meter Values will delete the plots from all the past simulations except the very last run The Erase Meter Values menu item is active only when you enable Retain Meter Values The meter information for all the stored simulations can also be exported to a file also see 9 6 Exporting Meter Data to a File T
157. e coefficient of friction of one or more bodies by entering a value directly into the Properties window Density Moment Material and Charge Initially all rigid bodies in Working Model 2D are considered to be one millimeter 1 mm thick no matter what unit system you are in For example if you drew a foot by 1 foot square object its default thickness would be 1 L Coulomb friction is modeled to be proportional to the normal force applied to the contact surface i e F uN 70 Chapter 3 Bodies Mass Moment of Inertia Charge mm or 3 28x10 ft If you chose the material to be steel which has a density of about 500 Ib ft the weight of the object would be shown as 500 times 3 28x10 gt or 1 639 Ib All objects are initially given a density of 1 0 g cm equal to the density of water Larger objects are initially heavier than smaller objects because they are both given the same density You can view the density of any body in the Properties window The only way to directly change a body s density is through choosing a material You indirectly change a body s density whenever you specify a new body By default bodies are assigned moments of inertia by assuming that they are planar and have a uniform mass distribution You can adjust the moment of inertia of bodies so that they behave as if their mass were distributed around their edge like a shell You can also specify the moment of inertia of circular b
158. e file A table file is an ASCII text file which contains multiple columns of numbers delimited by a tab By default Working Model 2D assumes that the first column of data holds time and the second holds the corresponding control values Using this feature you can combine experiment data with your simulations For example suppose you want to simulate the suspension system of an automobile You could take the contour data of a bumpy road and use that data as an input to the actuator length in Working Model 2D Working Model 2D can read a text file ASCII file which contains multiple columns of numbers Working Model 2D ignores all lines starting with an arbitrary non numeric character as comments If you are using a word processing program to edit a text file make sure that the file is saved as text of an ASCH file In order to read a table file 1 Double click on the control or select the control and then choose Properties from the Window menu 2 Select the table icon from the Properties window 3 Click on the Read Table button A pop up window prompts you to locate the text file you would like to use 4 Select the desired file and click OK At this point the table is read into Working Model 2D Even if you delete the table file Working Model 2D will still remember the data By the same token if you modify the table file Working Model 2D would not know of the change until you repeat Step 3 above which re reads the table d
159. e internal time step as necessary to produce robust simulation You will generally use large simulation time steps when you create real time simulations The internal time step must be decreased so that internal results are calculated more often For more information on time steps see Appendix A 9 8 Exporting Video for Windows Windows only Video for Windows is a standard animation data format used on Windows systems Working Model 2D simulations will play back more quickly as Video for Windows movies also known as AVI files To export Video for Windows movies 1 Create or open a simulation 2 Choose Export from the File menu The Export dialog appears see Figure 9 1 for general information on the Export dialog 3 Set the export type to Video for Windows 4 Set Export Options as necessary see below 5 Click Export Default suffix favi Export every E frames Cancel every sec More Choices Bitmap depth fa x Frame multiplier fr Playback rate fio Exported Image Default Suffix Export Every n Frames Bitmap Depth Frame Multiplier 9 8 Exporting Video for Windows Windows only 307 Working Model 2D exports the image of your document exactly as it appears on your application window Therefore if you have the Toolbars Coordinates bar and XY axes active they are so by default the exported file will have these images as well If you choose to export a Video for Windows file wit
160. e keyboard 8 3 Using the Tape Player Controls While playing a simulation Working Model 2D also records it using a feature called the tape player This allows you to play simulations backwards to skip frames of the simulation and to play simulations more quickly after all calculations have been completed The tape player controls provide a visual indication of the number of frames in the simulation To display the tape player controls if they are not already visible 1 Choose Workspace from the View menu The Workspace menu appears You can select options by choosing them from the menu Select the Tape Player Controls entry A check next to the entry will indicate the tape player option is selected Click OK The tape player controls and indicators appear along the bottom of the screen as shown in Figure 8 2 Frame Counter Run Forward 252 Chapter 8 Running Simulations Figure 8 3 Playing one frame at a time Stepping through Frames Working Model 2D allows you to view the recording of a simulation frame by frame Step Backward Step Foward You can step through a simulation in two ways e Click on the forward or backward step in the tape player control to move forward or backward one frame at a time e You can also press to step forward and to step backward To select the number of frames to skip with the step controls 1 Choose Skip Frames from the World menu
161. e or Delete key The Clipboard is unaffected by the Clear command Undoing Your Last Action Most operations in Working Model 2D can be undone for example if you have accidentally deleted an object or objects from the screen 1 Choose Undo from the Edit menu Usually the menu item names the action to be undone such as Undo Cut Moving an Object All objects can be moved To move objects 1 Select one or more objects To select multiple objects see Selecting Multiple Objects on page 212 2 Position the pointer on one of the objects in the selection If the object is a constraint do not position the pointer on an endpoint doing so changes the size of the object If the object is an input control make sure the pointer turns into the dragging cursor before dragging the object 3 Drag the selected object or objects to the desired position All selected objects move and remain selected after dragging You can select all of the objects in the simulation by choosing Select All from the Edit menu 216 Chapter 6 The Workspace Figure 6 24 Rotating an object You can move bodies and points more precisely by changing their horizontal and vertical locations in the Properties window Constraints joints pins slots connecting the objects in your simulation may mean that moving one object will force another to move or change the characteristics e g the length ofa spring ofa constraint To move an object in
162. e point element is attached to the background then the local coor dinates are identical to the global ones 98 Chapter 4 Constraints The set of values displayed in the Coordinates bar varies depending on the type of the constraint For example when a spring is selected the Coordinates bar shows the two endpoints Figure 4 7 and its rest length The x y pairs are shown in the coordinate system of the body to which each endpoint is attached Individual sections later in this chapter show which parameters can be edited in the Coordinates bar for each type of constraint Also Displaying the Coordinates Bar on page 201 provides useful tips on using the Coordinates bar Figure 4 7 Zoo r r r r Coordinates bar for a spring 2000 1 000 oop 1000 2000 300 4 40500 m y 0 000 m x2000 m yhoo m 14168 m P1 coordinates P2 coordinates Spring Length Editing in the Properties In the Properties window the position of a constraint endpoint is given in Window both local and global coordinates Figure 4 8 Figure 4 8 Properties window for a constraint endpoint 4 3 General Properties of Constraints 99 E Point 17 Point Point angle 0 000 Local Coordinates 0 600 m Always Editable y 0 100 m Connected to Body 16 r Global Coordinates angle 0000 Global Coordinates x Jo 200 m y 1 200 m The top set is given in local coordinates the values are given with respect
163. e positive x direction to all objects you would enter 5 in the Force Field dialog and select the Field radio button as shown in Figure 10 4 Force Field Ooff Pair Wise Sample Force custom _ v Field Fu 5 000 Fy 0 000 T 0 000 There are times when you want to access the properties of each individual body when applying a custom global force A good example of this is gravity at the Earth s surface A general description of the force generated by the Earth s gravitational field near the Earth s surface is given by F mg where g 9 81 m s 10 4 Defining Force Fields 335 This equation results from the more general equation describing the universal gravity Gmm 2 r Substituting the values of G 6 67x10 Nm kg gravitational constant m 598x10 kg mass of the Earth and r 6 38x10 m radius of the Earth into this equation reduces the problem to F 9 81m Defining Body Dependent Force Fields To model a gravitational field such as the Earth s you can enter the following equations for a custom global force FX 0 Fy 9 81 self mass Ts 0 This equation for F includes an identifier called self Self is used to calculate this force for each body in turn based on the body s mass You also need to select the Field radio button in the Force Field dialog The force will be applied as a field to each object individually Fand F are
164. e screen by selecting the meter and dragging it You can also position the meter using the Coordinates bar When a meter is selected the Coordinates bar displays the x y coordinates of the meter in pixel coordinates on the Working Model 2D document The origin 0 0 of the pixel coordinates are set at the top left corner of the document window Figure 7 4 The x axis extends to the right whereas the y axis extends downward note that the y axis of pixel coordinates runs opposite from the physical coordinates employed in Working Model 2D simulations The position of the meter is given in terms of its top left corner You can directly modify the x y values in the Coordinates bar Figure 7 4 Pixel coordinates for meters Modifying Meter Size Figure 7 5 Picking properties to be graphed 7 1 Meters 227 Untitled 1 Fie E units in pixels 0 0 200 150 Coordinates bar shows x y pixel coordinates x 200 000 y 150 000 _ ip You can modify the meter size by selecting the meter and dragging one of the selection handles small black squares shown at the corners Showing and Hiding Properties Selectively To show or hide properties you wish to display on a meter selectively 1 Select the meter 2 Click in the labeled buttons on the side of the meter to show or hide the property on the meter When the button is greyed the property will be hidden not displayed from the met
165. e simulation 7 1 4 Setting Up a Simple Simulation 5 To stop the simulation click the mouse button in the window background or click Stop in the Toolbar On MacOS systems the Run button turns into the Stop button while running a simulation Once you have finished watching a simulation you should close it to free more memory for other simulations Click here to stop TE ac Run Stop n Reset Windows Choose Close from the File menu to close the simulation window A dialog will appear asking if you want to save the changes before closing Click No in the dialog box To watch other demonstration simulations repeat steps 1 through 7 above To finish your session with Working Model 2D choose Quit MacOS or Exit Windows from the File menu 1 4 Setting Up a Simple Simulation In this exercise you will use tools from the Toolbar to create a simple simulation You will draw a circle representing a projectile and give it an initial velocity then you will watch the projectile move as you run the simulation 6 Chapter 1 A Guided Tour Opening a New Document If any simulation documents are currently open close them before opening a new document 1 Choose New from the File menu A new untitled document window appears Next you will create a circle to represent a body Creating a Circle The Toolbar provides a variety of tools for setting up simulations To choose a tool click on its ico
166. ear and Pulley tools are accessed through the Pulley pop up palette The Torque tool applies a torque on a body The Force tool applies a force on a body The point of application can be positioned anywhere on the body The direction of the force can be fixed with respect to the background or to the body On MacOS systems the Torque and Force tools are accessed through the Force pop up palette The Motor tool creates a pin joint that exerts a twisting force between two bodies A motor can be placed on top of a single body in which case it will connect the body and the background A motor that is placed on two overlapping bodies will be connected to both bodies The Actuator tool creates an object that exerts a force between its endpoints For example an actuator simulates a piston used in a hydraulic lift Actuators can be attached to two bodies or to one body and the background The endpoints of the actuator are the attachment points The Rope Separator pop up palette has two tools The Rope tool prevents objects from separating by more than a specific distance Ropes will go slack and have no effect when the objects they are connected to move close together Ropes can be attached between one body and the background or between two bodies the endpoints of the rope are its attachment points The Separator tool prevents objects from moving closer than a specific distance together Separators will have no effect when the objects th
167. eaved with simulation cycles of Working Model 2D in the following fashion Initialize remote commands loop while simulation continues send output to external application Execute remote commands get input data from external application run simulation step end loop 320 Chapter 9 Importing and Exporting Files and Data Data Exchange through Apple Events or DDE Working Model 2D communicates with an external application through Apple events MacOS or through DDE Windows To set up Working Model 2D for data exchange with an external application Setting up an Application 1 Interface 2 3 4 Figure 9 15 Properties window for an interface object 5 6 Create or open a Working Model 2D simulation Create meters and or controls for the properties you wish to exchange with the external application Select New Application Interface from the Define menu A blank interface icon appears in your document Double click on the interface icon The Properties window appears as shown in Figure 9 15 External DOCume W roperties wis fr External document 8 r x ho connection Comet ST 7 r Inputs Document Connect Outputs O Disconnect Variable X C Conect C Disconnect Initialize E Venable Execute C r Outputs Outputl4 l y2 Y Initialize f Connect Execute Disconnect Inus Variable RICZ Input 5 if Tint sode Connect Disconnect l Varable MacOS
168. ect and define a vector to show a contact forces incident to it see Displaying Vectors on page 242 The objects are overlapping if the force vector appears from the object at the first frame of the simulation 280 Chapter 8 Running Simulations Inconsistent Constraint Redundant Constraint Inconsistent Constraint warnings occur in Accurate mode if a set of constraints cannot exist in the real world Ifa motor is connected to a bar that is pinned to the background for example one of the constraints will not be enforced Working Model 2D will alert you if this happens Redundant Constraint warnings will occur in Accurate simulation mode if you join a rigid structure to the background with too many constraints Two dimensional rigid structures have three degrees of freedom x y and rotation If you use joints that constrain more than three degrees of freedom one of the constraints is redundant Structures such as bridges are typically illustrated with a pin joint connecting to the ground on one end and a slot joint on the other end The pin joint constrains two degrees of freedom while the slot joint constrains one degree of freedom If two pin joints were used there would be four constraints and one of the constraints would be redundant 8 14 Useful Simulation Tips Making Your Simulation Run Faster A small change in the model may require a lot less computational effort for Working Model 2D and may speed up your simulati
169. ed rigid joint will neither introduce extra forces in the simulation nor affect simulation speed the two rigidly connected bodies behave as one The optimization does not permit measurement of forces and torques on the locked joint they measure as 0 0 To obtain correct force and torque readings you can make the joint measurable Since the joined bodies will be treated individually the simulation will take slightly longer to compute Creating a Force or Torque meter for a rigid joint will automatically make it measurable non optimized To define the properties of a pin joint or rigid joint 1 Select the joint and choose Properties from the Window menu 2 Edit the fields corresponding to the coordinates of the point you want to move Figure 4 63 Properties windows for a pin joint and a rigid joint Precisely Positioning Pin Joints Figure 4 64 Pin joint positioning and point offset 4 18 Joints 153 E Constraint 11 Pin Joint E Constraint 14 Rigid Joir Pin Joint Rigid Joint Point Point Point 9 Point 12 a 1 000 m a 20 m yor m y 0 300 m C Measurable Optimized r Point r Point Point 10 Point 13 xjoz3 m on m y 0 600 m y 0 185 m Active when Active when M Always M Always p _ Pin Joint Rigid Joint The Properties window shows the coordinates of the two points composing the pin joint The coordinates are shown relative to the frame of reference of the body to which the point
170. elected Click OK A script file and several 3DGF files one per object are created and placed in the same folder Figure 9 12 MacroMind Three D export options Export Circles as Polygons Extrude Export 3DGF as Text Files 9 13 Exporting to Wavefront Advanced Visualizer MacOS only 315 Export MacroMedia 3 D r 3D Script Wg Default suffix Export every ce frames every 0 010 s Export data from every object D selected objects only Export circles as polygons with ee sides OO extrude 1 000 m oO Export SDGF as text files Most 3 D animation packages support shapes composed of polygon meshes When exporting a circle Working Model 2D creates a polygon mesh You can select how many sides exported circles will have Click an x in the box next to Extrude to create three dimensional objects in the 3DGF files You can also choose the extrusion depth To maintain a balanced geometry proportions among the objects try to choose an extrusion depth that is comparable to the width of the smallest object Use this option if you wish to edit the 3DGF object geometry files by hand 9 13 Exporting to Wavefront Advanced Visualizer MacOS only Working Model 2D will create complete Wavefront motion mov and shape obj files with all relationships between objects and keyframes stored in a script set file You can open the script directly from Wavefront Working Model 2D creates a scrip
171. element of the pin joint This point is where the slot pin is located on the body HOH Properties Aeyed Slol Joint Slot Point 4 angle j x m Point Point 5 Keyed Slot Joint 4 19 Slot Joints 165 Measuring Reaction Forces at Slot Joints You can create a meter to measure the forces acting on a slot by choosing Force from the Measure menu while the slot element is selected The meter has three components you can observe them in the Properties window constraintforce n x constraintforce n y constraintforce n where the number n may differ depending on your constraint ID The slot force components are given in terms of the coordinate system whose x axis coincides with the slot for linear slots or the tangent thereto for curved slots Therefore the slot joint force meter will always have zero x component If you wish to observe the reaction forces at slots in terms of the global coordinate system find the point element attached to the body constrained by the slot Simply bring the mouse pointer over the point element and read the Status bar Suppose the point element is point 5 Then the vector point 5 force represents the reaction force acting on the body from the slot You can replace the meter fields in the properties window with expressions like point 5 force x point 5 force y point 5 force to obtain x y components and the magnitude ofthe reaction force Fo
172. en select the point and choose Properties from the Window menu In the Properties window enter an offset that will place the point directly on the mass object s edge C 4 Troubleshooting C 7 You can take advantage of the object snap feature as well as parametrics Please refer to Positioning Constraints Precisely on page 101 for details C 4 Troubleshooting This section contains a list of questions and answers compiled from our technical support database The Force on a Rigid Joint Measures 0 Make sure the joint is set to measurable mode toggle the radio button in the Properties window of the joint For more details see Joint Properties on page 152 All Points in My DXF File Come Out Attached to Background Working Model 2D is actually designed to behave this way since a DXF drawing tells nothing about what points belong to what objects You can attach individual points to mass objects by selecting the points objects and choosing Attach to Mass under the Object menu See Attaching Points and Slots to Bodies on page 297 for detailed instructions My DXF imported Drawing Looks Strange Working Model 2D applies a set of well defined conversion rules when it imports a DXF file because not all the design primitives available in DXF can be interpreted in Working Model 2D Please refer to Incorporating DXF Files into Working Model 2D on page 292 for detailed descriptions on steps involved in importing DXF fi
173. endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The distance between two endpoints of the rope can be changed without changing the length of the rope See Slack rope on page 113 The Coordinates bar shows the coordinates for the two endpoints of the rope and its length as shown in Figure 4 21 Both coordinate values are given in reference to the body to which each point is attached x _ 4 500 m y _2 200 m x _ 1 600 m y 0 100 m 1 _2 285 m a l l J First Point Second Point Length Rope Properties To view and modify the properties of a rope select the rope and select Properties from the Window menu Figure 4 22 shows the Properties window for a rope HOH Properties Constraint 8 v Rope Courrent 1 781 m elasticity Active when Always O 112 Chapter 4 Constraints Length Current Length Elasticity Rope constraints have two parameters that can be defined length and elasticity The two endpoints of a rope can never be further apart than the rope s length The length of a rope does not change when the rope goes slack The current length of the rope is the shortest distance between the two endpoints of the rope Therefore when the rope is taut the magnitudes of the length and current length
174. enter of mass Similarly body 3 cofm v x returns the x component of COM s velocity width height radius vertex n x vertex n y p v a offset B 4 Fields B 7 The next four fields width height radius vertex n are called geometry based formula and return the geometric information of bodies You can use these fields to position endpoints of constraints precisely see Using Geometry based Formulas Point based Parametrics on page 104 Returns the width of a rectangle or a square The width field is not valid for other body types For squares width is always identical to height Returns the height of a rectangle or a square The height field is not valid for other body types For squares height is always identical to width Returns the radius of a circle The radius field is not valid for other body types For a polygon vertex n x and vertex n y return the x and y coordinates of the n th vertex respectively The number n n 1 corresponds to the vertex ID number shown in the Geometry window for the polygon The coordinates are given in terms of the frame of reference of the polygon see Frame of Reference FOR on page 67 For a rectangle and square the vertex 1 corresponds to the top right corner when the body orientation is 0 and the subsequent indexing 2 through 4 returns the other vertices in a counter clockwise order The expression vertex n is not valid for a circ
175. enter of mass can be moved by modifying the x and y offset fields as shown in Figure 3 17 These values are given with respect to the frame of reference for the object see Frame of Reference FOR on page 67 for details In Auto mode as indicated by the radio button on Figure 3 17 the COM is automatically recomputed whenever the polygon is reshaped so that the COM coincides with the geometric center Using meters you can take kinematic measurements of a body such as position velocity and acceleration in terms of its COM or of FOR See 7 1 Meters for details Also available in the formula language are explicit references to COM and FOR For example body n cofm p refers to the COM whereas body n p refers to FOR See Appendix B Formula Language Reference for more details Radius is the choice available in the Geometry window when a circular body is selected Circular bodies may be accurately sized by setting their radii The Radius can also be edited in the Coordinates bar Please see Creating Circles on page 61 80 Chapter 3 Bodies Height and Width Polygon Vertices and Curved Body Control Points Converting Between Polygons and Curved Bodies Height and width are choices available in the Geometry window when a rectangle is selected These parameters can also be edited in the Coordinates bar Please see Creating Rectangles and Squares on page 59 The Geometry window gives y
176. ep See Integration Time Step on page A 17 282 Chapter 8 Running Simulations To Expand Application Memory Memory Space and Simulation History Controlling the Duration of a Simulation The Pause Control dialog can be used to stop a simulation automatically at any time Enter an equation incorporating the word time in one of the pause condition fields and then use the pop up menu to specify what should happen stop pause loop reset when the condition is met Sample conditions include time gt 1 0 or frame 30 When using an equal sign in a pause condition make sure that the condition will really occur If the time step is set to 0 97 seconds time will never exactly equal 1 0 s see Pausing on page 254 Running Simulations Unattended When you create a complex model you may need to run Working Model 2D for a long time to obtain the simulation results letting the simulation run overnight for example If you decide to run the simulation unattended you should make sure that Working Model 2D can continue its computations uninterrupted Specifically e the memory space allocated to the application should be sufficient to run the simulation and store its results see below and e warning dialog boxes should be disabled so that Working Model 2D can continue computations uninterrupted To disable model related warnings 1 Choose Accuracy in the World menu The Simulation Accu
177. ep size to the animation step size and starts all over again to compute the next frame This process effectively breaks one animation frame into multiple intermediate frames that will not be displayed on the screen in order to ensure accuracy As a result you may notice that some frames require more time to display than others since the animation time step remains constant throughout the simulation If accelerations drastically change their magnitude during a simulation the integrator may be unable to find a time step small enough to meet the accuracy criteria In such cases a warning will be given to indicate that integration errors may have become excessive see Warnings on page A 19 A 5 How Working Model 2D Bounds Errors As discussed in A 4 Time Step and Performance Working Model 2D adjusts the integration time step by estimating the integrity of the calculation results This section explains how Working Model 2D checks its own results against user defined error bounds A 10 Appendix A Technical Information In principle Working Model 2D makes an error estimate on the calculation results The method of estimating the error is discussed in Integrators on page A 15 Working Model 2D compares the magnitude of the estimate to the user defined error bounds Fundamentally the integration error bound is defined as the greater of the two criteria discussed below Relative Acceptable Error and Absolute Accep
178. er Otherwise the meter will show the property Position of Rectangle Click on these buttons to show or hide properties to be displayed 228 Chapter 7 Simulation Interfaces Figure 7 6 Properties window with a meter selected Changing Scale on a Graph Min and Max All graphs that you create in Working Model 2D default to an auto scaling mode for both the x and y axes This auto scale feature will suffice for most of your data output purposes When you initially display meters in the form of a graph Working Model 2D auto scales data to fit within the display area of the graph If you wish to display only a part of the data on the graph you can manually select the scale for a graph s x and y axis through the Properties window Click in the check boxes beneath Auto to stop auto scaling Enter values in the Min and Max fields to explicitly scale your graphs HOHE Properties Output 2 P fasition of Rectangle t Label Equation time Body 1 p x Body 1 p y Body 1 p r xEI __o o00 1 000 y1 B 1 000 1 000 y2QJ 1 000 1 000 y2 0 000 1 000 To change the scale of a meter that is displaying information as a graph 1 Select the meter 2 Choose Properties from the Window menu 3 Enter Min and Max values for the quantity you wish to scale When you create a meter the appropriate equations automatically appear in the Scale dialog For more information about entering for
179. er Data in Non SI Units on page A 25 Equations can be up to 255 characters in length When the conversion constants are added however an equation becomes longer and may exceed 255 characters although the original length you entered was within the bounds In this case the equation is displayed as originally entered and the original unit system is retained for the equation The units are displayed as three consecutive questions marks or which means the original unit system Editing the equation will change its units to the current unit system 10 2 Linking Controls to Objects Whenever you create a control in Working Model 2D a link is made between the control and the object it affects For example to make an object to control a spring constant 1 Select a spring 2 Choose Spring Constant from the New Control submenu in the Define menu A slider and text box will appear on the screen This control is directly tied to the spring and can be used to change the spring s constant To see the link between the control and the spring constant 1 Select the spring 2 Choose Properties from the Window menu The Properties window appears 330 Chapter 10 Using Formulas Figure 10 1 Properties window with a spring Sprin selected Pa ko H K inputs N m length fi 310 m current 1 910 m Constraint 3 Spring Active when M Always In the area that defines the spring s constant you will see the foll
180. er of the object when it was created Coordinates for polygon vertices and curved body control points are measured relative to the FOR When these bodies are later reshaped the geometric center will move but the FOR will not In this way modifying one vertex will not affect the coordinates of others See Coordinates for Polygons and Curved Bodies on page 81 The center of mass COM of a body can be specified arbitrarily See 3 4 Body Geometry for instructions For bodies meters can measure the position velocity and acceleration of COM and FOR Meters are further discussed in 7 1 Meters Initial Velocity You can use the Properties window to specify numerically the initial velocity of the center of mass COM of a body 68 Elasticity Chapter 3 Bodies You can also specify the translational initial velocity of the COM of a body using the mouse as follows 1 Choose Preferences in the World menu In the Preferences dialog check an item titled Allow velocity vector dragging 2 Click OK to close the Preferences window 3 Click the body for which you wish to specify the initial velocity 4 Drag the blue dot located at the center of mass to specify its initial translational velocity The magnitude of the velocity is directly proportional to the length of the velocity vector You can adjust the relationship between the length of the velocity vector and the magnitude of the velocity it represents
181. eserved The Clipboard is a holding area where you can place a selection for temporary storage Windows You can view the contents of the Clipboard by running the Clipboard Viewer which should be located in the Program Manager s Main group See your Windows documentation for more information on the Clipboard Cut removes the current selection from the simulation and places it on the Clipboard 1 Select one or more objects to cut 2 Choose Cut from the Edit menu Copy duplicates the current selection to the Clipboard without erasing it from your document 1 Select one or more objects to copy 2 Choose Copy from the Edit menu Paste places a copy of the Clipboard in your document 1 Use Cut or Copy to store a selection on the Clipboard 2 Activate the window belonging to the document where you wish to place the selection You may paste the selection in the same or another document 3 Choose Paste from the Edit menu When pasting objects with parameters that contain formulas Working Model 2D attempts to update the formulas if any objects have to be renumbered Objects need to be renumbered if an object with the same number as the pasted object already exists in the document Clear Delete 6 5 Modifying Objects 215 Clear removes the current selection from the document without storing it on the Clipboard 1 Select one or more objects to remove 2 Choose Clear from the Edit menu or simply press the Backspac
182. esizing hold down the Option key C 2 Appendix C Useful Tips and Shortcuts Using the Command key To maintain the current connections of constraints and mass objects when dragging hold down the Command key Windows Using the Shift key To select more than one item hold down the Shift key while clicking the items you want Clicking on an already selected object while holding down the Shift key deselects the object Using the Control key Holding down the Control key while dragging the endpoint of a constraint will maintain its current length Control drag will also maintain the current connections of constraints and mass objects C 2 Keyboard Shortcuts C 3 C 2 Keyboard Shortcuts MacOS Key Action Command Join Command Split Shift Command R Runs from the last computed frame F1 or Command Z Undo F2 or Command X Cut F3 or Command C Copy F4 or Command V Paste Space bar Selects the Arrow tool rR Selects the Rotation tool a A Selects the Anchor tool Z Selects the Zoom in tool Z Selects the Zoom out tool C 4 Windows Key Control F1 Control F2 Shift Control R Space bar rR a A Z Z Alt Enter Ctrl I Alt Backspace Delete Shift Delete Control Insert Shift Insert F1 F2 Alt F4 F5 F12 Shift F12 Control F12 Control Shift F12 Appendix C Useful Tips and Shortcuts Action Join Split Runs from the last computed frame Selects the Arrow tool Select the Rotation too
183. ete pin joint or rigid joint 1 Align the bodies that will be connected by the pin joint or rigid joint 2 Select the appropriate Joint tool from the Toolbar Click here to create a pin joint 3 Click the mouse to create the joint at the proper location The top two bodies will be joined The Coordinates bar shows the coordinates for the Base Point point element on the bottom layer and the Top Point point element on the top layer as shown in Figure 4 60 Both coordinate values are given in reference to the body to which each point is attached x _0 600 m y _0 050 m x _0 750 m y 0 700 m b i llill il l L Base Point Top Point You can precisely align the position of the pin joints by typing in coordinates See Joint Properties on page 152 for instructions You can build a pin joint by joining two points that are attached to separate bodies You can build a rigid joint by joining two square points that are attached to separate bodies To build a pin joint or a rigid joint from primitive elements 1 Create point elements at the desired location of the joint on each of two bodies Figure 4 61 Selecting two point elements to make a joint Join Figure 4 62 Creating a pin joint by joining two point elements Pin Joints Connecting More Than Two Bodies 4 18 Joints 151 Use square points if you wish to create a rigid joint Use regular points if you wish to create a pin joint
184. eters are initially set to default values For example the density of every body is initially set to 1 000 kg m Please see 3 2 Body Properties for more information Once a body is created you can attach constraints at precise locations on the body Please refer to Positioning Constraints Precisely on page 101 for details Creating Rectangles and Squares To create a rectangle or a square 1 Click the Rectangle or the Square tool on the Toolbar On MacOS systems the Square tool is hidden in the Rectangle Square pop up palette by default Click and hold on the Rectangle tool to bring the Square tool in view and select it 2 Position the pointer in an empty area of the background The pointer changes from an arrow to a crosshair indicating that you can start drawing 3 Hold down the mouse button and drag diagonally until the rectangle or square attains the desired dimensions 60 Chapter 3 Bodies Figure 3 3 Creating a rectangle Alternative Way to Create Rectangles or Squares Editing Position and Geometry Quickly Note that the Coordinates bar shows the current dimensions and position of the object see Figure 3 3 You can edit these values later If you chose the Square tool all four sides of the body always have equal lengths 4 Release the mouse button Click here X The Coordinates bar shows N the current position and dimension and drag to here a 0 300 m y 0 200 m hi1
185. ewed positionally from the point in the upper right hand corner of the square yet with the orientation of the background Figure 10 8 Simulation from the block s reference frame without rotation 10 8 Defining Frames of Reference 341 In order to define the frame of reference shown above Attach a point element to the body that is to be used as a reference frame In the example above the body would be the tumbling block Select the point and choose Properties from the Window menu The Properties window appears Enter the following formula in the angle field of the point n is the ID number corresponding to the tumbling block body n p r The formula specifies the orientation of the frame of reference to oppose that of the body Now the point will rotate to compensate the rotation of the body Select the point and choose New Reference Frame from the View menu Now the frame of reference is attached to the point You are ready to run the simulation 342 Chapter 10 Using Formulas 10 9 Using Meters as Variables in Formulas At times it might be useful to define a variable to be used in equations For example you may wish to use the expression body 3 p body 4 p which defines the distance between two bodies in many places To avoid repetitive typing you can define a meter and use it as a variable or intermediate placeholder To define a meter and use it as a variable
186. exactly which objects are colliding select two bodies at a time and verify the Object menu for each pair See Minimizing Collisions on page 283 for more information on optimizing simulation performance The section A 7 Simulating Collisions provides detailed information on how Working Model 2D simulates collisions 90 Chapter 4 Constraints CHAPTER 4 Constraints 4 1 What is a Constraint In Working Model 2D a constraint is an object that applies forces and torques to bodies based on certain specified conditions Some constraints such as joints explicitly constrain the movement of bodies by limiting the degrees of freedom in translation or rotation while other constraints such as springs apply forces or torques based on the configuration of the bodies e g relative velocity displacement or angular acceleration Unlike bodies constraints do not have mass or volume Accordingly constraints do not collide with themselves or with bodies A constraint applies forces and torques only at the locations of its endpoints which are attached to a body or to the background Each constraint is associated with a specific definition of how it applies forces and torques For example a linear spring applies forces at its endpoints proportionally to the distance in between i e F kx All constraints have one or two point elements embedded in them A constraint object can be considered as a set of point elements
187. exerts a force in the positive y direction on the element B and when element C exerts a force in the negative y direction on the element B e The bending moment is positive when element A exerts a moment in the positive z direction coming out of the page on element B and when element C exerts a moment in the negative z direction on element B Normal Stress Induced by Bending Moment This choice of sign convention determines that a beam with a positive bending moment has its top surface in tension and its bottom surface in compression The formula which relates the stress to the bending moment M is o Lavea where y is the distance from the beam s neutral axis and Zarea is the area moment of inertia of the beam cross section Tarea is defined and shown below L a y avaz Figure D 16 Falling Smoke Stack Appendix D Scripts Example the Falling Smoke Stack The falling smoke stack is a well known example where dynamic loads lead to a structural failure A falling smoke stack is known to break in two before it hits the ground because of high tensile stresses caused by a bending moment during the fall Figure D 16 shows a simple representation of the falling smoke stack in Working Model In Figure D 17 we show both the static and dynamic analyses of this event In the static beam analysis the beam is rigidly attached to the background In the dynamic analysis the connection is made with
188. ey are connected to move far apart Separators can be attached between one body and the background or between two bodies the endpoints of the separator are the attachment points On MacOS systems the Rope and Separator tools are accessed through the Rope pop up palette The Rod tool creates a massless inflexible link between two bodies Rods cannot be compressed or extended Rods can be attached between one body and the background or between two bodies The endpoints of the rod are its attachment points About Working Model 2D New Open 30 Close W Save S Save As Print 38P Page Setup Show Page Breaks Import Export Quit 2 2 Working Model 2D Menus 47 2 2 Working Model 2D Menus Working Model 2D provides a standard menu bar with pull down menus The Apple Menu MacOS only About Working Model 2D presents information about the Working Model 2D software including the version number copyright and licensee information The File Menu New creates a blank untitled document using the current default settings Open opens a previously created document You can have multiple documents open at once Close closes the currently active document If there are changes that need to be saved you will be so prompted Save saves the currently active document to disk If the active document was saved previously it is updated Save As lets you name and save a copy of the
189. fficult The following ad hoc rules can assist you in your selection of a time step Small time step improved accuracy Large time step improved computing speed You do not always have to choose an extremely small time step just because you are concerned about accuracy More often than not a reasonably small step size produces a simulation result with sufficient accuracy For example you might begin simulating a problem with a large time step so you can quickly obtain rough ideas about the model When you want precise details you can let Working Model 2D run a long simulation with a smaller time step to verify the accuracy of the model Fortunately Working Model 2D does a good job at shielding you from needing to pick precise time steps unless you decide to choose it yourself Working Model 2D has facilities for automatically choosing appropriate time steps and monitoring simulation errors of various types see Variable Time Step on page A 9 for more details For example an ideal time step should be variable during the course of a simulation adapting to the complexity of the problem in order to get the most out of the speed accuracy trade off discussed previously If you are simulating an automobile collision you could quickly approach the critical part of the experiment with a large time step while the car is nearing an obstacle and subsequently use a smaller time step during the collision Ifthe small time step was used for
190. fied 8 Click the Join button in the Toolbar The linkage will reassemble itself moving its component pieces around to make them overlap where necessary If the points that make up the pin joint are a long distance apart the Smart Editor will ask you to move the points closer together before making the join Precision Numerical Assembly The Smart Editor assembles mechanisms based on numerical values Whenever you enter the position of a body point or joint the Smart Editor makes sure that joints are not broken If necessary the smart editor will move other bodies to maintain the integrity of all joints in a mechanism You can use the Smart Editor to set the initial conditions of a simulation In this example you will use the Smart Editor to return the mechanism to its exact initial position 1 Click the rectangle A as indicated in Figure 1 27 Figure 1 27 Selecting a rectangle Figure 1 28 Coordinates bar for a body 1 8 The Smart Editor 25 Click the rectangle A to select it The Coordinates bar displays the set of parameters you can edit immediately 42300 m yl0 750 m hiO500 m w3400 m O 15000 ni E m ip gt X position y position height width rotation Enter the value 0 in the rotation field of the Coordinates bar Enter a Tab or Return The rectangle will be moved to a position where its rotation is 0 00 The other bodies in the mechanism w
191. following operators require one or two numbers The letters a and b are used as place holders for any number or formula that evaluates to a number Numeric Operators The following is a listing of numeric operators that are available for use in formula entry B 10 Appendix B Formula Language Reference Operator Input s Output negate a a plus a b a b minus a b a b multiply a b a xb divide a b a b mod a b a mod b power a b ab gt a gt b 30740 lt a lt b 1 or 0 gt a gt b 1 or 0 lt a lt b 1 or 0 equal a b 1 or 0 lt gt not equal a lt gt b 1 or 0 These operators require numbers as their inputs This means that you cannot add most formula elements that are not a number Incorrect body 3 point 3 cannot add a body to a point body 3 p 34 5 cannot subtract a number from a vector point 7 v body 3 cannot add a vector to a body body 3 p gt 44 0 cannot compare a vector to a number Correct body 3 p x point 3 p x body 3 p x 34 5 point 7 v y body 3 v y body 3 p y gt 44 0 negate plus minus multiply divide mod power gt greater than lt less than gt greater than or equal to lt less than or equal to equal B 5 Operators B 11 body 3 p y 44 0 body 3 p y 44 0 Takes a single number and returns the negative of the number Takes two nu
192. formula language For example you can create a reference frame that doesn t rotate with the body For more information on using formulas consult Chapter 10 Using Formulas and Appendix B Formula Language Reference Deleting Reference Frames Deleting reference frames is done directly from the View menu 1 Select Delete Reference Frame from the View menu This is a hierarchical menu The names of all reference frames appear to the right 2 Select the name of the reference frame you wish to delete 3 Click OK The reference frame will be deleted 268 Chapter 8 Running Simulations Viewing a Simulation from the System Center of Mass To view a simulation from the reference frame of the center of mass of all objects 1 Choose Show System Center of Mass from the View menu to create a system center of mass point 2 Select the system center of mass point 3 Choose New Reference Frame from the View menu 4 Type a name for the new reference frame 5 Click OK When you run the simulation you will view the simulation from the reference frame of the system center of mass 8 9 Tracking Tracking leaves an image trace of moving objects only applying to bodies and constraints at adjustable time intervals You can track individual objects or all objects Objects can leave visible tracks of their outline center of mass or vectors so that you can follow the physical action throughout a simulation
193. ge shape as you enter new coordinates Also notice how the control point currently being edited is highlighted on the curved slot To add a control point 1 Click the slot to select it 2 Choose Geometry from the Window menu The Geometry window appears as in Figure 3 19 3 Select a control point that will be adjacent to the new control point Figure 4 78 Adding a control point to a curved slot Insert Figure 4 79 New curved slot with two identical control points Select this control point jeometr Curved Siol Jini Slot is Closed Display in Oo s 3 oO Cartesian coordinates Polar coordinates i Table te Incl interp pts fod g Radius Click the Insert button in the Geometry window 4 19 Slot Joints 169 A duplicate control point will be created in the list The shape of the slot will not change until you edit the duplicate control point See Figure 3 20 These two control points have the same coordinates Edit the coordinates of the new control point to create a geometrically distinct point jeometri Curved Sio Jini Slot is Closed oO zs 3 Display in O Cartesian coordinates Polar coordinates i Table Izal Incl interp pts fod 8 Radius 170 Chapter 4 Constraints Figure 4 80 Deleting a control point from a curved slot How is the Data Represented T
194. ging a mouse cursor to draw a rectangle while pressing the button down to select the two points and the body 2 Choose Attach to Body under the Object menu The two points are now attached to the polygon If you mistakenly attach points to a wrong body you can either immediately Undo Ctrl Z in Windows Command Z in the MacOS or select the points and choose Detach from Body under the Object menu Furthermore if you wish to construct a pin joint we need to duplicate Point A attach it to the other polygon and join the two to form a pin joint 3 Select the point A and read the global coordinates of the point in the Properties window The Properties window for a point object looks like Figure 9 4 Figure 9 4 Properties window for a point element Join Attaching a Slot to a Body 9 4 Importing CAD Geometries as DXF files 299 Foin 5f v Faint angle d x 0 068 m y 0 768 m Connected to Body 4 Global coordinates of the Point Global Coordinates angle 0 000 x 0455 m y L__0 777 m 4 Choose Duplicate from the Edit menu A copy of the point appears offset 5 Set the global coordinates of the duplicated point to be the same as that of point A 6 Shift select the other polygon 7 Select Attach to Body under the Object menu Now the other polygon also has a point 8 _Box select the two overlapping points The Join button becomes active in the toolbar 9 Click the Join butt
195. gle step Vnt1 Ynt AOp ty Working Model 2D does not provide the variable time step option for the Euler method Kutta Merson inte gration is a more complex but robust scheme for obtaining increased accuracy The method solves the above differential equation in the following fashion N Hat EO ta L The Kutta Merson method is also known as 5th order Runge Kutta or Runge Kutta 5 A 16 Appendix A Technical Information Only Int EIU ty Zh iq ty 1A Ons Int EAOn ty Zh Ony ta Zh Only Int AOp ta SAA Onda tt Eh 2h Oye ty Eh 1 2 1 1 Wns Int EAOn fy SHA Ona tn 5A AOp ty h Vrsi On s Working Model 2D checks the result against error bounds by comparing 1 5 Ons i On s to the Acceptable Error Please see A 5 How Working Model 2D Bounds Errors Animation Step The Animation Step box determines the time between frames of animation Data from the simulation is presented on the screen as a new frame at this interval This box does not represent the integration time step By default Working Model 2D automatically tries to choose a good animation step based on the type of simulation that has been created Using the size of the objects their spacing and their velocities Working Model 2D determines an ideal animation step size Thus if you are modeling the solar system its large size spacing and velocities will force an automatic animation step size in the range of h
196. gon and choose Convert to Lines under Object menu 2 Immediately following the above step choose Convert to Curved Slot from Object menu Attaching Points and Slots to Bodies Since a DXF imported drawing does not contain any information as to which points are attached to which object you need to specify these relationships in the model Working Model 2D provides a useful facility for this purpose Initially all points in DXF files are imported as attached to the background You can select a set of points along with a body and assign the points to be attached to the body 298 Chapter 9 Importing and Exporting Files and Data Figure 9 3 Attaching points to a body Constructing a Pin Joint For example Figure 9 3 shows a model of two polygons and two points just imported from a DXF file Recall that all DXF imported polygons have no fill patterns hence the transparent appearance Suppose that you want one of the points to be a pin joint connecting the two whereas the other to be just a point element attached to one of the polygons 24 A a B 1 Just imported 2 Select body and points 3 Choose Attach to Body In order to attach the two points to the vertical polygon for example 1 Select the two points A and B you may need to use the box select since some options are covered by polygons and a body Use either shift select selecting an object while pressing down the Shift key or box select drag
197. gon Ca D Curved Body Rectangle Anchor Join Spite Join Split Point ES Point ola Square Point Horizontal Slot Vertical Slot ir Closed Curved Slot Curved Slot Figure 2 4 Joint and Constraint Toolbars Windows 2 1 The Working Model 2D Toolbars 37 Pin Joint Horizontal Pinned Slot Joints Vertical Open Rotational Spring Rotational Damper Gear Torque Motor Rope Pulley Rigid Joint Horizontal Keyed Slot Joints Vertical Closed Spring Damper Spring Damper Force Actuator Separator Rod Each individual toolbar can be hidden by clicking on the close box in the upper right hand comer Once hidden a toolbar can be restored by selecting Workspace in the View menu and clicking the appropriate checkbox see Displaying Workspace Tools and Controls on page 196 for more details 38 Chapter 2 Guide to Tools amp Menus MacOS Toolbar In the MacOS every Working Model 2D document has a single toolbar on the left side To minimize clutter in the workspace the toolbar Figure 2 5 provides access to many tools via pop up palettes which are special tool icons indicated by a small arrow shown as P in the lower right hand corner of the icon To open a pop up palette position the pointer on a tool icon with an arrow in the lower right hand corner and press the mouse button The pop up palette appears to one side of the icon Drag the pointer to highlight t
198. gth Capitalization and spacing do not affect formulas although identifiers and function names must not contain spaces Parentheses behave as they do in standard algebraic manipulations B 2 Numeric Conventions Numbers in Working Model 2D use the standard scientific notation of spreadsheets such as Lotus 1 2 3 and Excel and computer languages such as BASIC PASCAL and C B 2 Appendix B Formula Language Reference Exponents Exponents are displayed in the following way In Printed Text In Working Model 2D 123x103 123e3 1 001x10722 1 001e 22 Angle Measures All angles are expressed in radians An angle of 360 has a radian measure of 24 NOTE Angles in formulas are expressed in radians although the default display mode for Working Model 2D is degrees B 3 Identifiers Identifiers are used in formulas to identify an object There are five types of identifiers When creating formulas you can use one or more of these types body 3 point 2 constraint 44 output 12 input 5 The number within the brackets is the object ID Each object in Working Model 2D has a unique ID To find the ID of an object double click the object to display the Properties window for that object The ID appears with the proper formula syntax in the top of the Properties window In addition the identifier of an object is displayed in the Status bar when the pointer is over the object see Chapter 6 The Workspace Body Poin
199. he Coordinates bar and the Tape player controls along the bottom of the window The Toolbar contains tools you will use to create simulations Tools are provided for creating bodies springs ropes forces and many other objects The Toolbar also contains buttons for running and resetting simulations NOTE The Toolbar configuration differs between the Windows and MacOS versions of Working Model 2D Please see 2 1 The Working Model 2D Toolbars for more information on these differences The Coordinates bar provides useful information such as the mouse cursor position object configurations and object dimensions The display mode is context sensitive and changes swiftly to attend to your needs while you are using Working Model 2D You can also edit object parameters by entering information directly in the Coordinates bar The Tape player controls give you more flexibility for running and viewing simulations You can use the Tape player controls to step through simulations play simulations backwards or move to a specific time in a simulation The Status bar gives a concise description of the tool or object located at the mouse cursor Note that it is located at the top of the document window in the MacOS version but at the bottom of the window in the Windows version 1 2 Steps for Creating a New Simulation These quick steps provide a survey of how to use Working Model 2D to create and run a simulation The steps you take may diffe
200. he Simulation Accuracy dialog under the World menu You may wish to modify your simulations to make them more accurate and efficient Inaccurate Integration warning is an indication that bodies have a velocity or an acceleration large enough to violate the given error tolerance specified in the simulation see A 5 How Working Model 2D Bounds Errors for more information This warning can be overridden at run time but the remainder of the simulation may be grossly inaccurate and or unstable Initial Body Overlap warning is generated when all of the following conditions are met e two bodies overlap at the beginning of a simulation e they are not directly connected by a joint or gears and e they are not given Do Not Collide designation In such cases Working Model 2D assumes that these two objects are colliding and tries to generate enough force to separate the two see A 6 Simulation Accuracy Dialog and Simulation Parameters potentially yielding unexpected results Two objects overlapping at the beginning of a simulation should be given Do Not Collide designation under the Objects menu If you are designing a model where two objects are close together and are meant to interact you should ensure that they are not colliding at the beginning of the simulation You can find out whether a particular object is colliding with another at the beginning of a simulation by measuring the contact force For example choose the obj
201. he Smart Editor see Chapter 5 The Smart Editor will automatically modify the rest of the model to accommodate the specification If you used a formula expression to specify the length the formula will be immediately evaluated as t 0 and the rod length will be modified accordingly Again the Smart Editor will automatically modify the rest of the model to accommodate the specification 4 13 Separators A separator applies forces at its endpoints so that they do not become closer than the specified distance A separator applies no force at all when the distance between the endpoints are greater than this specified distance Figure 4 45 Coordinates bar for a separator HH 4 13 Separators 137 Creating a Separator To create a separator 1 Select the Separator tool from the Toolbar On MacOS systems the Separator tool is hidden in the Rope pop up palette by default Click and hold on the Rope tool to bring the Separator tool in view and select it 2 Position the mouse pointer at where you would like to define the first endpoint The pointer changes from an arrow to a crosshair indicating that you can start drawing 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an e
202. he arrow keys on the keyboard When dragging an object the coordinate information shows displacement relative to the initial position of the object i e how far the object has been dragged The displacement is shown in terms of x and y values as well as total displacement distance from starting point and displacement angle Releasing the mouse button will return the coordinates to showing the global x and y coordinates of the mouse The Coordinates bar shows the pixel coordinates of the meters and controls The coordinate system is designed so that the top left corner of the simulation window is x y 0 0 The x coordinate increases toward the right side of the window whereas the y coordinate increases downward The Coordinates bar shows the position of meters and controls in terms of their top left corner Figure 6 12 NOTE These pixel coordinates are used only for meters and controls Figure 6 12 Pixel coordinates 6 2 Viewing Options 203 Untitled 1 olx units in pixels 0 0 200 150 190 I 200 Coordinates bar shows Ea x y pixel coordinates x 200 000 y 150 000 x _ E E KA T J The Status Bar The Status bar displays information about the tool or object currently under the pointer Itis found at the top of the simulation window on MacOS systems and at the bottom of the window on Windows systems If the pointer is over a square body for example the Status bar wi
203. he currently open document windows in a tiled fashion each window is visible but reduced in size Arrange Icons Windows only neatly aligns the iconized Working Model 2D documents List of open documents A list of open documents is appended to the bottom of the Window menu when more than one document is open You can use the tab key to navigate from one text field to the next on a utility window The tab key can also be used to select a utility window If you have an object in the workspace selected then pressing the tab key will automatically select the last selected utility window associated with the object 58 Chapter 3 Bodies CHAPTER 3 Bodies Figure 3 1 Bodies square polygon circle rectangle and curved body In this chapter you will find steps to e Create edit and manipulate bodies Define body properties and parameters e Define the appearance of bodies e Define the geometry of bodies 3 1 Creating Bodies Bodies include circles rectangles squares polygons and curved bodies see Figure 2 6 You can create a variety of shapes to represent bodies using the tools shown in Figure 3 2 Circle 3 r 4 Polygon Curved Body Figure 3 2 The body tools 3 1 Creating Bodies 59 Circle Tool Polygon Tool Square Tool Rectangle Tool Curved Body Tool o ewe Each body has a number of parameters that define its behavior when you run a simulation These param
204. he desired tool and release the mouse button The selected tool is now displayed in the toolbar and can be used to re select the tool without opening the pop up palette Using Tools If you click once on a tool it will be selected for the next operation after that operation the selected tool will revert to the Arrow tool To use a tool for several successive operations double click on it MacOS only the difference between single vs double clicking is indicated on the Toolbar by shading a double clicked item is dark gray while a single clicked item is light gray To quickly select the Arrow tool press the space bar To quickly select the Rotate tool press the r key 2 1 The Working Model 2D Toolbars 39 Figure 2 5 The toolbar and pop up palettes Run MacOS Reset Rotate Arrow Text Zoom In Zoom Out Circle oO oO Rectangle Square Anchor Zz oj Polygon Curved Body Point Square Point Slots Slot Joints Join Split Rope Separator kva IHE 5 Damper Rotational Damper Pulley Gear E EFJ Force Torque Motor Actuator Working Model 2D Tools The following is a synopsis of the tools available for building simulations in Working Model 2D Standard Toolbar Windows only The Standard Toolbar is part ofthe Windows interface guideline and includes the New Open Save Cut Copy Paste Print and About buttons These commands are also accessed through the File Edit and Help menus o
205. he variable time now returns the value in minutes according to Rule 1 above The values displayed by Meter objects are always associated with the current unit system ifa meter shows 2 feet in the English pounds unit system it will show 24 inches after you change the length unit to inches 328 Chapter 10 Using Formulas Notes on Precision However in order to enforce the Rule 2 preserves the physical behavior of the simulation the values returned by formula references e g output 5 y2 remain the same throughout the unit change Such behavior is useful especially when you are using meters as variables see section 10 9 Using Meters as Variables in Formulas for details For example suppose you created a time meter output 6 while the current unit for time is seconds The Properties window for the Meter object shows the variable time in the y1 field At this point the formula reference output 6 y1 would return the value 60 0 after 60 seconds elapsed in the simulation If you change the unit system to minutes the meter itself will display the proper values in minutes it will show 1 0 min after 60 seconds elapsed But the Properties window will show output 6 y1 time 60 0 so that the reference output 6 y1 will return 60 0 after 60 0 seconds Without the conversion factor references to output 6 y1 would return 1 0 after 60 0 seconds because time now returns the value in minutes according to Rule 1 The meter itse
206. he vector constraintforce x constraintforce x y B 6 Functions B 21 Simulation Functions Simulation functions are used to extract data from the simulation These functions are used in the various meters and vectors of Working Model 2D Name Inputs Output constraintforce number vector number number vector number number number vector frame number frictionforce number number vector groupcofm number vector kinetic number length number number number normalforce number number vector section number vector number Takes the ID number of a constraint x and returns a vector describing the current force being applied by the constraint To find the compression in a spring use the formula constraintforce 3 x In point to point constraints the x component of the force vector is always measured along the line connecting the two endpoints In constraints that apply a torque the r component of the constraint force contains the value of applied torque For pin joints the x and y components are given in terms of the global coordinate axes Takes the ID number of a constraint x and the ID number of a body y Returns the amount of force being applied by the constraint on the body as a vector This function is used by meters which measure gravity air resistance electrostatic and custom force fields The ID numbers for these four constraints are constant and are described in the next section The gravity constrain
207. his value to start files with a suffix other than PICT 0001 All sequential PICT files will be place in the same folder 314 Chapter 9 Importing and Exporting Files and Data 9 12 Exporting to MacroMind Three D MacOS only Working Model 2D will create complete MacroMind Three D scripts and 3DGF shape files with all relationships between objects and keyframes You can open the script directly from MacroMind Three D Working Model 2D creates a script that contains a numerical keyframe for each object in a simulation Each frame of Working Model 2D simulation is translated into a MacroMind Three D keyframe Motion data from each object is placed in the x and y positional keyframes and the z axis rotational keyframes The z positional and x and y rotational keyframes are set to the value 0 0 Working Model 2D creates 3DGF files for each object in a simulation These are placed in the same folder as the motion script and are correctly referenced by name from the script Working Model 2D can create flat or extruded 3 D shapes when creating the 3DGF files To export complete MacroMind Three D animations 1 2 Create or open a Working Model 2D simulation Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog Set the export type to MacroMind Three D Set Export Options as necessary You can choose to export all objects or just those that are s
208. hout the Working Model 2D viewframe 1 Choose Workspace form the View menu 2 Turn off all the options in the Workspace submenu menu Your document will have nothing but the caption title bar and your model 3 Proceed to export the Video for Windows file Export Options Video for Windows export provides the following parameters The default settings are appropriate for most purposes By default a Video for Windows animation file has a avi suffix Windows associates the avi extension with the Media Player Specifies how many frames of the Working Model 2D simulation should be exported to the animation file The default value is 1 meaning every frame generated by Working Model 2D will be exported Specifies the number of colors available in the bitmap The default value is 8 meaning 2 256 colors can be used The other option is 16 meaning 65 636 colors can be stored Specifies how many times each exported frame is repeated during the playback The default value is 1 For example if you set the Frame Multiplier to 4 the Video for Windows file will have 4 successive copies of each Working Model 2D frame resulting in a playback 4 times slower slow motion than the default 308 Chapter 9 Importing and Exporting Files and Data Playback Rate Example of Playback Setting Specifies how many frames per second will be displayed during the playback The maximum value that can be entered is 100 The default value
209. i i i i TOTP TTT PTT TTT ATT PET TTT TTT T 6 000 5 000 72 000 Ad Friday August 02 96 09 12 AM 7 Displaying the x and y Axes Solid lines mark the x and y axes The intersection of the x and y axes marks the location of the origin 0 0 To display the x and y axes choose X Y Axes from the Workspace submenu or dialog A checkmark appears next to this command when the axes are displayed To hide the x and y axes choose X Y Axes again The checkmark next to X Y Axes disappears Displaying Rulers Working Model 2D provides both rulers and grids to enable you to accurately position and scale objects See Figure 6 9 To display rulers choose Rulers from the Workspace submenu or dialog A checkmark appears next to this command in the menu when the rulers are displayed To hide rulers choose Rulers again The checkmark next to Rulers disappears 200 Chapter 6 The Workspace By default the rulers measure in meters with precision to 3 significant digits Ruler measurements may be changed to other distance units and number of significant digits For information on changing units and numerical precision see Numbers and Units on page 205 of this chapter Displaying Grid Lines You can display grid lines to help accurately position and measure objects The spacing between grid lines is automatic and is adjusted as you zoom in or out To display the grid choose Grid from the Workspace submenu or dialog
210. ible beside the menu item Please see Aligning Objects to the Grid on page 200 for more information The Coordinates bar Figure 4 12 displays constraint parameters that are frequently edited such as the endpoint coordinates For rotational constraints the first set of x y values holds the coordinates of the Base Point point element attached to the body in the lower layer see Figure 4 12 The values are given in terms of the local coordinate system For linear constraints the first set of x y values holds the coordinates of the first point created see Figure 4 12 For Rotational Constraints Base Point on the background is at 6 0 4 0 Top Point on the disk is at 1 0 0 0 4 000 m _1 000 m y __0 000 m Base Point Top Point Suppose that the Spring is drawn from the body to the background Then the first point is at 1 0 0 0 The second point is at 2 0 1 0 x _ 1 000 m y _0 000 m x __2 000 m y _1 000 m b j DE l l l First Point Second Point Furthermore if you select an individual endpoint the Coordinates bar displays the values in local and global coordinates The local coordinates are shown with x y labels whereas the global coordinates are shown with Gx Gy labels 104 Chapter 4 Constraints Figure 4 13 Local and global coordinates for a x_1500 m yl 0 750 m Gx _1 850 m__Gy _0 75
211. icked If you experiment with the Smart Editor you will begin to see what is involved If you try to drag an object too far it will follow the mouse and then stop after going as far as it can The best way to learn how to use the Smart Editor is to play with it Set up assemblies in the workspace move them around use Split and Join and use the Properties window to fix positions The Working Model 2D Tutorial comes with examples showing how to construct increasingly complex mechanisms using the Smart Editor 190 Chapter 5 The Smart Editor Controlling the Accuracy of Editing Operations The Working Model 2D Smart Editor uses the Assembly Error term in the Accuracy dialog to determine how exactly it will position objects The Smart Editor becomes active whenever you drag join or numerically adjust systems of joined bodies After joining two points to create a pin joint the distance between the two points will be less than or equal to the distance specified as Assembly Error or the tolerance allowed in assembly Larger tolerances will allow faster Smart Editing especially when dragging objects with the mouse Smaller tolerances will give more exact alignment of various components When experimenting or making initial designs it is a good idea to use the automatic option for Assembly Error and Animation Step values in the Accuracy dialog see A 6 Simulation Accuracy Dialog and Simulation Parameters If you need more exac
212. igure 1 34 1 Working Model Untitled1 ioj x ty File Edit World View Object Define Measure Script Window Help lj x is amp ESEE amp RJoJA Pe Run gt Stopi Reset ai Circle Velocity r m Friday August 02 96 09 12 AM 4 To move a menu button 1 Click near the button s border or drag a selection rectangle around the button to select it Position the pointer near the selected button until the pointer changes to a crosshair 1 9 A Simple Simulation with Controls and Menu Buttons 31 3 Drag the button to the desired location For more about menu buttons see 7 3 Menu Buttons Player Documents Finally you will change this document into a player simulation Player simulations are simplified documents suitable for demonstrations or for use by people without experience using Working Model 2D Player simulations are simplified in a number of ways For example there are no toolbars objects cannot be dragged or resized and menus are greatly simplified 4 Choose Player Mode from the Edit menu The Toolbar disappears and the document becomes a player simulation Figure 1 35 Working Model Untitled1 Beg iby File Edit Run Script Window Help 18 I Player document Circle Velocity Friday August 02 96 09 12 AM 4 32 Chapter 1 A Guided Tour 1 10 Summary In this guided tour you learned how to use the tools in the toolbar to
213. ill move to satisfy this condition 26 Chapter 1 A Guided Tour Figure 1 29 Using numerical editing for precision alignment This body now has a rotation of 0 00 1 9 A Simple Simulation with Controls and Menu Buttons In this tutorial you will create a simple simulation of a bouncing ball with controls and sliders You will be able to control the velocity of the ball with aslider on the screen You will also use buttons to make a simple stand alone simulation that can be easily used by others who have no experience using Working Model 2D Building Your Model Your model consists of a ball and a table The table represented by a rectangle is fixed to the background the ball represented by a circle bounces on the table 1 Create a new Working Model 2D document by choosing New from the File menu 2 Select the Circle tool and create a small circular body in the middle of the workspace Figure 1 30 A small circle and a small rectangle 3 A 4 Figure 1 31 Anchored Rectangle Rune Reset Reset 1 9 A Simple Simulation with Controls and Menu Buttons 27 Ld Select the Rectangle tool and create a rectangle similar to the one shown in Figure 1 30 Click the Rectangle tool in the Toolbar and then draw the rectangle on the screen Position the circle and rectangle to resemble Figure 1 30 Select the Anchor tool in the Toolbar The pointer becomes an anchor
214. ime t 0s the second frame at t 0 01s the third frame at t 0 02s and so forth This time interval between frames is called the time step or delta t Y To varying degrees the accuracy of every simulation is influenced by t Generally the smaller the t the slower the simulation will run and the more accurate the simulation becomes Conversely the larger the t the faster the simulation will run and the less accurate the simulation becomes Different simulations demand different time steps A simulation of a thrown baseball creates good results when the time step is about 0 01 seconds This time step would not be appropriate for a simulation of the solar system however At arate of 0 01 seconds per frame it would take a very long time to see any motion of the earth around the sun Working Model 2D automatically selects a time step for each simulation based on the size and mass of the objects If necessary you can override this automatic time step and enter your own value To change the value of t 1 Choose Accuracy from the World menu 278 Chapter 8 Running Simulations Figure 8 23 Simulation Accuracy dialog The following dialog box Figure 8 23 appears Simulation Accuracy Integrator Error Automatic Animation Step Fast Automatic Accurate 0 050 s 0 024 Custom 20 000 s OL Snes 2 Enter your own value for the time step The radio button next to Autom
215. inates The shape coordinates of a vertex do not change unless the object is reshaped at that point itself or the entire object is resized The world coordinates of the FOR are shown as the x y and in the Properties window see Initial Position and Orientation on page 67 The type of coordinate system used for Shape coordinates depends on whether the object is a polygon or a curved body Polygon Shape coordinates are given in Cartesian coordinates Shape coordinates for curved bodies are given in polar coordinates 82 Chapter 3 Bodies Copy Paste Reshaping with the Geomeiry Window Figure 3 18 Geometry window You can copy and or paste vertex coordinates to and from other applications such as spreadsheets or text editors See Copying Polygon or Curved Body Geometry to and from Other Applications on page 85 for specifics Reshaping Polygons and Curved Bodies Numerically You can accurately modify the shape of polygons and curved bodies by specifying coordinates for each vertex in the Geometry window If you want to reshape a polygon or curved body by dragging please see Reshaping Polygons and Curved Bodies Graphically on page 64 for mouse driven reshaping In the Geometry window you can also e Add or delete vertices e Copy a coordinates table to and from the Clipboard for exchange of precise geometric data with other applications To reshape a polygon or curved body using the Geometry window 1 Click o
216. ing this the simulation may have to be run in a more accurate mode For more information see Appendix A Technical Information Running a Simulation Beyond What Can Be Recorded When the memory allocated for recording a simulation is full you can either stop the simulation or continue the simulation while erasing the initial frames of the recording To illustrate what happens when the initial frames of a recording are erased suppose the tape player memory allows room for 100 frames If you continue the simulation when the tape player memory is full then stop the simulation at frame 160 you can play the simulation backward to frame 60 but not back to the beginning Frames 1 to 60 were overwritten by frames 100 to 160 Clicking Reset in the Toolbar reverts to frame zero You can also continue to observe the simulation without losing the initial frames 1 Save the current simulation to a file For instructions please see 8 10 Saving a Simulation 2 Bring the tape player control to the last frame Tape player control is discussed in 8 3 Using the Tape Player Controls 3 Choose Start Here from the World menu The command erases the existing simulation history and makes the last frame to be the first frame preserving all configurations such as object positions and velocities 4 Save the file under a different name This way you will not accidentally overwrite the history previously saved Notes for
217. ing force on a body Joints Joints connect two bodies and constrain how they move relative to one another Working Model 2D provides Pin Joints Rigid Joints and Slot Joints Slot joints can be straight or curved See 4 18 Joints and 4 19 Slot Joints for more information You can construct joints in one of two ways e choose the appropriate Joint tool from the Toolbar or 92 Chapter 4 Constraints Figure 4 1 The endpoints of a rope connected to a circular body e join primitive components with the Join command for example joining two point elements creates a pin joint 4 3 General Properties of Constraints This section provides hints and techniques that apply to most types of constraints Shown below are some common properties of constraints e Each constraint behaves according to its defined characteristics and parameters e Many constraint properties can be controlled dynamically using an appropriate control See 7 2 Controls for more information e All constraints except Forces and Torques have two endpoints The positions of the endpoints coincide for rotational constraints e When constraints are created each endpoint is automatically attached either to a body or to the background e The connection symbol on the end of each constraint indicates whether the constraint is attached to the background or to a body see Figure 4 1 This endpoint is anchored to the background This endpoint
218. ing importing or exporting the geometry data of polygons to and from other applications The Geometry window can also be used to modify vertex locations for polygons and control points for curved bodies This section shows how to use the Geometry window For the use of the Coordinates bar Please refer to 3 1 Creating Bodies To display the Geometry window 1 Select the body whose geometry you wish to change 2 Choose Geometry from the Window menu Alternately if the Geometry window is already visible you can simply select the desired object from the selection pop up menu at the top of the window Figure 3 17 The menu will show the list of ID numbers and the names of all objects in the document You can change and assign meaningful names by typing into the name field in the Appearance window see 3 3 Body Appearance Assigning custom names will help you search through the list of objects Figure 3 17 Geometry window for a rectangle Area Center Of Mass Offset Radius 3 4 Body Geometry 79 bagi te Selection Pop up Menu Rectsngle area 5 070 m 2 height 1 300 m width m Bodies in Working Model 2D are defined with an area rather than with a volume The only way you can change the area of a body is by resizing the object with the mouse or by changing values in the Geometry window By default all bodies are created with the Center of Mass COM at the geometric center of the object The c
219. int 4 Point Point 2 Active when Always ie 2 Select the type of the motor and enter the magnitude of the constraint appropriate for your simulation 4 18 Joints Pin joints allow rotation while forcing points on two different bodies to overlap Rigid joints lock two bodies together Unless the force exerted on them is being measured rigid joints do not introduce extra force equations into a simulation and thus do not significantly decrease simulation speed See Joint Properties on page 152 for more details Creating a Joint There are two ways to create joints You can either attach a joint directly or build a joint from primitive elements Attach a joint to two overlapping bodies directly by selecting the appropriate joint tool in the toolbar Click on the desired location for the joint The top two bodies that lie beneath the pointer will be joined The slot component of a slot joint will be attached to the second body or to the background beneath the pointer For control and accuracy you can build joints out of primitive elements just as you would build a real pin joint out of two holes Point elements are synonymous with the holes drilled in a real body The Join command forces the two points to overlap and combines them to form a pin joint 150 Chapter 4 Constraints A Figure 4 59 Creating a pin joint Figure 4 60 Coordinates bar for a joint Adjusting Joint Position To construct a compl
220. ints at control points and or the midpoints between them convert the curved body into a polygon attach a constraint and then convert back into a curved body see Converting Between Polygons and Curved Bodies on page 80 FOR Quadrants Circle FOR Vertices Polygon Midpoints Corners FOR Midpoints Rectangle Square Two Extra Points shown below 1 7 h 1 5h 1 ah h min Height Width When a constraint is attached to a snap point on a body Working Model 2D automatically generates the geometry based formula to define the endpoint coordinates See Using Geometry based Formulas Point based Parametrics on page 104 for information on this feature You can disable this automatic formula generation through the Preferences dialog When formula generation is disabled Object Snap will still be active but the coordinates of the attachment points will be given with numeric values rather than geometry based formulas See 8 4 Preferences for more information Using Grid Snap Using the Coordinates Bar Figure 4 12 Coordinates bar 4 3 General Properties of Constraints 103 When the Grid Snap feature is active you can attach a constraint endpoint to the background so that it is automatically aligned to the regular intervals of the grid You can also align bodies with the Grid Snap To activate Grid Snap 1 Choose Grid Snap in the View menu Grid Snap is already active if a checkmark is vis
221. ion Eg Compressor Ok Microsoft Video 1 ha Cancel Compression Quality 100 Wil E Configure About IV Key Frame Every 75 frames I Data Rate 58 KB sec 9 9 Exporting Object Motion Paths or Keyframes MacOS only You can automatically export the positions ofall objects in a Working Model 2D simulation The x y and rotational position of each object is stored for each frame of a simulation Object position data is exported as tab delineated text The positional data may be exported as either rows or columns By default data is exported as columns in the following format Data From Untitled 1 at 9 02 22 PM 3 4 93 Mass 2 Mass 4 x y x y 0 000 1 250 3 000 0 000 1 250 0 020 1 365 2 884 0 000 1 365 0 040 1 480 2 772 0 000 1 480 0 060 1 595 2 664 0 000 1 595 0 080 1 710 2 559 0 000 1 710 0 100 1 825 2 459 0 000 1 825 You can also export data by rows Data From Untitled 1 at 9 02 22 PM 3 4 93 NNNNNWA 000 884 772 664 559 459 310 Chapter 9 Importing and Exporting Files and Data Figure 9 10 Object Positions export options Include Header Mass 2 x 0 000 1 250 3 000 0 000 Mass 2 y 0 020 1 365 2 884 0 000 Mass 2 0 040 1 480 2 772 0 000 Mass 3 x 0 060 1 595 2 664 0 000 Mass 3 y 0 080 1 710 2 559 0 000 Mass 3 9 0 100 1 825 2 459 0 000 Object positional data can be used to create keyframes in animation packages If you are using an animation pac
222. ion assumes you know how to construct and edit bodies and constraints A Working Model 2D document contains two rectangles connected by a pin joint 1 Grab one rectangle and drag it around the workspace The rectangles move together as shown in Figure 5 8 because they are Joined by a pin joint Figure 5 9 Pinned rectangles before and after a drag 5 2 Dragging and Rotating Joined Bodies 179 2 Join the vertical rectangle to the background with a pin joint Your screen should resemble the gray rectangles in Figure 5 9 3 Drag the horizontal rectangle towards the right The vertical rectangle must resolve a dilemma it is attached to the rectangle moving to the right but it is also attached to the background The Working Model 2D Smart Editor accommodates both constraints by pulling the horizontal rectangle to the right and tilting the vertical rectangle clockwise The Working Model 2D Smart Editor allows the user to manipulate objects and constraints while preserving the fundamental relationships that exist between them Manipulate in this context has three possible meanings e dragging or rotating using the Join command e typing values into the Properties window The Smart Editor prevents a mechanism from disintegrating when its components are moved around Instead other components are moved or rotated subject to their own constraints until the desired
223. ion at specific intervals 1 2 Click Reset in the Toolbar if you have run but not yet reset the simulation Choose Tracking from the World menu and then choose Every 8 frames from the submenu When you run the simulation Working Model 2D will display the position of the circle at eight frame intervals 16 Chapter 1 A Guided Tour 3 Click Run in the Toolbar The projectile s path will be traced as it moves see Figure 1 14 Figure 1 14 Em untitled Tracking 3 000 m s 14 993 m s f 15 291 m s e 0 000 r3 4 Click Stop to stop the simulation Creating or editing objects erases the track For more information about vectors see 8 9 Tracking 1 7 Saving a Simulation Once your simulation is complete you can save it to replay or edit later To save a simulation to disk 1 Choose Save from the File menu The Save As dialog appears if you have not yet given the simulation a name 2 Type a name for your simulation document Then click Save The changes you have made in all dialog boxes are saved when you save a simulation document If you have already selected and entered a name for your simulation you can sequentially save without interrupting your work Figure 1 15 A single rectangle 1 8 The Smart Editor 17 Use the Save As command to save a copy of your simulation under a different name 1 8 The Smart Editor In this tu
224. ion variable there is a good chance that the system is highly dependent on initial conditions or is unstable in some way Systems that Gain Energy Systems that gain energy usually need to be simulated with a more accurate simulation method Ifa simple pendulum begins to swing higher and higher the system is gaining energy If a system is gaining energy reduce the time step or try using a variable time step Accuracy and System Properties Simulation accuracy depends to a large extent on the physical system being modeled Certain physical systems such as a four bar linkage with a single driving force lend themselves to very accurate simulation Physical systems that have a high dependence on initial conditions will lend themselves to simulations that are also sensitive to initial conditions If your system would never produce the same results twice in a row in the real world you can only expect a simulation to give you insight into possible behaviors of the system Dropping a linked human figure down a flight of stairs is an example of this If your system is reproducible in the real world you should be able to get simulation accuracy to any degree you choose A 8 Simulation Accuracy A 25 Why Numbers like 1e 19 Appear in Position Fields These numbers are caused by round off that occurs when dragging objects with the Grid Snap turned on After a number of drags very small differences in the last digit of large floating point nu
225. ional Constraints Editing in the Coordinates Bar 4 3 General Properties of Constraints 97 The Appearance window appears 3 Type the desired name in the name field of the Appearance window Figure 4 6 Appearance Name Field Show Name Checkbox Show Checkbox To display these names in the simulation check Show Name checkbox in the Appearance window Figure 4 6 Coordinates for Constraint Point Elements All constraints have one or two point elements embedded in them Working Model 2D can represent the coordinates of these points in global coordinates with respect to the world or in local coordinates with respect to the center of the body to which the point is attached You can view and edit these coordinates in the Coordinates bar or in the Properties window You can also refer to these values using the formula language Linear constraints contain two endpoints Each point has coordinate values x y measured in the local coordinate system of the body to which it is attached Rotational constraints also contain two points one of which is called the Base Point As above each point has x y values measured in the local coordinate system of the body to which it is attached The Coordinates bar located near the bottom of the document window shows various information regarding objects currently selected You can also edit these coordinates on the fly to modify your model easily and quickly If th
226. ipts but will not be able to create or edit them The Smart Editor is the core of the user interface keeping track of connections and constraints among objects as they are constructed To develop a mechanism a user draws components on the screen and indicates where and how the pieces should be joined The Smart Editor allows a mechanism to be rotated and dragged while maintaining the fundamental integrity of the components and of the joints between them Users can position objects via the standard click and drag paradigm or by specifying precise coordinates in dialog boxes In all cases the Smart Editor makes sure that no link is broken and no body is stretched A robot arm composed of several parts held together by pivot joints can be positioned accurately using the Smart Editor By clicking and dragging the hand the arm stretches out to the desired configuration Point and Geometry based Parametrics Object Snap Editing Objects On the fly Inter application Communication What is Working Model 2D xix Working Model further enhances its flexibility by incorporating point and geometry based parametric modeling capabilities You can specify the position of a constraint based on a body s geometry so that its relative position remains fixed even when the body is modified For example you can position a pin joint at a vertex of a polygonal body You can then reshape or resize the polygon and the pin joint will remain at the vertex
227. is attached Ifa point is attached to the background the window shows the global coordinates You can modify these values to position individual points precisely If you modify the relative position of one of the points belonging to a pin joint the other point will move to match the repositioning For example one of the points of the pin joint as shown in Figure 4 64 is attached to the circle In the left figure the point has offset 0 0 If you change the coordinates of the point to 0 0 3 in the Properties window the other body the rectangle moves along to match the repositioning Offset 0 0 Offset 0 0 3 154 Chapter 4 Constraints Figure 4 65 Measuring joint reaction forces Measuring Reaction Forces at Joints When you select a joint and create a meter to measure the reaction force the meter measures the force exerted on the body located at the top layer when the joint was created The components are given in terms of the global coordinate system Figure 4 65 illustrates this principle The joint force meter measures the reaction force acting on the body at the top layer when the joint was created Body on Top Layer Fx 6 227 N 11 715N 13 268 N Typically the meters for joint meters have the formula expressions in its Properties window Body on Bottom Layer constraintforce n x constraintforce n y constraintforce n for x y components and the magnitude the
228. is exercise to familiarize yourself with the usage of the external interface Working Model 2D can also function as a DDE or Apple events server Please see 9 15 Controlling Working Model 2D from Another Application for more information Interface Objects Remote Commands Simulation Cycles and Data Exchange 9 16 Exchanging Data in Real Time with External Applications 319 MacOS Working Model 2D can communicate with applications that support the Table Suite of Apple events These applications include Microsoft Excel 4 0 and Claris FileMaker Check with your particular application s user guide to see if the Table Suite is supported Windows Working Model 2D can communicate with applications that support DDE Excel Table or Text formats These applications include Microsoft Excel Quattro Pro MATLAB version 4 2 or later and Microsoft Word for Windows Check with your particular application s user guide to see if DDE is supported Working Model 2D communicates with external applications through meters and controls Meters function as output devices and controls serve as inputs Working Model 2D also allows you to specify commands in external applications during the simulation cycles You can specify e Initialize commands that are executed at the beginning of a simulation and e Execute commands that are executed at every frame during the simulation Data exchange and remote command executions are interl
229. ive acceptable error would be 10 Asa result when the value of Yis small Working Model 2D would Figure A 2 Acceptable Error A 5 How Working Model 2D Bounds Errors A 11 waste computing time trying to meet this exceedingly small error criterion To avoid this problem Working Model 2D uses a second error bound called Absolute Acceptable Error Absolute Acceptable Error Absolute error is a positive number which designates a small absolute lt q value of Y That is when Y is less than integration continues without cutting the integration step Therefore in effect this criterion accelerates the integration process for small values of Y The Absolute Acceptable Error is simply defined as Absolute Acceptable Error You can specify the magnitude of e as the Integrator Error in the Accuracy dialog see A 6 Simulation Accuracy Dialog and Simulation Parameters Acceptable Error The acceptable error is the maximum of Absolute Acceptable Error and Relative Acceptable Error In Figure A 2 the acceptable error is denoted as a thick line When the error estimate exceeds this line Working Model 2D proceeds to cut the time step in half see Variable Time Step on page A 9 Relative Acceptable Error Yl Acceptable Error Absolute Acceptable Error a Pa r Absolute Value of Variable Being Integrated Y A 12 Appendix A Technical Inf
230. ject is a device which introduces non linear equations into the Smart Editor When dragging mechanisms that contain many ropes the Smart Editor may lock ropes in their fully extended position If an extended rope will not go slack release the mouse button and then continue dragging What If the Smart Editor Fails Situations can arise in which it is impossible to satisfy all of the constraints imposed on a system Consider the example in Figure 5 25 The rectangle is held to the background by the left pin joint and the other two point elements are highlighted There is no way to join the two point elements without destroying the left pin joint 5 3 Understanding the Smart Editor 189 Figure 5 25 An impossible Join Figure 5 26 The impossible join warning box Ss gt If you try to Join them the warning box in Figure 5 26 appears Windows Attempting to move the objects into position The number below will increase if assembly is possible 0 finished Trying to Join S MacOS Attempting to join the bodies Joining may not be possible The bar will move to the right if moving is possible eee cancer Trying to drag an object to a position inconsistent with the constraints will not cause an error message The Smart Editor will try to find the best solution by moving objects to minimize the distance between the pointer and the place on the object where the pointer was originally cl
231. jects collide with one another during a simulation Do Not Collide will prevent the selected objects from colliding with one another during a simulation Font MacOS allows you to choose the font in which selected text will be displayed Size MacOS only allows you to choose the size in which the selected text will be displayed 2 2 Working Model 2D Menus 53 Style MacOS only allows you to choose the style in which the selected text will be displayed Font Windows causes the Font dialog to appear allowing you to select the font type for selected object s The Fonts Font styles and Sizes available include the fonts installed in your system The following menu items Attach Picture and Detach Picture appear alternately depending on what objects are selected For more information see Attaching Picture Objects to Bodies on page 248 Attach Picture attaches a picture to a single body The picture replaces the standard representation of the body in the workspace Detach Picture detaches a picture from the body which it represents The standard representation of the body reappears and the picture becomes a separate object in the workspace The following menu items Attach to Body and Detach from Body appear alternately depending on what objects are selected For more information see Attaching and Detaching a Slot Element on page 163 Attach to Body attaches a set of points and or slots to a body while maint
232. kage that supports pasted in keyframes you can build realistic motion based on Working Model 2D simulations To export an object position data file 1 2 Create or open a Working Model 2D simulation Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog Set the export type to Object Positions Set Export Options as necessary Click OK Export Object Positions ty D Default suffix t Export every cA frames every 0 010 s Export coordinates from every object D selected objects only K Include header C Export in rows per object horizontally This option includes the file name date object name and column or row names before all numerical data This option will help in referring to specific columns of data When this option is turned off only numerical data is exported Export in Rows 9 10 Exporting Motion Data to Animation Systems MacOS only 311 This option creates rows of positional data rather than columns Some animation programs such as Electric Image support pasted in rows of keyframe data 9 10 Exporting Motion Data to Animation Systems MacOS only Animation systems such as Electric Image and Wavefront Technologies Advanced Visualizer allow you to define motion paths with rows or columns of positional data Motion in most 2 D and 3 D animation systems is defined by a series of keyframes If an animatio
233. king Model 2D whenever graphics data is pasted into the workspace The MacOS version accepts PICT data the Windows version accepts metafile data You can drag cut copy and paste picture objects You can also attach picture objects to bodies Creating Picture Objects To create a picture object 1 Copy a picture from a paint program onto the Clipboard On MacOS systems the picture must be in PICT format On Windows systems the picture must be in metafile format 2 Paste the picture into your simulation document The picture will appear as a picture object Attaching Picture Objects to Bodies To attach a picture object to a body 7 6 Pictures 249 CHAPTER 8 1 Select both the body and picture by holding down the Shift key and clicking on each one Both the picture and the object appear selected The Attach Picture item in the Object menu becomes highlighted 2 Choose Attach Picture from the Object menu The picture is attached to the body To detach a picture from a body 1 Select the body by clicking on it The menu item Attach Picture changes to Detach Picture 2 Choose Detach Picture from the Object menu The picture and body can now be selected separately NOTE Pictures do not zoom or rotate with the bodies attached It is best to attach pictures to bodies that are being observed for linear rather than rotational motion Running Simulations This chapter contains information on how to e Runa si
234. l Select the Anchor tool Selects the Zoom in tool Selects the Zoom out tool Invokes the object Properties window Undo Clear Cut Copy Paste Help New document Quit Run Stop Save As Save Open Print C 3 Useful Tips for Using Working Model 2D C 5 C 3 Useful Tips for Using Working Model 2D Building and Debugging a Complex Model Instead of trying to model all the components of a complex model the first time around we recommend starting with a simplified model 20 objects or less and getting that model working first Although this initial model may not be accurate enough for meaningful analysis it serves a few purposes For one it allows you to lay out major components and verify their behavior Should the model behave unexpectedly this simplified system will be a lot easier to debug Furthermore you will be able to take order of magnitude measurements early in the model development enabling any system level issues to be identified Once the basic system is modeled we recommend increasing model fidelity gradually verifying overall behavior at each step This approach might seem slower than the everything at once approach but our experience shows it is actually much faster since it saves a lot of debugging time Another useful approach is modeling subcomponents in separate Working Model 2D documents testing them as stand alone subcomponents and then incorporating them in the main model simply by using copy and pas
235. l and choose Elasticity located in the New Control submenu in Define Turn on tracking every 4 frames and run a simulation with the elasticity of the ball set to 1 0 You can turn on the tracking by choosing Tracking under the World menu Now turn off AutoErase Track and run multiple simulations decreasing the elasticity of the collision every time You can turn off the AutoErase feature by selecting AutoErase Track under the World menu The simulation should look similar to the one shown in Figure 8 17 Figure 8 17 Running multiple simulations with AutoErase Track disabled Actions that Erase Tracks 8 9 Tracking 271 Circle 3 Elasticity To be most effective in using multiple tracks one should understand the organization of the basic drawing layers in Working Model 2D The layer where tracks are drawn is called the Interface layer or back layer see 6 1 Physical Objects and Interface Objects for more details Meters controls sliders text boxes buttons and pictures that are attached to the background are also drawn on this Interface layer When AutoErase Track is disabled Working Model 2D will not erase tracks under the following actions e changing the geometry position and properties such as initial velocity elasticity mass of a body or a constraint e adding or removing a body or a constraint e changing the color and or the pattern of a body and e changing the settings of a control
236. l Torque Gravity Force Electrostatic Force Ait Force Force Field Kinetic Energy gt Gravity Potential Shown below are some examples of quantities that can be measured using meters Bodies Position Velocity and Acceleration of FOR frame of reference or COM center of mass Linear Momentum Angular Momentum Total Force Applied Total Torque Applied Gravity Force Electrostatic Force Air Resistance Kinetic Energy Translational and or Rotational Gravity Potential Linear Constraints Tension Length Velocity Acceleration Power Rotational Constraints Torque Transmitted Rotation Angular Velocity Angular Acceleration Power Reaction Force Force and Torque Force Torque respectively Joints Reaction Force Torque non zero only for Rigid Joints or Keyed Slot Joints 224 Chapter 7 Simulation Interfaces You can also select two bodies to measure properties that pertain to their interactions such as the contact force friction force and electrostatic potential see Measuring Interactions between Two Objects on page 224 In addition Working Model 2D is capable of communicating with other applications in real time by exchanging data thorough meter objects The section 9 16 Exchanging Data in Real Time with External Applications provides more information on this feature Measuring Interactions between Two Objects Several Measure menu choices require that you select two objects at the
237. l life A scale of 1 means that objects in the workspace are the same size as they are in reality 1 meter of the workspace equals meter in real life A scale of less than 1 means that objects in the workspace are smaller than they are in the real world To exactly specify the size or scale of the view 1 Choose View Size from the View menu You will see the following dialog box Figure 6 6 wieurke Scale field Objects on screen are 0 021 times actual size Window width 7 050 m Window width field 2 Enter a value in the scale field to specify the exact scale of the view When you click OK the view will be zoomed such that its scale is the value you specified 3 Enter a value in the Window width field to specify the exact size of the view When you click OK the view will be zoomed such that its width is the value you specified 4 Click OK Displaying Workspace Tools and Controls The Workspace command in the View menu lets you display or hide the following workspace tools and controls e Toolbar Figure 6 7 The Workspace submenu MacOS only 6 2 Viewing Options 197 Scroll bars Coordinates bar Tape player controls Rulers Status bar On MacOS systems choosing Workspace presents a submenu you can either toggle options in the submenu or set multiple options by selecting the Workspace dialog from the submenu On Windows systems there is no submenu of individual options the Workspace me
238. late more history data e Toggling Retain Meter Values and Erase Meter Values cannot be undone 232 Chapter 7 Simulation Interfaces Figure 7 8 Text box button and slider Figure 7 9 Slider controlling a spring constant 7 2 Controls Controls allow you to adjust simulation parameters before and while a simulation is running Rectangle 1 Y Position Initial Velocity A control can be a slider default a text box or a button For example Figure 7 9 shows a slider that you can use to control the spring constant of a spring In addition you can let Working Model 2D read a text file as an input See Types of Controls and Properties on page 235 for details In addition Working Model 2D is capable of communicating with another application in real time by exchanging data through control objects The section 9 16 Exchanging Data in Real Time with External Applications provides a detailed discussion ing Constant 35 15 If you highlight a spring and then create a control for its spring constant you automatically replace the number in the spring s spring constant field with a formula that gives the current value of the slider You can see this change by displaying the Properties window for the spring as in Figure 7 10 7 2 Controls 233 Figure 7 10 Properties window for a spring with i Sprin a control on its constant ae K inputs N m length fi 310 m
239. lation you can sequentially save without interrupting your work 8 11 Printing a Simulation 273 Figure 8 18 Macintosh HD Save As dialog Eject Desktop D Read Me MacOS TeachTexrt Working Model Save this document as Untitied 1 O Save As Student Edition Save As Save in 5 Engg z Sl c a i Windows Filename Untitled 1 Save as type jes x eyes 2 Select the folder in which to save 3 Type the filename and click Save Your simulation model initial condition and time history are saved to disk When you open this simulation the tape player memory will be filled with the recorded time history and the simulation will run quickly the first time through 8 11 Printing a Simulation You can print a frame of your simulation to any printer supported by your MacOS or Windows system using the Print command All objects inside the simulation window will be printed Choose the proper window Zoom to reduce or enlarge your printouts 274 Chapter 8 Running Simulations Selecting Page Size and Orientation Figure 8 19 Page Setup dialog for LaserWriter printers Printing MacOS Printing Before choosing Print you can specify options for printing such as the size of the paper and the orientation of objects on the printed pages To specify print options 1 Create or open a simulation 2 Choose Page Setup from the File menu The Page Setup dialog for your printer appears
240. le Body 3 Follower Tube Bod ody 5 Cam handle Point 1 Cam slot Point 6 te Handle Pivot Vy Jo oo0 m s vo 0 000 ts material Standard mass kg stat fric Jo 300 kin fic 0 300 elastic psa charge 000e 004 c density 1 000 kg m 2 Planar he moment L Y O kg m 2 If objects do not have meaningful names yet you can use the status bar to identify object IDs such as Body 2 The status bar will show the name of objects as you move the mouse over them Turn on the status bar to assist in finding object names To turn on the status bar 1 Select Workspace in the View menu and then select Status bar in the Workspace submenu or dialog Using Formulas to Refer to Body Properties The kinematic properties of any body position velocity and acceleration can be accessed by Working Model 2D s powerful formula languages See Appendix B Formula Language Reference in particular Body Fields on page B 6 Figure 3 13 Appearance window for a body Using the Selection Pop up Menu Changing Color and Fill Pattern 3 3 Body Appearance 75 Using Formulas to Control Body Motion You can use formulas to control position or velocity of a body By attaching the Anchor tool and using formula language you can control the motion of a body independently from the rest of the simulation model Please see 10 6 Specifying Body Path by Position and 10 7 Specifying Body Path by Velo
241. le Point Fields These are the current values of position velocity and acceleration Each of these fields returns a value of type vector Thus to use any of these fields you need to add one of the vector fields x y r point 1 p x X position of point 1 The position of a point is given in terms of the global coordinates The offset field returns the vector containing the current configuration x y and xr of the point element in terms of the FOR frame of reference of the body to which the point is attached local coordinates B 8 body force length dp dv da p1 p2 Appendix B Formula Language Reference If the point element is attached to the background the offset field is equivalent to the p field of the point element That is point n p x point n offset x and similarly for the y and r fields The body field returns the body to which the point element is attached See Body Fields on page B 6 for associated fields The force field returns a vector representing the force acting on the point to be more precise the force acting on the body at the point The components are given in terms of the global coordinates regardless of what the point element is attached to Constraint Fields This is the current distance between the two points of the constraint To find the current length of a spring you would enter constraint 3 length length of constraint 3 These are
242. lectrostatics e Wind e Air resistance Using the sample button is an excellent way to get a glimpse at the formula language you can use with Working Model 2D 3 Click one of the top three buttons to select the type of custom global force 4 Enter an equation for the force 5 Click OK to save the changes Formulas entered in the Force Field dialog are applied as forces and torques to all objects A more detailed description of the process of customizing forces using formulas is given in Chapter 10 Using Formulas 6 5 Modifying Objects Selecting Multiple Objects Selecting multiple objects is useful for moving groups of objects around or for changing parameters of many objects at once There are three ways to select multiple objects Shift select Selection Rectangle and Select All Normally when you click the selection tool on one object all other selections are automatically canceled If you hold down the Shift key when you click an object previously selected objects remain selected and the new object becomes selected as well If you click on a selected object while holding down the shift key the object becomes de selected Objects near to each other can be selected by enclosing them in a selection rectangle Select All 6 5 Modifying Objects 213 1 Click the Arrow tool 2 Place the pointer at one corner of an imaginary rectangle that will enclose all of the objects you want to select 3 Drag the
243. ler components of some bigger object Sometimes you will use two fields in a row To obtain the rotation of a body you enter the following formula B 4 Appendix B Formula Language Reference body 2 p r This equation has two hierarchical fields First body 2 p produces the position field of body 2 which is a vector Next the r produces a rotation value 1 e the orientation of the body from the position field body 2 body type body 2 p vector type body 2 p r number type The following is a list of all fields with the type of value that each field produces See the following sections for field descriptions Type Type Field Returned Vector X number Sy number et number Body p Vector V Vector a Vector mass number moment number charge number staticfric number kineticfric number elasticity number cofm Point width number height number radius number vertex n x number vertex n y number Point p Vector V Vector a Vector B 4 Fields B 5 offset Vector body Body force Vector Constraint length number dp Vector dv Vector da Vector p1 Point p2 Point force Vector Output x number syi number y2 number wy number y4 number Input number Vector Fields X y r Notice that position velocity and acceleration are always returned as type vector in the above table For example point 4 a acceleration of point 4 body 3 v velocity of mass cen
244. les C 8 Appendix C Useful Tips and Shortcuts I Cannot Select Points Inside Body Objects Point objects are always drawn in the graphics layer below that of body objects When the fill pattern of a body object is set to transparent such as polygons and circles imported from DXF files you can still observe the points that are actually covered by the body But you cannot move the mouse over to those points and click on them You can select the points by using box select Start the box select from somewhere outside the body object covering the points and draw a box select rectangle so that the desired points are within the box No body object will be selected unless it is completely within the boundaries of the box select rectangle I Cannot Drag Points Constraint Controls or Meters The Lock Points and or Lock Controls features in the View menu may be turned on Lock Points prevents points from moving relative to their mass objects whereas Lock Controls prevent meters and controls from being moved at all Use the Lock Points feature when editing complex linked figures or mechanisms These features prevent you from inadvertently changing a joint s geometry or offset by dragging a point Points Not Highlighted When Selected If you select multiple points that directly overlap they do not appear highlighted as if neither point is selected This is because Working Model 2D uses a fast exclusive or algorithm to draw selection high
245. lf knows that the unit change has taken place and multiplies output 6 y1 by an internal conversion factor of 1 60 does not appear in the Properties window to display the data properly in minutes If you edit this field this internal conversion factor is reset to 1 0 Suppose you edited time 60 0 to time 60 0 by inserting a white space between time and then the meter will display 60 0 after 1 minute elapsed while output 6 y1 would still show 60 0 after 1 minute The conversion constants are internally stored with full precision but are displayed with the significant digits given in the Numbers and Units dialog default is 3 digits Editing an equation containing conversion constants will cause those constants to be part of the equation string with the precision shown instead of being internally stored with full precision Let s look at our example equation Even after the units have been changed to inches and minutes internally the equation is still stored as Length time sec 5 ft yet displayed as Length 12 time 60 5 in If we edit the equation even by just removing blank spaces it is now internally stored as Maximum Equation Length 10 2 Linking Controls to Objects 329 Length 12 time min 60 5 in Note that if some of the constants had multiple significant digits modifying the equation could lead to slightly different answers in the simulation See also Precision of Met
246. lighting You can verify that the points are selected by choosing Properties from the Window menu The Properties window will show mixed selection in the Selection pop up menu Multiple points may overlap in the following circumstances e When you split a pin joint the result will be two points that lie directly on top of each other Each point will be connected to a different body e When you import a CAD drawing the original may have had multiple overlapping points Since Working Model 2D preserves each point individually when importing files such points may not appear highlighted when you selected them APPENDIX D Scripts Figure D 1 Before Running Flexbeam D 1 The Flexbeam Script Flexbeam enables users to simulate the behavior of flexible beams Introduction Flexbeam replaces a selected rectangular body with a set of smaller rectangular ele ments attached with rotational springs Flexbeam chooses values for the spring con stants which depend on the material and geometry of the selected rectangular beam and creates an assembly that approximates a flexible beam Figure D 1 and Figure D 2 show a sample document before and after running Flexbeam respectively Notice that Flexbeam works on beams with an arbitrary orientation and maintains constraint relationships An undo script called Unflex restores beams to their origi nal rigid form D 2 Appendix D Scripts Figure D 2 After Running Flex
247. ll identify the body giving its identification number and type Figure 6 13 204 Chapter 6 The Workspace Figure 6 13 Working Model Untitled1 lolx thy File Edit World View Object Define Measure Script Window Help lj x olsa amp ESEE amp 2 Run Stop ii Reset Status bar identifying a square body Windows Status bar Friday August 02 96 09 12 AM 7 If the pointer is over a tool in the Toolbar the Status bar will identify it See Figure 6 14 Note that the pointer is over the Circle tool On Windows systems a brief description of the tool under the pointer also appears in a small tooltip box Figure 6 14 Status bar identifying a tool e lt a MacOS Figure 6 15 Default units Figure 6 16 Numbers and Units dialog 6 3 Numbers and Units 205 6 3 Numbers and Units Each new simulation document that you create defaults to the SI metric unit system The following units are the default values Working Model 2D internally converts all quantities to metric units before performing any calculation However you can have Working Model 2D display the results in various unit systems You are free to choose the unit system most appropriate to your simulation so you can enter and monitor values in the units system To specify a different unit of measurement for any quantity 1 Choose Numbers and Units from the View menu
248. lly defined in physics textbooks as F mg where g 9 81m sec Working Model 2D models this force with the same formula To see this formula select Linear Earth Gravity from the Samples menu in the Force Field dialog box You will see the following formula Fy self mass 9 81 This force is applied to each massive object in the simulation The term self mass means that each body should use its own value of mass when calculating the amount of force applied to it Self is equal to each body in turn as the global force is applied to each body one after the other A pair wise global force is applied to each pair of bodies rather than to each body individually This means there will be many more forces occurring in the simulation A simulation with 10 bodies will have 50 pair combinations of bodies A good example of a force that affects objects in a pair wise fashion is the gravitational force between planets To change force fields in the world 1 Choose Force Field from the World menu The Force Field dialog appears as shown in Figure 6 23 Force Field Eg eor Sample Force fanaa C Pairwise f Field eooo Fy P j EOe 2 Click the Sample menu to see samples of some global forces You will see sample formulas for the following global forces Linear Gravity Planetary gravity 212 Chapter 6 The Workspace Shift select Selection Rectangle Box select Magnetic field E
249. long transient state which may take a long time to compute 1 Choose Preferences in the World menu The Preferences dialog appears Figure 8 7 2 Put a checkmark in the check box Loop when tape player is full Essentially the simulation will run forever or until you stop it If you want to set an automatic pause in the simulation see Controlling the Duration of a Simulation on page 282 Using Working Model Basic you can program Working Model 2D to calculate multiple simulation runs while taking measurement data and saving the results Please refer to the accompanying Working Model Basic User s Manual for information on the programming language Minimizing Collisions You can control whether any two objects are meant to collide By default Working Model 2D makes all objects collide except those that are directly connected to each other with a joint or gears You have complete control for designating that multiple objects do not collide with one another See 3 6 Controlling Collisions among Bodies for instructions 284 Chapter 8 Running Simulations If your simulation has many objects that overlap Working Model 2D will compute collision forces for each pair of overlapping objects The computation is not only a waste but also can cause slow and unstable simulations Make sure that only the objects that you want to collide are actually designated to collide For a model composed of many objects for exam
250. lt reference frame is the background or world For example in a model of the solar system the sun is commonly used as the reference frame it essentially is and the planets rotate around the sun If the earth is chosen as the reference object the effect is similar to the pre Copernican view of the solar system The earth will be viewed as a stationary object on the workspace while the other planets and the sun revolve around it NOTE In Working Model 2D defining a frame of reference provides a point of view during the simulation and does not affect the coordinate values of any object in your model All numerical measurements in Working Model 2D remain the same no matter what frames of reference you define Using Reference Frames There are two general uses for reference frames First you can use reference frames to quickly jump between various views of a simulation A reference frame contains the current settings of Scroll and Zoom Keyboard equivalents allow you to toggle quickly between reference frames Each new reference frame is given a keyboard equivalent from 0 9 You can see the keyboard equivalents in the View menu You can also use reference frames to watch a simulation from any object s point of view You can attach reference frames to points to the system center of mass and to bodies When you make a new reference frame from an object that rotates you will see the world from the object s point of view The worl
251. ly opened in Working Model 2D are listed above Exit Windows or below Quit MacOS This list is preserved even after you quit Working Model 2D and restart it at a later time The Edit Menu Undo reverses the last action performed in the simulation The menu item shows the last action taken as shown in the figure on the left or shows Can t undo if the action is irreversible Cut removes the selected object s from the document and places them on the clipboard Copy places a copy of the selected object s on the clipboard Paste places a copy of the object s on the clipboard into the active document Clear MacOS or Delete Windows removes the selected object s from the simulation without placing the contents onto the clipboard Select All selects all of the objects in the active simulation window Duplicate creates a copy of the selected object s Reshape if active allows click and drag editing of polygons curved bodies and curved slots to change their shapes A checkmark appears before the menu item when it is active Player Mode is a toggle command that reduces or expands the menu structure of the Working Model 2D program For more information on Player Mode see 8 7 Simulation Modes The World Menu Gravity causes the Gravity dialog to appear allowing you to select and control various types of gravity within the active simulation 2 2 Working Model 2D Menus 49 Air Resistance causes the Air
252. many rows as necessary to store the data from the simulation with most animation frames If some of the simulations lasted for fewer frames than others the remaining rows at the bottom of the data columns are filled with minus signs to match the length of the longest columns If new meters are created while you are experimenting the data from earlier experiments will have blank columns to represent the fact that the meters did not exist at the time All such columns are filled with minus signs This way the file would contain sets of columns where each set represents one simulation run and all the sets have the same number of data columns Since complete simulation histories have to be maintained for each run memory usage can be quite high when Retain Meter Values is enabled This feature is disabled by default for optimal memory usage and Working Model 2D uses an automatic refresh mechanism to discard simulation histories whenever anything that could affect the simulation result is modified such as changing object properties and World settings For other memory optimization reasons the Retain Meter Value feature has a few limitations as follows e Every modification to a document requires that Working Model 2D check against the entire history data For example deleting a meter needs to erase the history of the meter data For this reason you may notice that a modification to a document progressively slows down as you accumu
253. mbers and returns the sum Takes two numbers and returns the difference Takes two numbers and returns the product Takes two numbers and returns the quotient Takes two numbers and returns the remainder of the first value divided by the second Takes two numbers and returns the first value raised to the power of the second value Takes two numbers and returns the value if the first value is greater than the second value Otherwise returns the value 0 Takes two numbers and returns the value 1 if the first value is less than the second value Otherwise returns the value 0 Takes two numbers and returns the value 1 if the first value is greater than or equal to the second value Otherwise returns the value 0 Takes two numbers and returns the value 1 if the first value is less than or equal to the second value Otherwise returns the value 0 Takes two numbers and returns the value 1 if the two values are equal Otherwise returns the value 0 This operator does not assign any value to the left side of the equation The formula body 3 p y 3 B 12 Appendix B Formula Language Reference lt gt not equal Arithmetic Operators returns 1 if body 3 s y position equals 3 0 This formula does not set any values of body 3 s position Takes two numbers and returns the value 1 if the two values are not equal Otherwise returns the value 0 Operator Precedence Use parentheses to set the order of equation evaluation
254. mbers can accumulate The number le 19 means 0 0000000000000000001 This round off is so small that it will not affect your work If you wish you can change the numeric display settings in the Numbers and Units dialog to make this number appear as 0 000 Choose the Fixed decimal point display type You can also replace numbers like 1e 19 with the value 0 0 if you are bothered by them Precision of Meter Data in Non S Units Meters which measure forces energy or power can be slightly less accurate in non SI unit systems than they are in SI For example suppose you create a meter to measure the translational kinetic energy ofa body Working Model S ene 2D uses kad as the formula The SI unit system is designed so that 1 J Joule 1 kg m s However in the English unit system where Btu British Thermal Unit is used to measure energy 1 Btu is not equal to 1 Ib ft s Therefore if a meter is to report correct values in Btu while using im to compute energy a special conversion mechanism needs to be used As a result of this conversion the formula in the translational kinetic energy meter appears as 9 49e 4 0 5 body 1 mass 0 454 sqr body 1 v 0 305 where the constants 9 49e 4 0 454 and 0 305 convert Joule to Btu pounds to kilogram and feet to meters respectively Since these constants are generated with the number of digits specified in the Numbers and Units dialog meters may present slight discrepa
255. mbined with an if function as follows if time lt 100 20000 100 time 10000 Turning Constraints On and Off The above equation accurately describes the rocket s mass for all times Any forces that are related to the changing mass of the rocket should also correspond to the fact that after 100 seconds all of the fuel in the rocket is burned up There are various ways to do this In the Properties window of the force you are using for the rocket s thruster you could enter the value of some force like this if time lt 100 5000 0 This means that if time is less than 100 seconds the force will exert 5000 N Otherwise the force will exert 0 N Working Model 2D also provides an easy way to turn constraints on and off using the Active when field of the force Properties window To turn the force off after 100 seconds simply enter 5000 as the value of the force and enter time lt 100 in the Active when field of the Properties window for the force see Figure 10 3 Figure 10 3 Active When field of a constraint 10 3 Customizing Objects 333 Constraint 3 Spring Sprin Force fk M aa K inputs N m length 1 310 m current 1 910 m Active when field Active when M Always Positioning Constraints Relative to Body Geometry You can use the formula language to create a constraint whose endpoint positions are defined relative to the geometries of the bodies For example you can
256. metric data are transferred via the Clipboard as a list of vertex coordinates The data are text consisting of a list of number pairs x y delimited by a tab Each number pair is on a separate line Almost all spreadsheets or text editors can import text data by pasting it from the Clipboard CAD programs may require different methods such as text ASCII data input To transfer polygon or curved body data from Working Model 2D to another application 1 Select the polygon or curved body and choose Geometry from the Window menu 86 Chapter 3 Bodies Pasting a Polygon or Curved Body from Another Application Figure 3 22 Microsoft Excel spreadsheet showing point coordinates The Geometry window appears and shows the vertices 2 Choose the coordinate system to represent the data points Shape or World coordinates are available 3 Click the Copy button in the Geometry window The point coordinates are copied to the Clipboard 4 Switch to the target application and use Paste from its Edit menu to paste the data points Each row of data represents a pair of point coordinates separated by a tab To transfer polygon or curved body data from another application to Working Model 2D 1 Select the table of points in source application The data should be tabulated in a two column format where each row represents a pair of point coordinates delimited by a tab Otherwise Working Model 2D assumes a list of numbers to be sequen
257. mmand Z MacOS or Control Z Windows will undo the change and restore the recorded frames If you make more than a single change you will lose your old initial conditions and the frame counter will reset to frame zero You will not be able to reset back to the initial conditions of the simulation prior to the editing Change Cursor to Stop Sign During Run Working Model 2D normally allows you to stop a simulation by clicking anywhere within the workspace The cursor changes to a stop sign while the simulation is running 258 Chapter 8 Running Simulations If you uncheck this checkbox the cursor will not change to a stop sign while the document running Clicking on the document still stops the simulation Regardless of this option you can always stop a simulation with the Stop button on the Toolbar the Stop button on the Tape player controls or the Stop menu item in the World menu Loop When the Tape Player is Full By default Working Model 2D stops a simulation when there is not enough memory available to store further frames in the tape player However you can loop when the tape player becomes full Additional frames will be computed and stored on top of currently stored frames The simulation will run forever or until it is stopped by the user Resetting in this state will still return to the initial conditions Dragging the tape player s frame counter box will show the most current calculated frames See also Run
258. mmary of how collisions are modeled in Working Model 2D You may find this section helpful in understanding the measurement data obtained from Working Model 2D simulations How Working Model 2D Simulates Collisions Since Working Model 2D numerically integrates in discrete steps bodies may overlap with others by a small amount For instance two bodies may be close to each other but apart at time step n but their velocities may cause them to overlap each other in the next frame at time step n 1 A 20 Appendix A Technical Information Collision Impulse Working Model 2D detects collisions geometrically by finding intersections between bodies When bodies are colliding Working Model 2D computes the forces necessary to prevent interpenetration Based on these forces Working Model 2D calculates the new velocities of the bodies and continues the simulation In variable time step mode you can define the error tolerance to bound the amount of overlap see Simulation Error Tolerances on page A 17 Working Model 2D automatically uses appropriately small integration steps near collisions and maintains the overlap to be within the tolerance which is specified as the Overlap Error in the Accuracy dialog The Overlap Error is used to detect collisions in fixed time step mode as well but collisions may exhibit overlap greater than the tolerance due to the fixed time step Once a collision is detected Working Model 2D computes forces
259. move is accomplished Sometimes a drag or rotation may be inconsistent with the constraints that are imposed For example if the mechanism in Figure 5 9 was dragged farther and farther to the right it would eventually stop following the pointer In this case a compromise between the constraints and the move is reached but the constraints are always respected 180 Chapter 5 The Smart Editor Figure 5 10 A dragged pin joint can alter your mechanism Clicking and Dragging The Smart Editor is designed to follow the click and drag paradigm as much as possible When you are dragging a mechanism the Smart Editor strives to minimize the distance between the initial click point on the mechanism and the current pointer position without breaking the constraints NOTE The Smart Editor does not account for collisions Lock Points and Lock Controls Lock Points in the View menu provides a safety feature while editing a model you constructed When this option is active Working Model 2D prohibits all the points including pin joints and endpoints of constraints from being dragged repositioned by the mouse Consider the following example As shown in Figure 5 10 you could accidentally select and drag the joint p connecting the two rectangles while you are trying to edit the model by modifying the configurations of the rectangles A or B You can prevent such mistakes by activating Lock Points When activated the Lock Points feat
260. mulas see Chapter 10 Using Formulas You can edit the name labels as well as the formulas in the Properties window Figure 7 7 Appearance window with a meter selected 7 1 Meters 229 The x axis measures time by default As more data is added to a graph the scale of the graph is reduced to allow the full run of your simulation to be displayed Quantities on the y axis are also in an auto scale mode by default You can override the auto scaling by removing the check from the check box When you turn off auto scaling the scale is defined by the values in the minimum min and maximum max boxes for each quantity If you have already run your simulation these values contain the minimum and maximum values that were computed by the auto scaling feature and are a good starting point for adjusting your own scale NOTE Ifthe meter measures multiple values y1 y2 the y axis scale and the position of x axis and the grid lines telates solely to the first output yl The other outputs are scaled according to the minimum and maximum values shown in the Properties window but their y coordinates or x axis intersect cannot be viewed Changing Line Colors on a Graph There are many display options for meters that are shown as graphs You can show or hide grid lines labels axes units and the frame of each graph You can select a line color and name label for each graphed property Bl soe sr tar Se amp Fram
261. mulation e Replay a simulation e Control the speed and accuracy of a simulation e Save a recorded simulation e Create Player documents e Specify a reference frame Track objects 250 Figure 8 1 Run Controls Chapter 8 Running Simulations Print 8 1 Running a Simulation To run a simulation 3 Click here to run MacOS V a Run stop i Heset Windows Click Run in the Toolbar or choose Run from the World menu See Figure 8 1 On MacOS systems the Run button turns into the Stop button while running a simulation Click Stop to stop the simulation or choose Stop from the World menu To resume the simulation click the Run button Click the Reset button to rewind the simulation Once you have run a simulation the calculations are stored in the tape player Ifyou run the simulation again without making any changes it will play much more quickly 8 2 Stopping a Simulation You can stop a simulation in various ways Click Stop in the Toolbar Click the Stop icon on the Tape player controls Click anywhere within the window if the cursor appears as a stop sign Choose Stop from the World menu Click on a Stop menu button if one exists Figure 8 2 Tape Player controls 8 3 Using the Tape Player Controls 251 Automatically stop the simulation using the pause feature To pause a simulation see Pausing on page 254 of this chapter MacOS only Press Command and period from th
262. mulation in Working Model 2D We also recommend that you use POLYLINEs wherever possible when describing rigid body objects in a CAD drawing Since POLYLINEs are automatically converted to polygons at the DXF import time you will benefit from a faster importing process for example importing 20 lines takes longer than importing a single polygon consisting of 20 sides Converting Lines into Physical Objects Once imported into Working Model 2D you can convert lines to either polygons or curved slots The curved slot conversion may come in useful for acam design for example To convert lines into a polygon 1 Select all the lines that will form the polygon We recommend that the lines form a closed polygonal shape If the lines have gaps between them Working Model 2D will add line segments where necessary to form a closed shape You can drag or resize individual lines to improve the arrangement of the lines You have to use the mouse to select lines since for speed performance reasons no lines appear in the object list of the Properties window like the Working Model 2D objects such as bodies and constraints 2 Select Convert to Polygon from the Convert Objects item in the Object menu Working Model 2D generates a polygon A line converted polygon initially has no fill pattern i e they appear transparent This way you can still see the objects such as points and lines that may be otherwise hidden behind the polygon You ca
263. n Figure 4 26 Coordinates bar for a damper H 4 6 Dampers 117 4 6 Dampers A damper exerts a force that depends on the difference in velocity between its two endpoints A damper applies no force at all when the endpoints have the same velocity i e equal in magnitude and direction For example you can use a damper to simulate a shock absorber of an automobile suspension Creating a Damper To create a damper 1 Select the Damper tool from the Toolbar 2 Position the mouse pointer where you would like to define the first endpoint 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The Coordinates bar shows the coordinates for the two endpoints of the damper as shown in Figure 4 26 Both coordinate values are given in reference to the body to which each point is attached x _ 1 000 m y _0 000 m x _2 000 m y _1 000 m b C O 0K m l l First Point Second Point Damper Properties To view and modify the properties of a damper select the damper and select Properties from the Window menu 118 Chapter 4 Constraints Damper Constant Damper Type Figure 4 27 Choosing a damper ty
264. n Windows systems The Standard Toolbar is not implemented on MacOS systems where these commands are accessed through the Apple File and Edit menus gt Stee f ee l v br 0 Chapter 2 Guide to Tools amp Menus The New button creates a blank untitled document using the current default settings The Open button opens a previously created document You can have multiple documents open at once The Save button saves the currently active document to disk If the active document was saved previously it is updated The Cut button removes the selected object s from the document and places them on the clipboard The Copy button places a copy of the selected object s on the clipboard The Paste button places a copy of the object s on the clipboard into the active document The Print button causes the Print dialog to appear allowing you to print your simulations The Help button presents a list of the main Help options More detailed information can be obtained by traveling down the help structure Edit Tools The Arrow tool is used to select an object or a group of objects or to drag a selected group of objects on the screen Pressing the space bar will automatically select the Arrow tool The Rotate tool is used to rotate an object or a selected group of objects Objects can be rotated about their center of mass about pin joints or about measurement points When using the Rotate tool you will see a line
265. n Reshape mode using the Reshape option in the Edit menu 2 Select the curved slot so that its reshape handles appear 3 Select the reshape handle corresponding to the control point you want to delete The handle will be highlighted 4 Select Cut from the Edit menu or press the delete key 160 Chapter 4 Constraints Creating Slot Joints from Elements You can build a slot joint by combining a point or a square point and a slot using the Join button Specifically you can e create a pinned slot joint by joining a point and a slot or e create a keyed slot joint by joining a square point and a slot straight slots only NOTES e Ifyou attempt to join a square point and a curved slot the resultant combination will be a pinned curved slot joint e No more than one point round or square can be attached to a single slot If you want multiple points to be attached to the same slot you will need to duplicate the slot using for example Duplicate in the Edit menu as many times as the number of points you need to have attached For more information on joining elements and splitting constraints see 5 1 Joining Elements and Splitting Constraints To build a slot joint from primitive elements F Fal 1 Create a point element and a slot element on separate bodies Use the point tool in the toolbar to create the points Use a square point if you wish to create a keyed slot joint straight slots only
266. n change the fill pattern through the Appearance window of polygons See 3 3 Body Appearance Lines to Curved Slot Conversion Polygon to Curved Slot Conversion Attaching points to bodies 9 4 Importing CAD Geometries as DXF files 297 3 _ If the polygon is not of the desired shape you can either reshape the polygon see Reshaping Polygons and Curved Bodies Graphically on page 64 or you can turn the polygon back into lines re arrange the lines and start again with step 1 To turn the polygon into lines select the polygon then select Convert to Lines from the Convert Objects submenu in the Object menu The algorithm that converts lines into polygons tries to turn the lines that have been selected into a closed polygon Below is a simplified description of the algorithm employed in Working Model 2D 1 Pick an endpoint from one of the lines 2 Find the other endpoint of the same line 3 Look for the closest endpoint that has not already been converted 4 If the closest endpoint is farther than a certain tolerance add a new line 5 Loop back to 2 until all lines are exhausted To convert a line into a curved slot follow the same procedure as above The endpoints of the line segments are converted into control points for the curved slot This feature is useful for example when you want to import a cam design Polygons can be converted into a closed curved slot through two simple steps 1 Select a poly
267. n choose from standard metric SI units such as kilograms meters and radians standard English units such as yards feet inches degrees seconds and pounds or other units e g light years Working Model has a formula language system for creating arithmetic and mathematical expressions including conditional statements that is very similar to the formula language used in Microsoft Excel and Lotus 1 2 3 Any value can be a formula rather than a number To simulate a rocket you can write an formula for its mass so that it decreases as fuel is spent Using trigonometric functions you can write a formula that simulates the force generated by an actuator that induces an oscillation Player mode provides a window with a limited menu bar and no toolbar leaving more room to display the simulation You can switch between player mode and the standard edit mode by selecting a menu command Player documents are useful for people who are unfamiliar with Working Model s modeling capability You can track all objects or limit tracking to selected objects Individual objects can leave tracks of their outline center of mass or vector displays You can also connect tracks with lines The simulation world consists of two layers one for user objects such as meters and one for physical objects such as bodies and constraints Full control of which objects collide is provided Working Model provides a complete set of vector display capabilities fo
268. n if being created that is 100 frames long several of these frames will exactly specify the position of objects The position of objects at other frames will be created by tweening or interpolating between keyframes Working Model 2D simulations specify the exact position of all objects at every frame When Working Model 2D motion is used in an animation system every frame becomes a keyframe At every frame numbers exactly define the x y and rotational position of all objects Working Model 2D motion data can be used in any animation package that allows editing of keyframe data Some animation packages such as Electric Image allow you to paste in keyframes as rows of tab delineated data Some animation packages allow you to import files that contain motion information such as Wavefront mov files To import motion data to an animation package not directly supported by Working Model 2D you will have to consult your owner s manual as to the best way of bringing in motion data Motion data generated by Working Model 2D is two dimensional The Working Model 2D workspace is a plane and all objects are flat Each object is defined by three positional parameters x position y position and rotation 3 D animation packages can use Working Model 2D motion information 3 D animation packages describe the position of objects with six positional coordinates Three positional coordinates x y and z describe the object s location Three rotatio
269. n in the Toolbar To create a circle see Figure 1 4 Figure 1 4 Working Model Untitled1 Begs C R ty Eie Edit World View Object Define Measure Script Window Help lel x reating en R a A Pje Run Stop ii Reset Click here to select the circle tool Press and hold down the mouse button here drag to here and release the mouse button m y 0 900 m 0700 m goo H f Friday August 02 96 09 12 AM 4 C3 1 Click the Circle tool 2 Position the pointer at any starting point in the blank area of the screen Optional Method for Creating Circles oj Resizing Objects with the Mouse 1 4 Setting Up a Simple Simulation 7 The pointer changes from an arrow to a crosshair This means you are ready to create an object Click and hold the mouse button and drag the mouse until the circle is the size you want Release the mouse button A line appears inside the circle During an animated sequence this line indicates the circle s rotational orientation There is another way to create circles If you are used to using a CAD applications you may want to create a circle as follows 1 2 Click the Circle tool Position the pointer at any starting point in the blank area of the screen Click the mouse button and release it Drag the mouse Note that the circle is being resized Drag the mouse until the circle is the size you want Release the mouse button Changing the Size
270. n the gear ratio For circular gears the gear ratio is computed as the ratio of the radii of the bodies In the case of two circular gears in contact as shown in Figure 4 37 the point of contact is the point where the gears make contact If the two gears were separated however the virtual point of contact would lie somewhere between the two gears Figure 4 41 below shows examples of how the points of contact indicated by the arrows are located for several pairs of external and internal gears For example given two gears that have the radial ratio of 3 to 1 Working Model 2D computes the default gear ratio as 3 0 Then as shown in Figure 4 41 the point of contact for each pair of gears is located so that the ratio a b is always 3 0 132 Chapter 4 Constraints Figure 4 41 Examples of computing point of contact for gear pairs External Gears AA a a Internal Gears The driving gear exerts a gear force on the driven gear in the direction perpendicular to the line connecting the two Working Model 2D computes the force necessary to maintain proportional rotation angular velocity and angular acceleration on both disks at the point of contact Since all gears are simulated according to this principle you can create gears that are more generalized than what one might expect in the physical world Specifically e gears need not be touching each other and e gears need not be disk shaped NOTES ON GEARS e All
271. n the polygon or curved body to select it 2 Choose Geometry from the Window menu The Geometry window appears as in Figure 3 18 A crosshair labeled FOR will appear in or near the body to indicate its frame of reference GEESE Geometry iiit Polygon area 1 780 m 2 com auto O x offset 0 000 i y offset 0 000 i C Curved body Display in oO Shape coordinates World coordinates Table _ 3 4 Body Geometry 83 3 Enter new coordinates for the vertex The object will change shape as you enter new coordinates Notice how each vertex is highlighted on the object as you scan down the vertex table with the tab key Adding a Vertex To add a vertex 1 Select the polygon or curved body 2 Choose Geometry from the Window menu The Geometry window appears as in Figure 3 19 3 Select a vertex that will be adjacent to the new point Click to put the blinking cursor in either coordinate of the vertex or highlight one of the coordinates Figure 3 19 SEE E i Adding a vertex i Polygon area 1 780 m 2 o Curved body Display in oO Shape coordinates World coordinates Table _ y x Select this vertex 1 100 4 Click the Insert button in the Geometry window A duplicate vertex will be created in the vertex list The shape of the object will not change until you edit the duplicate See Figure 3 20
272. n to Start Working Model 2D Open and run the sample simulation documents packaged with the program Create a new simulation document Draw a circle and set its initial velocity Run your simulation Display a velocity meter Display a vector Track a circle as you run your simulation Create and edit a complex linkage Create controls and action buttons Save your simulation 1 1 Starting Working Model 2D Please refer to the Getting Started booklet that accompanies this manual for installation instructions if you have not already installed Working Model 2D on your system Double click the Working Model 2D icon to start the program Working Model 2D starts up and opens a new untitled window Your screen will look something like Figure 1 1 2 Chapter 1 A Guided Tour Figure 1 1 Working Model Untitled iol Untitled Working Model 2D ES E U a E a ae Se sala Window Coordinates bar Tape player controls Status bar m E Friday August 02 96 0812 AM Windows T File Edit World View Object Define Measure Script Window 2 a a Ej untitled Ej Run p Res i A m ofa Status bar TA apa Toolbar e Join Split o o S Coordinates bar A e Tape player controls 4 pa x m y aje ijih Trash MacOS 1 2 Steps for Creating a New Simulation 3 The new untitled simulation document appears in its own window You will see t
273. n to compute a velocity and position one time step later Further Working Model 2D incorporates a scheme to check and correct its prediction This process is then used again to find a new velocity and position For example numerical integration for linear motion proceeds as follows 1 Nowatt 0 Calculate a using force equations 2 Use ato calculate the new velocity vat t yt Vi 4 Z 4 Att v _ 69 approximating v faat Vo 3 Use vto calculate the new position x at t t X 4t Xr 0tYr 0 At This process is called numerical integration There are many methods for numerically integrating acceleration to calculate new velocity and position terms at a later time The method shown above is known as the Euler method one of the simplest numerical integrators available Working Model 2D features another more accurate numerical integrator called Kutta Merson method See Integrators on page A 15 for more discussion on numerical integration A 8 Appendix A Technical Information A 4 Time Step and Performance The size of a time step is a critical parameter in fixed step numerical integrators because it affects the speed and accuracy of the results significantly In general a small time step produces more accurate simulation results but requires more computational effort per given time period than a larger integration time step Choosing a Proper Time Step Choosing a time step for a particular problem is very di
274. n window Toolbars Windows checkboxes allow you to show or hide each of the toolbars shown in Figure 2 2 Figure 2 3 and Figure 2 4 In addition you can show or hide a Simple toolbar consisting of several of the most commonly used tools Grid Snap if active causes all objects to automatically snap to predefined grid lines in the workspace A checkmark before the menu item indicates that it is active Object Snap if active causes all point elements including constraint endpoints to automatically snap to predefined snap points of bodies such as their frame of reference and vertices as you bring them closer to these points A checkmark before the menu item indicates that it is active System Center of Mass if active shows the center of mass of all bodies as an X in the simulation window A checkmark before the menu item indicates that it is active Lock Points if active prevents points from being moved on bodies during editing For more information about Lock Points see Lock Points and Lock Controls on page 180 A checkmark before the menu item indicates that it is active Lock Controls if active locks all control objects buttons sliders and meters to the background Selecting resizing and moving controls is prevented A checkmark before the menu item indicates that it is active Numbers and Units causes the Numbers and Units dialog to appear allowing you to specify a simulation s system of me
275. nal coordinates describe the object s orientation When exporting motion data into a 3 D animation package 3 of the 6 motion coordinates are not used The x and y positional data from Working Model 2D is used directly in the 3 D application The rotational position data from Working Model 2D is used to define rotation about the z axis in the 3 D application 312 Chapter 9 Importing and Exporting Files and Data To export motion data into a 3 D animation program 1 Create a Working Model 2D simulation that describes the planar motion you wish to achieve This could be a falling stack of blocks or a car rolling down a hill Export positional data from Working Model 2D as either rows or columns Export complex shapes from the Working Model 2D simulation as DXF geometry files Create objects in your 3 D animation package that correspond to the objects in the Working Model 2D simulation You may wish to use Working Model 2D DXF files as a template in creating objects For simple simulations composed of squares and circles you will probably be able to directly create objects in your 3 D animation package Edit the exported object positions with a word processor or spreadsheet and then paste rows or columns of keyframe data into the corresponding object in your 3 D animation application 9 11 Exporting PICT and PICT Animation MacOS only PICT files are the standard graphics format for the exchange of picture data between M
276. ncies between the SI and non SI unit systems You can increase the number of sub decimal digits in the Numbers and Units dialog to increase the precision of these conversion factors generated by Working Model 2D A 26 Appendix A Technical Information A 9 Technical References Interested readers may wish to refer to more comprehensive documentation on numerical methods and mechanics Shown below are but a few books of the vast array of literature devoted to the subject matters On Numerical Methods Leslie Fox Numerical Solution of Ordinary and Partial Differential Equations Addison Wesley 1962 Robert W Hornbeck Numerical Methods Prentice Hall 1961 Gene H Golub and James M Ortega Scientific Computing and Differential Equations An Introduction to Numerical Methods Academic Press Inc 1992 C William Gear Numerical Initial Value Problems in Ordinary Differential Equations Prentice Hall 1971 Germund Dahlquist and Ake Bj rck Numerical Methods Prentice Hall 1974 On Mechanics Thomas R Kane and David A Levinson Dynamics Theory and Applications McGraw Hill Publishing Company 1985 Ferdinand P Beer and E Russell Johnston Jr Vector Mechanics for Engineers McGraw Hill Book Company 1977 Nicholas P Chronis Mechanisms amp Mechanical Devices Sourcebook McGraw Hill Inc 1991 Edward J Haug Computer Aided Kinematics and Dynamics of Mechanical Systems Allyn and Bacon 1989 A Bedford
277. nd Color Coordinates Electrostatics Exit xl 2 Choose a command from the list You can scroll down the list or enter the first letter of the command For finer selection you can also use the arrow keys to move the list up or down one item at a time 3 Click OK The button will perform its menu command when clicked Linking Multiple Documents with Menu Buttons You can build multi document workbooks by creating menu buttons that close the current document and open a new document With menu buttons you can link simulations together to build sequential activities To link several simulation documents MacOS 1 Create the simulation documents you want to link and for convenience store them in the same folder 2 Open the first document 3 Choose Menu Button from the Control menu A dialog box appears asking you to choose the command you want this button to execute 7 4 Vectors 241 4 Choose Open from the File menu and then select the name of the document you want the button to open when pressed The Open button appears as a user object on the workspace When you click the Open button inside the current simulation the simulation closes The simulation you selected when creating the Open button will open Windows 1 Create the simulation documents you want to link and for convenience store them in the same directory If Working Model 2D cannot find a file in the local directory
278. nder into the screen For a square multiply k by W width of the box into the screen To activate air resistance 1 Choose Air Resistance from the World menu Air Resistance x F k velocity cross section High speed E 0 300 kg m s 2 Select Low speed or High speed as the model for air resistance Low speed air resistance introduces a force proportional to an object s velocity High speed air resistance introduces a force proportional to the square of an object s velocity 3 Enter a value to adjust the magnitude of air resistance Electrostatics Each body in Working Model 2D has a charge By default each object has a positive charge of 1 0 x 104 Coulombs This charge is enough to produce interesting results between objects in the default physics workspace although it really is an extreme amount of charge You can model electrostatic forces between objects by turning on Electrostatics You will also need to set the charge values of various bodies to values other than 0 to see the effects of charge 210 Chapter 6 The Workspace Figure 6 22 Electrostatics dialog Electrostatics works as if all of the charge of a body were concentrated at its center of mass Charge is not distributed over the surface of a body To change electrostatics in the world 1 Choose Electrostatics from the World menu The Electrostatics dialog appears as shown in Figure 6 22 Electrostatics x 124piEof8 990e
279. nditions Automatically Since this option is turned off by default Working Model 2D does not perform computations until you start a simulation The meters and graphs are initially blank at frame zero the initial conditions Meters and vectors indicate meaningful results at frame zero only after you run and reset a simulation at least once When you turn on this option Working Model 2D automatically calculates the results of frame zero after every editing operation sketch drag rotate resize This calculation may produce a slight delay between editing operations in complex simulations Also Working Model 2D de selects every object after each editing operation The advantage of automatic frame zero calculation is that meters and vectors are immediately displayed with the proper values at all times This is especially useful for statics problems where vectors are being used to show forces After every small adjustment to a simulation the statics problem will be recalculated and the proper force vectors will be displayed Prevent Editing Except at Initial Conditions Working Model 2D normally forces you to reset your simulation to frame zero the initial condition before making any changes in the middle of a simulation Resetting the simulation helps to maintain the initial conditions you may have set up Alternately Working Model 2D can allow you to make changes in the middle ofa simulation If you make a single change pressing Co
280. ndpoint it will be attached to the background The Coordinates bar shows the coordinates for the two endpoints of the separator and its length as shown in Figure 4 45 Both coordinate values are given in reference to the body to which each point is attached x _ 4 500 m y _2 200 m x _ 1 600 m yl 0 100 m 1__2 285 m First Point Second Point Length Separator Properties Separators behave like ropes except that they act in the opposite direction Ropes prevent their endpoints from being greater than a certain distance apart separators prevent their endpoints from being less than a certain distance apart 138 Chapter 4 Constraints Length Current Length Elasticity This is the actual length of the separator when the endpoints are at their closest position The endpoints of a separator can never be closer than this length If you specify the length as a numeric constant the separator will be modified to the specified length immediately The Smart Editor see Chapter 5 The Smart Editor will automatically modify the rest of the model to accommodate the specification If you use a formula expression to specify the length the formula will be immediately evaluated as t 0 and the separator length will be modified accordingly Again the Smart Editor will automatically modify the rest of the model to accommodate the specification This is the current length of the separator measured as the sh
281. ng a DXF file Working Model 2D creates a body a point object or a line segment for each corresponding entity recognized in the DXF file and places them in the current workspace using the current unit system After these automatic conversions you might need to edit the imported model before you run the simulation in Working Model 2D For example your original CAD drawing does not contain physical representations of pin joints slot joints or springs in the drawing they only bear shapes but not meanings In essence you must attach physical meanings to what used to be a drawing Please read Converting Lines into Physical Objects on page 296 Working Model 2D recognizes the BLOCKS and ENTITIES sections of a DXF file The conversion rules are listed as follows e Only one copy of a BLOCK is imported into Working Model 2D Each copy is placed according to its local coordinates usually the placement is near the origin and may appear offset from the original drawing Avoiding duplication of BLOCKs leads to not only a shorter import time but also a simpler simulation model If necessary you can select the objects contained in a BLOCK convert them to physical objects see Converting Lines into Physical Objects on page 296 and place them in Working Model 2D duplicate them as needed e The CIRCLE entities are imported as circular bodies 294 Chapter 9 Importing and Exporting Files and Data Unit Assignment Rule e The POLYG
282. ngle by aligning its corner to the existing rectangle After you draw the two vertical links your screen should resemble Figure 1 l You will now create pin joints A pin joint acts as a hinge between two bodies The Smart Editor prevents joints from breaking during drag operations 1 Double click on the Pin Joint tool 2 Sketch two pin joints by clicking once with the mouse for each joint Try to attach it to a Snap Point where a small X symbol appears whenever possible Note that the Object Snap is still active when you attach a constraint such as a pin joint As shown in Figure 1 18 possible Snap Points include the center of links and their corners Figure 1 18 Aligning pin joints based on Snap Points Figure 1 19 Pinning the mechanism together 1 8 The Smart Editor 19 Ze As you bring the mouse closer to the links a small X appears at the nearest Snap Point After you create the two pin joints your screen should resemble Figure 1 19 Click here to create pin joints Pin joints automatically connect the top two bodies If only one body lies beneath a pin joint then the pin joint joins the body to the background 3 4 Select the Arrow tool by clicking in the Toolbar Try dragging any rectangle All three rectangles will follow the motion of the mouse because the pin joints connect them The Smart Editor does not allow joints to separate
283. nical document Modeling Uniform Flexible Bodies in Working Model by Keith Reckdahl D 8 Appendix D Scripts Copies of these documents may be obtained by sending e mail to info workingmodel com or by contacting MSC Software s technical support at 800 732 7284 D 2 The Shear Force and Bending Moment Script Shear Force and Bending Moment creates shear force and bending moment diagrams for rectangular beams in Working Model 2D simulations These diagrams are useful for predicting structural failure in beams Introduction In general the shear force and bending moment vary along the length of the beam and can be strongly affected by the beam s motion Using a graphics window as shown in Figure D 11 this script displays shear force and bending moment versus the position along the length of the beam and updates these diagrams at each frame This script also records and displays maximum and minimum values of both the shear force and bending moment over the history of the simulation In addition this script provides for the export of shear force and bending moment data to a text file for any time frame Figure D 11 Shear amp Bending Moment Example Shear Force Bending Moment Force in Newtons Moment in Newton Meters 13 67487 t 7 76141 12 0726 Operation Instructions Before running the script select the rectangular beam within your WM document to be analyzed Invoke Shea
284. ning a Simulation Beyond What Can Be Recorded on page 260 Automatic Point Equations on Object Snap When constraints are attached to a body while Object Snap is active Working Model 2D generates a geometry based formula expression for the point location used by point based parametrics Not only will the endpoints of constraints snap to the corresponding snap point but the attachment will retain its position even when you resize or reshape the pertinent bodies see Positioning Constraints Precisely on page 101 for more information To disable this automatic formula generation feature simply turn off the item Automatic point equations on Object Snap in the Preferences dialog Points will still snap to snap points but the coordinates will be specified as a numerical constant instead of point based parametrics Saving Preferences If you click Save Current Settings in the Preferences dialog a preferences file is created On MacOS systems the file Working Model 2D Prefs will be in the Preferences folder in the System folder On Windows systems the file named wmprefs4 wm is created in the Windows directory Figure 8 8 Full tape player memory dialog 8 5 Recording a Simulation 259 This preference file is opened and read each time you open a new Working Model 2D document and is used to customize the startup environment of your Working Model 2D session Saved preferences include the following e the size and location
285. nt 2 Choose Properties in the Window menu The Properties window appears 3 Hold the mouse button down at the Selection pop up menu Figure 4 2 Poini 1 Point Point 2 Point 2 300 m y 0 500 mo m Point Point 2 x bodyl6 reigh m y 0 0 im Active when M Always 94 Figure 4 3 Selection pop up showing a point s association with other objects Chapter 4 Constraints In the Selection pop up objects shown with asterisks Windows or printed in bold face MacOS indicate that these objects are attached to or associated with the selected object Figure 4 2 shows that Point 1 and Point 2 are associated with Constraint 3 Indeed Constraint 3 a pin joint consists of Point 1 and Point 2 Figure 4 3 shows another example In the figure Point 2 is selected from the Selection pop up and Constraint 3 and Body 8 have asterisks to indicate attachment Note that the middle part of the Properties window also confirms this relationship fr Point 2 Point x Body 8 Rectangle Constraint 3 Pin Joint Point 1 Point Paoint 2 Point Connected to Body 8 Part of Constraint 3 Global Coordinates Attachment information for angl 0 000 the selected point element J For point elements the Properties window also shows the constraint of which the point is an endpoint the body to which the point is attache
286. nt Constraint 131 Damper Wisc 0 000 m s vy 0 000 m s ver 0 000 s material Standard gt J The selected bodies are mass listed with a minus sign stat fric o 300 kin fric 0 200 The selected bodies have lastic _ 0 500 the same rotation charge 1 00ers CE density 1 000 kg m 2 Planar ba j moment 2 Enter the new value in the appropriate box of the properties window All of the selected bodies will have their values adjusted at the same time Changing Properties of Objects Successively The selection pop up menu at the top of each utility window displays the ID and the name of the currently selected object s All objects in Working Model 2D have default names such as circle and spring but these names can be easily customized using the Appearance window see 3 3 Body Appearance for instructions Meaningful names will assist you tremendously in selecting objects To select other objects in the workspace 1 Drag down the pop up menu and select the name of the object you wish to select 74 Chapter 3 Bodies Figure 3 12 Selecting an object using the selection pop up menu The utility window will show the properties of the selected object Remember that curved body objects are listed in the selection menu as polygons by default mixed selection z mixed selection Body 2 Hand
287. nu item leads directly to a dialog box which allows you to set many options at once To set individual workspace options MacOS only 1 Choose Workspace from the View menu The Workspace submenu appears as shown in Figure 6 7 Workspace gt Rulers Grid Lines H Y Axes v Coordinates v Toolbar v Status Bar v Scroll Bars v Tape Player Controls Workspace Select the option you want to change A checkmark indicates the option is on To set many options at the same time 1 Select Workspace MacOS only from the Workspace submenu in the View menu The Workspace dialog appears 198 Chapter 6 The Workspace Figure 6 8 Wi Workspace dialog indows TA I K KI I Workspace MacOS Show toolbar Show tape player controls Show scroll bars Combine tape control and scroll bar mr Show rulers 2 Show status bar 2 Click the check boxes for the options you want 3 Click OK MacOS or Close Windows Figure 6 9 Grid Rulers Tape player controls and Coordinates bar displays 6 2 Viewing Options 199 Working Model Untitled1 _ o x ty File Edit World View Object Define Measure Script Window Help laj x De i amp alej amp RJoJA Pje Run gt Stopii Reset i i Grid tines hn 1 i PEE RET EE ETETE EEE E THE Coordinates bar FE rrrererrirerrrrrrr jrr jrr pre 1 000 0 000 1 000 2 000 3 000
288. ny effect in simulations Creating a Force Forces are attached to the top body lying under the pointer at the time of the click To create a force 1 Select the Force tool from the Toolbar 2 Move the pointer to the location where the force is to act on a body 140 Chapter 4 Constraints Figure 4 47 Sketching a force Figure 4 48 Coordinates bar for a force 1 Click here to mark the point of application a I 2 Move the mouse here and click again to mark the magnitude 3 Drag the pointer to create a force object A force can be edited by grabbing and dragging the arrow or by using the Properties window To move the force click anywhere on it except on its endpoint tip of the arrow and drag it to a new location The Coordinates bar for Force shows the point of application x y and the force components Fx Fy Figure 4 48 The components are shown in terms of the global coordinate system The force components can be shown in polar coordinates as well Simply open the Properties window and choose Polar as the display mode Figure 4 48 The orientation is in the global coordinate system as well In Cartesian mode xL_0 183 m y 0 333 m Fx _ 20 00 N Fy 15 000 N l Point of Application X and Y components In Polar mode x 0 183 m yl 0 333 m IFIL25 000 N 143 13 SSS E J Point of Application Magnitude and Direction Figure 4 49 F
289. o delete a control point 1 Click the object to select it 2 Choose Geometry from the Window menu The Geometry window appears 3 Select the control point you wish to delete in the Geometry window i Geometr Constrain es v Lurved Sol Joint Slot is _ oO Open Closed Display in D Cartesian coordinates Polar coordinates Table zal Incl interp pts fod g Radius Select this control point 4 Click the Delete button in the window The control point is deleted from the list Copying a Curved Slot to and from Other Applications Working Model 2D allows you to copy and paste a curved slot as a collection of points control points or interpolated points so you can transfer its control points to and from another application such as a spreadsheet a CNC machining program or even a text editor Curved slots are transferred via the Clipboard as coordinates of the control points with the option of including interpolated points Specifically the data is simple text consisting of a list of number pairs x y or r 8 coordinates delimited by a tab Each number pair is on a separate line Copying a Curved Slot to Another Application Pasting a Curved Slot from Another Application 4 19 Slot Joints 171 Almost all spreadsheets or text editors can immediately import such data by pasting it from the Clipboard CAD programs may require different methods such as
290. o s material Standard mass Bo o kg stat fric Jo300 kinfric 0 300 elastic ps charge 1 000e 004 C density 1 000 kg m 2 Planar x moment E kg m 2 The Appearance window Figure 2 8 controls the appearance of selected objects Color fill tracking and center of mass display are controlled by this window Appearance Color Pattern Body 1 Recta w K Show DO E ee Frame Oo E o Track center of mass o Show center of mass o Track connect o Show charge K Track outline The Geometry window Figure 2 9 controls the geometry of selected bodies The properties that appear in this window depend on the type of object selected A rectangle s geometry is specified by width and height A polygon s vertices can be altered by editing the values in this window Figure 2 9 Geometry window The Tab Key and Utility Windows E Body 1 Rectangle Rectangle Area 3 420 m 2 COM Auto e yotset O00 m poset poo m Height fi 300 m Width fi 800 m For Rectangles 2 2 Working Model 2D Menus Geometry Body 2 Polygon hd Polygon Area 4 110 m 2 COMA Auto offset 10 033 m p ottset D 211 m I Curved body m Display in Shape coordinates tes For Polygons 57 Cascade Windows only arranges all the currently open document windows in a cascaded fashion the title bar for each window is visible Tile Windows only arranges all t
291. o select it as indicated in Figure 1 23 The pin joint turns black when selected Click here to select the pin joint 4 Click the Split button in the toolbar The pin joint is temporarily split At this point dragging rectangle B with the mouse will not move rectangle A since rectangle B is no longer connected to rectangle A The two points that used to constitute the pin joint p are connected by a dotted line to indicate they are temporarily split as you drag one of the rectangles away from the other Figure 1 24 A split pin joint Figure 1 25 Preparing to join 1 8 The Smart Editor 23 5 Try dragging the other rectangles Do not drag the pin joints as they may be removed from their respective rectangles 6 Move the rectangles A and B to a position where the pin joint is almost connected Try dragging each of the different bodies Your screen should resemble Figure 1 25 Move the bodies A and B so that the points are closer together 7 Click the rectangle B Note that the Join button is active The button becomes active whenever you select e two points e one of two points that were split from a pin joint or e a body with a point that was split from a pin joint 24 Chapter 1 A Guided Tour Join Figure 1 26 The re joined mechanism Modifying Initial Configurations The Join button is now active because the last condition given above is satis
292. o store the results of multiple simulations to a file 1 Create or open a simulation 2 Choose Retain Meter Values from the World menu 3 Create meters to measure the desired data and run your simulations as many times as necessary while changing parameters mass velocity etc for each simulation All measurement data will be saved in memory If you delete a meter however the measurement data for the particular meter will be lost 4 After you are done experimenting choose Export from the File menu The Export dialog appears see Figure 9 1 on page 291 for general information on the Export dialog 5 Set the export type to Meter Data 6 Set Export Options as necessary 7 Click OK Data Format for Meter Data From Multiple Simulations Meter Values and Histories 7 1 Meters 231 The exported meter data file is formatted in a multiple column format with each row representing a set of data from one animation frame The file contains as many columns as needed to store all the meter data existing at the time when you executed the Export command Data from multiple simulations are written side by side For example if you have three meters measuring time and x y 9 position of projectiles measurement data from two simulation runs will produce 3 meters 4 data columns each for t x y and 0 2 simulations 24 columns If you recorded 4 simulations then the file would have 48 columns The file will have as
293. o use the anchor tool to control the motion of a body See 10 6 Specifying Body Path by Position and 10 7 Specifying Body Path by Velocity 3 6 Controlling Collisions among Bodies Initially Working Model 2D assumes all bodies can collide with one another Working Model 2D automatically makes exceptions when two bodies are directly connected by a pin joint slot joint or gears see Chapter 4 Constraints in which case the two objects will not collide 88 Chapter 3 Bodies Figure 3 23 Objects connected in chain If two bodies are not directly connected with each other Working Model 2D assumes that they can collide For example if three bodies A B and C are connected by pin joints as shown in Figure 3 23 objects A and B will not collide by default but objects A and C will since the two do not have a direct connection The collision property is a property of a pair of bodies If you select more than two bodies to specify the collision property the specification will apply to all permutations of body pairs among the selected set For example to specify two or more objects so that they can all collide or do not collide at all with one another 1 Select the set of bodies that you want to collide or not to collide Use shift select or box select 2 Choose Collide or Do Not Collide in the Object menu as desired The collision menu items indicate the current collision specification among
294. object parameters that are frequently edited Each object has a set of parameters that can be modified quickly the Coordinates bar display for a rectangle for example shows the x and y position orientation width and height Changing Initial Position and Orientation Frame of Reference FOR Center of Mass COM Taking Measurements 3 2 Body Properties 67 Section 3 1 Creating Bodies describes effective uses of the Coordinates bar Ifthe Coordinates bar is turned off choose Coordinates from the Workspace submenu located under the View menu Initial Position and Orientation The initial position and orientation of a body can be specified numerically or graphically The initial position and orientation of a body is changed by dragging and rotating the body on the screen To rotate a body use the Rotate tool on the Toolbar You can also type numerical values directly in the configuration fields x y and to specify the initial configuration The angle labeled specifies the orientation of the body When you change the value of 9 the body rotates with its geometric center fixed in the World frame The x and y coordinates in the Properties window specify the position of a body s Frame of Reference FOR relative to the origin of the World frame For all bodies except polygons and curved bodies the FOR is the geometric center of the object For polygons and curved bodies the FOR is the geometric cent
295. object returned Example WMDocument Constraint name id WMConstraint The method above takes either name or id as the parameter and returns a WMConstraint object WMApplication constant WM WM ActiveDocument WMDocument DeleteMenultem Index Documents Collection of WMDocument GetMenultem Index filename String EnableMenulItem Index EnableFlag InsertMenulItem Index MenuName FileName M New WMDocument M Open filename WMDocument M LoadWMBLibrary filename M M SSSBSES ShowPropertiesWindow Boolean UnloadWMBLibrary filename WM Version String WMDocument Bodies Count Integer Bodies Item n WMBody Body name id WMBody Collide Constraint name id WMConstraint Constraints Item n WMConstraint Delete object Input name id WMInput Inputs Item n WMInput Output name id WMOutput Outputs Item n WMOutput Object name id WMObject Objects Item n WMObject Point name id WMPoint Points Item n WMPoint Reset Run frames RunScript filename Save SaveAs filename IsHistorySaved Selection Item n WMObject ScaleFactor Double ScrollTo x y Select obdject state SelectAll state SimulationMode String UnitSystem String Update WMBody AddVertex n x y DeleteVertex n 233333535359354 Working Model Basic Quick Reference Sheet GetVertex n x y Height WMCel1 Mass WMCel11 PX PY PR WM
296. ociate objects with keyframes Complete animation export creates a set of object geometry files as well as complete keyframe data for all objects Keyframes are generated for each frame of a simulation 9 3 Steps for Export To export any of the various types of data that Working Model 2D supports use the following steps 1 Create or open a Working Model 2D simulation 2 Choose Export from the File menu A dialog box appears as shown in Figure 9 1 Figure 9 1 Export dialog 9 3 Steps for Export 291 Odysseus Eject Exercises Desktop Orig Docmntn New C MacOS Export as Cancel untitled Movie Save Type QuickTime Movie w First frame Export Options Last frame Export 12 x Export to Enn Sl c EJ Windows Eet e Export type Meter Data dta im Cancei Frame pr First fo Last rs Choose the type of data you wish to export by clicking on the menu next to Type You will see a list of all the export data types that Working Model 2D supports Options that are not currently available will be dimmed Click the Export Options button to specify particular options for the export data type you will be using Each export type has options that are specific to its data type Enter values for the first and last frame 292 Chapter 9 Importing and Exporting Files and Data The current first and last frame of your simulation are placed in the fir
297. odies so they behave as if their mass were distributed like a sphere You can specify the moment of inertia numerically as well To set a body s moment of inertia to that of a shell or spherical weight distribution 1 Bring up the Properties window for the body by selecting the body and choosing Properties from the Window menu 2 Choose the desired moment from the pop up Moment menu The numerical value of the object s moment changes to reflect the new moment of inertia Charge dictates how a body will behave in an electrostatic field Bodies are given an initial charge large enough to produce movement between human scale 1 0 meters objects Charges only affect the simulation when the Electrostatics feature is turned on Electrostatics can be turned on by selecting Electrostatics in the World menu Working Model 2D assumes that electric charge is lumped at the center of mass for each body The charge is not distributed across the body and therefore is independent of the body geometry Material 3 2 Body Properties 71 You can quickly set many of a body s properties to reflect a specific type of material Some of these settings are approximate Materials include rubber rock plastic ice clay wood and steel The table below shows the list of values stored in Working Model 2D Static and kinetic friction coefficients are denoted u and uy respectively k Elasticity Charge c g em Ib ft Standard Steel
298. odies with the built in pin joint Rotational dampers exert a torque that depends on the difference in angular velocities of the two bodies attached to the endpoints For example you can use a rotational damper to simulate a pin joint that exhibits friction Rotational dampers cannot be built by joining two elements but they can be split to edit their individual point elements Creating a Rotational Damper To create a rotational damper 1 Select the Rotational Damper tool from the Toolbar On MacOS systems the Rotational Damper tool is hidden in the Damper pop up palette by default Click and hold on the Damper tool to bring the Rotational Damper tool in view and select it 2 Position the mouse pointer at where you want to create the damper and click once The Coordinates bar shows the coordinates for the Base Point point element on the bottom layer and the Top Point point element on the top layer as shown in Figure 4 32 Both coordinate values are given in reference to the body to which each point is attached 124 Chapter 4 Constraints Figure 4 32 Coordinates bar for a rotational damper Figure 4 33 Properties window with rotational damper selected Rotational Damper Type Rotational Damper Constant _x 1 300 m y _0 900 m x _ 0 750 m y _ 0 050 m fe Base Point Top Point Rotational Damper Properties To change the properties of a rotational damper 1 Select the dampe
299. ody whether or not they are located within the body To attach a point to a body 1 Select the points and the body use shift select or box select 2 Choose Attach to Body in the Object menu Splitting Rotational Constraints Figure 4 17 Splitting a constraint followed by deleting an endpoint Removing Constraints 4 3 General Properties of Constraints 107 The points are attached to the body without changing their position Splitting and Removing Constraints While editing a model you can temporarily disable rotational constraints so that you can freely move the bodies You can split two bodies connected with a rotational constraint delete one of the bodies The point that was attached to the deleted body remains and you can attach it to another body If you split a rotational constraint and if you delete one of the endpoints the matching endpoint will be deleted as well k 1 Split Constraints J 2 Delete one of the bodies 3 You can attach the endpoint to another body The ability to split and join constraints is a part of the Smart Editor feature Please see Chapter 5 for more information on the Smart Editor You can remove any constraint by selecting it and pressing the delete or backspace key or by choosing Clear MacOS Delete Windows or Cut in the Edit menu 108 Chapter 4 Constraints Turning Constraints On and Off Each constraint can be turned on and off during the course of a
300. ody object all of the points that are connected to the body will appear highlighted in the pop up menu If you select a point the body object to which the point is connected will appear highlighted If you select a constraint the points associated with the constraint will appear highlighted Using Rigid Joints to Build Complex Objects Rigid joints can be used to build large complex objects from simple shapes It is easier to create a hollow box shape by rigidly joining four rectangles than it is by sketching a complex polygon Rigid joints do not introduce extra equations of motion into a simulation and thus they are preferable to using two pin joints when locking objects together Settling Objects The Working Model 2D simulation engine can be used to align objects Take for example a block that needs to rest exactly on an inclined plane Select both the block and the plane and set their frictional coefficients to a high value like 1 0 Place the block so it is approximately in position over the plane and then run the simulation The block will come to rest in a stable position Stop the simulation at this time and choose Start Here from the World menu This will make the stable settled position the initial conditions The block will be perfectly aligned on the plane Placing Points Directly on the Edge of a Body To place a point directly on the edge of a body first sketch the point inside the mass near to but not on its edge Th
301. of any two colors including black and white Click on the two pop up menus next to Fill in the Appearance window to change the fill color and pattern You can also change both the width and the color of the outline of an object The fill pattern may not be apparent for thin outlines These three options determine which parts of a body will be traced on the screen when tracking is turned on in the World menu Track Center of Mass will leave a point at the body s center You can turn on Show Center of Mass to render the track more pronounced Track Connect will leave connecting lines between the body s center of mass at subsequent positions Track Outline will leave a trace of the body s outline Track of a of Mass axa Connecting Line x i x re N f y e k Track of Outline You can hide a body by clicking once in the field titled Show to remove the checkmark Hidden bodies behave exactly like displayed bodies All bodies are initially shown The name of a body is automatically set to its type circle rectangle square or polygon Remember that curved body objects are named polygons by default You can change this name by typing directly into the name field of the Appearance window Figure 3 15 Body with name displayed Show Center of Mass Figure 3 16 Center of mass symbol Show Charge Show Circle Orientation 3 3 Body Appearance 77 Choose Show Name to display the name of the body Figure 3
302. of the Circle To change the size of the circle you can either select one of the corners and drag it or type the desired radius directly in the Coordinates bar To change the circle s size by dragging 1 Click on the circle to select it The four reshape handles small black squares appear around the circle as shown in Figure 1 4 Hold the mouse button down on one of the reshape handles and drag it 8 Chapter 1 A Guided Tour Figure 1 5 Resizing a circle 3 The circle will change in size as you drag the mouse You can observe the Coordinates bar to see how the radius and the position of the circle changes see Figure 1 5 zm untitled EE Grab the reshape handle and drag it to resize circle D and ie how radius changes in the Coordinates bar x 1 000 m y 0 500 m rL_1 300 m l 0 000 Release the mouse button when the circle reaches the desired size Using the Coordinates Bar To specify the size of the circle using the Coordinates bar 1 Figure 1 6 Coordinates bar display for a circle Click on the circle to select it The Coordinates bar shows the position of the circle in terms of its center as well as the radius and orientation see Figure 1 6 Type the desired radius into the radius field labeled r of the Coordinates bar x _1 000 m y _0 500 m r 1 300 _0 000 X position y position
303. on export Meter Data Numerical data includes anything that you can measure in a Working Model 2D simulation such as the force on a joint or the angular acceleration of an object 290 Chapter 9 Importing and Exporting Files and Data Object Geometry Animation Object Motion Paths or Keyframes Complete Animation Data for other Applications Object geometry is the exact shape and size of the objects in your simulation The best format for transferring this information to another application is the DXF format Most CAD Computer Aided Design programs support the DXF format If you wish to capture animation use the QuickTime or sequential PICT export types MacOS only or the Video for Windows export type Windows only On MacOS systems QuickTime animations are exported as a single file and are thus more convenient than sequential PICT files MacOS only If you are using an animation package that gives you access to numerical keyframe data you can create realistic animations by using Working Model 2D motion data in your animations The Object Position export type will create a tab delineated file of each object s position on a frame by frame basis Object Position data can be exported in either row or column format Working Model 2D supports complete export of object geometry and motion path data to MacroMind Three D and Wavefront When using either of these applications you do not have to paste columns of keyframe data and ass
304. on frames For example if only every second frame of the recording is shown the playback speed doubles To replay the recorded frames for faster animation 1 Record the animation and calculate the motion by running the simulation once 2 Click Reset in the Toolbar 3 Run the simulation again The animation replays faster this time because Working Model 2D did not have to calculate the motion while replaying the simulation Pausing The Pause feature enables you to automatically stop a simulation when some condition is met For example you can pause when time gt 1 00 seconds Figure 8 6 Pause Control dialog 8 4 Preferences 255 To control under what conditions a running simulation will pause 1 Choose Pause Control from the World menu The Pause Control dialog appears Figure 8 6 Pause Control xi OK Pause when Pause when yY Pause when Y Click on the New Condition button A sample formula is placed as the first pause condition Select the event type you wish to occur when the condition is met You can pause stop loop or reset when the formula evaluates to a value greater than 0 0 evaluates to true For specific information on how to use formulas see Chapter 10 Using Formulas and Appendix B Formula Language Reference 8 4 Preferences The Preferences dialog gives you control of several important run time features To change any of the preferences 1 Ch
305. on in the Toolbar You have the pin joint connecting the two polygons Attaching a slot to a body is just as simple as attaching a point For example suppose you imported a curved slot geometry from a CAD program via DXF file format and you just constructed a curved slot following the directions shown in Converting Lines into Physical Objects on page 296 In order to attach the curved slot to a body 1 Make sure that the slot is located properly relative to the target object 300 Chapter 9 Importing and Exporting Files and Data Figure 9 5 Aligning a curved slot to a body Conversion Rules in DXF Export The Attach to Body command will not move anything as the Join button may do Make sure they are aligned properly as shown in Figure 9 5 ae Pad WK Drag the slot joint over to the target object 2 Shift select or box select the slot and the target body 3 Select Attach to Body under the Object menu alternatively you can press Ctrl M Windows or Command M MacOS Now the slot is attached to the body If you mistakenly attach points to a wrong body you can either immediately Undo Ctrl Z in Windows Command Z in the MacOS or select the points and choose Detach from Body under the Object menu 9 5 Exporting DXF Files The DXF file format can also be used to export the shapes of objects toa CAD or graphics program The DXF file created by Working Model 2D is a text file containing an
306. on while maintaining sufficient accuracy Shown below are the list of modifications you may consider applying to your model for faster simulation runs e Use the Fast simulation method and set the time step to the largest value that allows stable simulation and acceptable accuracy e Reduce the number of objects that are in contact Make sure to use the Do Not Collide command in the Object menu with all groups of objects that do not need to collide This modification allows Working Model 2D to bypass many collision tests To visually check for contacts display collision force vectors by selecting all objects and choosing Define gt Vector gt Contact Force e Set the frictional coefficients of contacting objects to 0 0 if friction is not needed in your simulation e Use rigid joints to build complex objects Using two pin joints to lock objects together introduces extra simulation overhead and redundant constraints e Use rods instead of ropes wherever possible 8 14 Useful Simulation Tips 281 e Userods instead of pinned bodies wherever possible A truss constructed of small bodies connected by rods will simulate more quickly than a truss constructed of pinned rectangles e Make your window size smaller A smaller window size requires less graphics processing time Avoiding Inconsistent Initial Velocities Working Model 2D enforces positional consistency with the Smart Editor Velocity consistency is not enforced Object
307. oose Preferences from the World menu The Preferences dialog appears Figure 8 7 256 Chapter 8 Running Simulations Figure 8 7 Preferences dialog Edit objects as T Allow velocity vector dragging I Calculate initial conditions automatically IV Prevent editing except at initial conditions IV Change cursor to stop sign during Run I Loop when tape player is full I Automatic point equations on Object Snap Save Current Settings Cancel 2 Place checkmarks to the desired preference boxes to activate the features The following sections provide discussions on each of these features please read them for more information Preferences are saved for the current simulation document only therefore they do not affect any new documents you create 3 Click OK Edit Objects as Outlines or Objects When you drag objects while editing Working Model 2D can display the objects as outlines alone or as solid objects Displaying outlines results in smoother animation while editing Allow Velocity Vector Dragging While this option is turned on a selected body shows a small blue dot at its center of mass You can drag this dot to drag out the vector that specifies the initial velocity Specifying Initial Velocity on page 9 shows an example This feature is a graphical complement to the Properties window which allows you to specify the initial velocity numerically 8 4 Preferences 257 Calculate Initial Co
308. or this method please refer to Creating Slot Joints from Elements on page 160 156 Chapter 4 Constraints E amp Figure 4 67 Creating a straight slot joint Figure 4 68 Coordinates bar for a straight slot joint To construct a straight slot joint using a Slot Joint tool directly Align the bodies that will be joined by the slot joint or keyed slot joint Select the appropriate Slot Joint tool from the Toolbar Click here to make the slot joint Click the mouse to create the joint at the proper location The top two bodies will be joined The slot element will attach to the second body from the top if only one body lies under the pointer the slot will attach to the background The Coordinates bar Figure 4 68 for a straight slot joint shows the slot base point and the slot pin coordinates the point at which the body is attached to the slot x _0 600 m y _0 050 m x _0 750 m y 0 700 m al 141 11D dal m l Slot Base Point Slot Pin Coordinates Creating a Curved Slot Joint You can create a curved slot joint by either using the Curved or Closed Curved Slot Joint tool from the Toolbar or joining a curved or closed curved slot element with a point element to create a pinned slot joint For this method please refer to Creating Slot Joints from Elements on page 160 Figure 4 69 Body on an open curved track Figure 4 70 Coordinates bar showing offset from pre
309. orce whose line of action does not rotate with body Figure 4 50 Force whose line of action rotates with body 4 14 Force 141 Force Properties A force has one endpoint this point indicates where the force is applied You can define a force in Cartesian x and y force or polar rotation and magnitude coordinates To change the on screen length of the vector without changing the physical magnitude of the force use the Vector Length dialog found in the Define menu The display scales in the dialog box apply to all vector displays in Working Model 2D including the Force constraint The direction of a force can be specified either in relation to a body or in relation to the background A force is considered to rotate with its body if its line of action changes with the body Wl ia To change the properties of a force object 1 Select the force object and choose Properties from the Window menu 142 Chapter 4 Constraints Figure 4 51 Properties window with a force Force selected Fx N Fy N Cartesian O Polar Rotate with body Don t rotate Base Point Point 1 Active when Always 8 Cartesian Polar In Cartesian mode you can specify the x and y component of the force vector In Polar mode you can specify the magnitude F and angle of the force vector Rotate with Body A force that rotates with a body has its line of action fixed in the body s
310. ormation Case Study a Space Probe Simulating the Probe s Position Simulating the Probe s Internal Mechanism NOTE The Absolute Acceptable Error remains constant regardless of the value of Y whereas the magnitude of the Relative Acceptable Error is proportional to Y Choosing an Acceptable Error for Your Simulation Now that you have two types of error bounds to control how can you optimize the simulation performance in terms of its speed and accuracy The answer really depends on what you are interested in getting out of Working Model 2D By default Working Model 2D automatically chooses error parameters which suffice for most purposes This section is for those who wish to fine tune their simulation runs As acase study consider simulating a space probe that is launched from the Earth For simplicity we will assume that the probe cannot propel itself and its dimension is about 20 feet across If you are interested in the position of the space probe after one year from launch and if you can afford an error of 1 mile you should set the Absolute Acceptable Error to 1 mile Since the numerical magnitude of the solution you are interested in is fairly large compared to the size of the body a tight absolute error would require an excessively long computation time On the other hand you should keep the Relative Acceptable Error low e g 10 which translates to setting Significant Digits to 6 because 1 mile
311. ortest distance between its two endpoints The current length is always greater than or equal to the length Separators apply a repulsive force and absorb energy when they move from a slack configuration to their minimum length The coefficient of elasticity for a separator determines how much energy will be preserved during this transition The coefficient of elasticity determines the difference between the relative velocities of attached bodies before and after a separator reaches minimum length A coefficient of 1 0 results in a completely elastic separator i e attached bodies which are moving together will bounce apart with the same kinetic energy due to the separator repulsion On the other hand a separator with a coefficient of 0 is completely inelastic the kinetic energy of attached bodies will be completely absorbed by the separator as it reaches minimum length To change the properties of a separator 1 Select the separator and choose Properties from the Window menu Figure 4 46 4 14 Force 139 Properties x Properties window with a separator J Constraint 3 Separator selected Separator lenath f2 234 m current 2 517 m elasticity Jo c00 Active when M Always _ 4 14 Force Unlike most other constraints a force contains only one point element the point of application and applies the specified force at that point A force must be attached to a body to have a
312. ou complete control of polygon vertices and curved body control points By default the coordinates are given with respect to the world i e global coordinates You can add vertices control points delete vertices control points and reshape polygons curved bodies using the Geometry window The Geometry window allows you to convert polygons into curved bodies and vice versa though the Curved body checkbox For polygons this box is unchecked and the point coordinates refer to the polygons vertices Clicking to check the box converts the polygon into a curved body with control points at the former vertex coordinates of the polygon Using Formulas to Reference Body Geometry You can use Working Model 2D s powerful formula language to refer to geometric properties of any body such as width height and vertex coordinates For example you may wish to use the geometry of the objects in the following situations e Specifying the attachment position of constraints with respect to object geometry see Positioning Constraints Precisely on page 101 Defining relationships between the geometries of different bodies e g the width of body 5 is equal to twice the height of body 1 See Appendix B Formula Language Reference for a complete listing of the formula language Using Formulas to Define Body Geometry You can define the geometry of a body by using a formula expression For example you can define a four bar linkage
313. ours or days You can override the automatic animation step decision and set your own time step size between animation frames See Integration Time Step on page A 17 for discussion on how to set the integration time step Fixed Variable A 6 Simulation Accuracy Dialog and Simulation Parameters A 17 Integrator Error The integrator error corresponds to the Absolute Acceptable Error or the parameter discussed in A 5 How Working Model 2D Bounds Errors Fundamentally the value is used as the lower bound for numerical errors Working Model 2D cannot attain higher accuracy than what is specified in the Integrator Error Integration results can violate this bound as long as they are within the Relative Acceptable Error Integration Time Step You can specify the integration time step in two ways by directly entering the time step or by entering the number of integration steps per animation frame When the integration time step is less than the animation step one animated frame reflects results from several integration steps The integration step size cannot be greater than the animation step In Fixed mode the integration time step is locked The default value for integration step is equal to the animation step You can make the integration time step smaller than the animation step by typing the desired step size in the text box By doing so you are packing multiple integration steps into one animation frame In
314. ous section If you already know how to create objects and give them initial velocities create a single circular body and give it an initial velocity similar to that shown in Figure 1 10 Figure 1 10 untitled A circular projectile with an initial velocity x 1 000 m y _0 500 m r _1 300 m _0 000 3 Choose Velocity from the Measure menu and All from the Velocity submenu A digital velocity meter appears Figure I 11 1 5 Measuring Properties from a Simulation 13 Figure 1 11 4 Working Model Untitled1 Fela a File Edit World View Object Defne Measure Script Window Help lel x A velocity meter D Slt see a2 ALALELE Rune sorn rese Velocity of Circle 1 aE m pa m dozo m glooo gt X a C E Friday August 02 96 09 12 AM 4 4 Click the Run button in the Toolbar As the projectile moves you can monitor the velocity of its center of mass by watching the velocity meter 5 Click the Stop button in the Toolbar to stop the simulation Changing the Display Style of a Meter To change a digital meter into a graph 1 Click Reset in the Toolbar to reset the simulation 14 Chapter 1 A Guided Tour Figure 1 12 Changing a digital display into a graphical display Figure 1 13 A graphical display 5 Click here to change elocity of Circle 2 the display format Click the arrow button in the top left corner of the meter On
315. overlapping points and has a built in pin joint If a motor is created over a single body the body will be attached to the background beneath it If a motor is drawn over the background it will do nothing Ifa rotational constraint is drawn over two bodies the motor will bind the two bodies with the built in pin joint Motors cannot be built by joining two elements but they can be split to edit their individual point elements Creating a Motor To create a motor 1 Select the Motor tool from the Toolbar 2 Position the mouse pointer at where you want to create the motor and click once The Coordinates bar shows the coordinates for the Base Point point element on the bottom layer and the Top Point point element on the top layer as shown in Figure 4 57 Both coordinate values are given in reference to the body to which each point is attached x _0 600 rn y _0 050 m x _0 750 m y 0 700 m b lat tpl mmi l l Base Point Top Point 148 Torque Rotation Velocity Acceleration Chapter 4 Constraints Motor Properties A motor has a built in pin joint which is composed of two points Given two bodies or one body and the background attached to these two points a motor functions as a multi purpose constraint that exerts the torque necessary to maintain the specified rotation angular velocity or angular acceleration between the bodies A motor is similar to an actuator except that a mo
316. ow digital graph and bar meters GA Position of Rectangle L4 Position of Rectangle iy T Postion of Flectangle m x 2 250 m m rot ly 0 350 m at rot 0 000 rad ET Digital Meter Graph Meter Bar Meter To select the display mode for a meter 1 Select the meter Corner handles appear to indicate that the meter is selected Click on the arrow button on the top left corner see Figure 7 3 On MacOS systems a pulldown menu appears for you to select the type of the meter On Windows systems each click cycles the meter types in the order of digital graph bar graph and digital again 226 Chapter 7 Simulation Interfaces Figure 7 3 Changing meter display types Meter Position Click here to change meter types Position of Rectangle 1 Position of Rectangle 2 250 m rot 0 350 m 0 000 rad MacOS Windows Modifying Meters to Display Customized Properties You can use meters to display customized properties by taking advantage of the powerful formula language available in Working Model 2D For example you may wish to display the sum of the linear momenta of two colliding bodies to verify the conservation of momentum You may also wish to plot a sinusoidal function to compare results from a vibrating system Please refer to 10 5 Customizing Meters for examples and instructions Modifying Meter Position and Size You can position the meter anywhere on th
317. owing input 5 When Working Model 2D is running a simulation it will look for a value to use as the spring s constant Instead of using a number it will use whatever value is being generated by input 5 Input 5 is the formula name for the value generated by the slider The formula Input 5 was automatically placed in the spring constant field when the slider control was created If you delete the slider control the formula will be removed and replaced by the original value of the spring constant You can link input controls to any property you wish by selecting an object and creating a new control from the object menu or by entering the name of the control in this case input 5 in any field that accepts formulas Each control has a minimum and maximum value that you can change from the control s Properties window Figure 10 2 Formula entered in properties window 10 3 Customizing Objects 331 10 3 Customizing Objects You can use formulas in place of numbers in any field of a Properties window This means that you can attach equations to govern the motion as well as the physical properties of objects during a simulation For example you can use formulas to model the mass of a rocket that becomes lighter as its fuel is consumed Arithmetic Expressions Typically an object keeps its mass constant during a simulation You can inspect an object s mass by selecting the object and then choosing Properties f
318. p If an object is moving large distances in a small time and interacting with another object through a joint or contact incorrect results and instabilities may result A good rule of thumb is that the time step must be small enough to capture small motions that occur in the system If you are modeling a guitar string you will need a very small time step If the guitar string oscillates 440 times per second you would need at least four time steps to accurately model each back and forth motion of the string Thus you would need 1760 time steps per second or a time step of 1 1760 second Other systems requiring a small time step include very heavy bodies interacting with very light ones chains that are being stretched and light wheels on heavy cars Instabilities can usually be corrected with the Accurate simulation method use the Simulation Accuracy dialog The Accurate simulation method automatically adjusts the time step for you As an alternative use the Fast simulation method but decrease the time step Through a bit of playing around you will get a feel for how the time step affects the simulation When using the Fast method fixed time step reducing the time step increases the accuracy When using the Accurate method variable time step reducing the value in the Integrator Error increases the accuracy The error value determines how much numerical error is allowed during each time step The smaller the error value the more acc
319. pe A damper with a high damper constant resists motion more than a damper with a low damper constant You can create dampers that exert forces proportional to the velocity velocity squared or velocity cubed between their two endpoints A linear damper exerts a force proportional to the difference in velocity between its endpoints This choice is available in the damper type pop up as Kv Constraint 3 v Lemper _1 206 W s m ti909 5m Hold the mouse button here and the damper type menu appears Active when Always 2 To change the type of damper 1 Select the damper and choose Properties from the Window menu The Properties window appears 2 Click the pop up menu next to Force and drag to select the desired damper type The damper will exert forces as specified by the relationship of Force to velocity v that you have chosen If you choose Ky the damper will exert a force equal to its damper constant K times the difference in the velocity of its endpoints v cubed 4 7 Spring Dampers A spring damper is simply a combination of a spring and a damper see 4 5 Springs and 4 6 Dampers for more information The force exerted by a spring damper is equal to the sum of the forces applied by the spring component and the damper component Figure 4 28 Coordinates bar for a spring damper al 4 7 Spring Dampers 119 For example you
320. pin joint to the center of the other The second disk is now free to rotate with respect to the pin Open the Properties window of the gear constraint and select the body that appears on top i e the body that was first selected to be a gear to be the internal gear see Figure 4 40 below EOE Properties Lonstraintf tif w beer aw Ratio y 3 Auto Ci ti In automatic mode the gear ratio L e is computed as Rod Active radius body 2 radius body 1 B Always amp Internal Gear This is the body first selected gt Mass 2 when you created the gear pair O Mass 1 m Gear Force Constrai nt 12 r Active when Always S This step ensures that the automatically computed gear ratio is correct You could select the body that appears on the bottom to be the internal gear in that case however you must invert the gear ratio Click Run The two disks will rotate as if they are driven by a chain Principle of Simulating Gears 4 11 Gears 131 NOTE The gear tool simulates a chain drive mechanism through a constraint on the rotations of the two disks Therefore physical properties of chains such as mass or tension are not incorporated in the simulation A gear constraint allows two rigid bodies to exert forces on each other at a single point of contact The point of contact is located along the line passing through the centers of mass of the two bodies its location depends o
321. ple more than 20 we recommend that you start out by selecting all objects in the workspace use Select All in the Edit menu and choosing Do Not Collide from the Collision submenu under the Object menu You can then select sets of bodies that are meant to collide and choose Collide from the collision submenu Preventing Interpenetration of Objects Working Model 2D allows objects to penetrate each other by a very small distance This penetration distance can be controlled from the Simulation Accuracy dialog When two fast moving objects collide you may find them overlapping each other by an unacceptably large distance This is because the objects move a large distance for each new frame of calculations You can solve this problem in a number of ways In variable time step mode the results of two small time steps are compared to the result of a single time step If the difference in object positions is large asmaller time step will be used The Accurate simulation mode will therefore deal with most interpenetration problems Smaller time steps almost always improve simulation results You can use either a smaller animation step or a smaller integration time step Objects that Move Apart after Inelastic Collisions When objects with zero elasticity collide and they overlap by a large distance a small correctional force is applied to bring the overlap distance back to the amount specified in the Overlap Error field of the Simulation
322. ported in Working Model 2D the peak value of the discrete force profiles approaches the experimental value as the step size becomes closer to the physical duration of the collision Collision Force in Meters The collision force can be displayed using the contact force meter in Working Model 2D To create the meter 1 Select the two bodies that will collide 2 Choose Contact Force in the Measure menu The contact force meter appears in the document The contact force meter reports the sum of the normal force and the collision force When one body is resting on top of another the contact force reports non zero values because of the normal force acting from one body to the other During collisions the contact force meter reports a force whose magnitude is significantly greater than the normal force because of the collision force discussed earlier A 8 Simulation Accuracy Preventing Unstable Simulations An unstable simulation is indicated by bodies moving in random directions at high velocities When simulations become unstable it is immediately apparent A 8 Simulation Accuracy A 23 Simulation instabilities can occur when bodies that initially overlap are allowed to collide Any two bodies that are not connected with a joint can collide If you overlap two bodies without using the Do Not Collide command large forces will be generated to move the bodies apart Instabilities usually indicate the need for a smaller time ste
323. r amp Bending Moment from the script menu D 2 The Shear Force and Bending Moment Script D 9 Figure D 12 Shear Force and Bending Moment Diagram Figure D 13 Maximum Minimum Table The script creates a window like that shown below which displays both shear force and bending moment diagrams It shows the shear force diagram in red and the bending moment in blue and is updated each time frame The numbers to the left of the diagrams are the maximum and minimum values of the shear force the numbers to the right are the maximum and minimum values of the bending moment Shear Force Bending Moment Force in Newtons Moment in Newton Meters zl 13 67487 7 76141 gt em Max Min soso ml 12 0726 ame Done There are six buttons which control various aspects of the simulation The Run Stop button starts and stops the simulation While the simulation is running this button has the word Stop on it and only this button is enabled The gt and lt buttons allow for forward or backward stepping through the simulation The Max Min button reports the maximum and minimum value of the shear force and bending moment over the entire history of the simulation When the Max Min button is selected the diagrams are replaced by the dialogue box shown below Selection of any of the other control buttons will bring back the shear moment diagrams Shear Force Bending Moment an Maximums and Minimums Moment gt Max 7 86e
324. r showing velocity acceleration and force Vectors can be displayed for electrostatic forces for planetary forces and at multiple contact points when two objects collide They can be displayed in a variety of colors and formats You can calculate and record complicated or time consuming simulations overnight and play them back quickly You can then save entire simulations to disk You can stop or pause simulations automatically For example you can set a simulation to pause when two seconds have elapsed by entering the following formula Pause when time gt 2 You can also have your simulations loop and reset xxii Apply Control Unlimited Objects You can apply forces and constraints at various times For example you can apply a constant force on an object for one second or you can apply a force when an object s velocity is greater than 10 You can create as many objects such as bodies constraints and meters as your computer s memory allows Combined format for Windows and MacOS About This Manual xxiii About This Manual This manual contains all the information you need to use the Working Model program and to create and run your own simulations on either a Windows or MacOS computer The illustrations in this manual show screens and dialog boxes from both MacOS and Windows computers Both versions appear only when the two are substantially different Any information pertaining to only one of the systems will be
325. r and choose Properties from the Window menu Properties Constraint 3 v or Damper Torque K O 017 Nms Base Point Point 4 Point Point 2 Active when Always ie A rotational damper exerts a torque that is proportional to the difference in angular velocity between the two bodies attached to the endpoints You can create a rotational damper that exerts a torque proportional to the square or cube of the relative angular velocity between the two bodies attached Use the menu next to Torque in the Properties window to change the rotational damper type A rotational damper with a larger damping constant exerts more torque than one with a smaller constant The amount of torque exerted by a rotational damper is equal to the relative angular velocities of the two bodies attached to the endpoints multiplied by the constant Figure 4 34 Pulleys can have multiple points 4 10 Pulleys 125 Enter the value for the rotational damper constant next to K in the Properties window 4 10 Pulleys Pulleys behave as a single rope going through multiple fixed points The total length of the rope is fixed but the partial length between each pair of adjacent points can vary Creating a Pulley System Pulley systems can have multiple points along with two endpoints The force applied between each pair of points is equal Each point in a pulley system can be connected to either the background or to a body
326. r depending on the type of simulation you are setting up The basic steps for creating and running a simulation are 1 Choose New from the File menu to open a new document 2 Draw and position bodies and constraints Use the Toolbar to draw objects just as you would with a paint or draw program Figure 1 2 Run button Chapter 1 A Guided Tour 3 Double click an object to display and or edit its initial specifications for example velocity friction coefficients or elasticity Choose from the items in the Measure menu to install meters and graphs that display the information to be analyzed during the simulation Click the Run button in the Toolbar Choose Save from the File menu to save the simulation 1 3 Running a Sample Simulation In this exercise you will open and run sample simulation documents included with the program 1 Choose Open from the File menu The Open dialog appears Macintosh Double click on any of the demonstrations folders located in the Working Model 2D folder in the Open dialog Windows Double click any of the samples directories located in the Working Model 2D directory in the Open dialog The contents of the demonstrations folder or directory appear Select one of the demonstrations by clicking it Then click the Open button Click Run in the Toolbar The simulation will run Click here to run MacOS Run Sip i Heset Windows Figure 1 3 Stopping th
327. r more information please refer to Point Fields on page B 7 166 Chapter 4 Constraints Figure 4 77 Geometry window for a curved slot joint Open Closed Slot Defining the Geometry of a Curved Slot A curved slot is generated by creating a series of control points The control points are fitted using a third order B spline interpolation to produce a smooth slot The location of the control points can be viewed modified and exchanged to and from the Clipboard using the Geometry window you can also modify the curve geometry graphically see Reshaping a Curved Slot on page 158 Geome H tr ji SUR eS w Lurved Slol Joint Slot is _ oO Open Closed Display in ie Cartesian coordinates Polar coordinates Table _J 4 Incl interp pts fio g Radius To display the Geometry window 1 Select the curved slot 2 Choose Geometry from the Window menu Alternately if the Geometry window is already visible you can simply select the curved slot whose geometry you want to view from the menu at the top of the window You can convert between open and closed curved slots by selecting the appropriate radio button When curved slots are open the slopes of the spline curve at the boundary points are used to linearly extrapolate from there to infinity Display Coordinates Copy Paste Table Control Point Coordinates FOR of a
328. r whether the rod should be active You can define when the rod should be active using formulas as with any other constraint See Turning Constraints On and Off on page 108 for details By default Working Model 2D assumes that all gears are external gears This option lets you make one of the bodies into an internal gear The Properties window provides radio buttons to select which body is meant to be the internal gear The gear ratio cannot be 1 0 when an internal gear is used unless the centroids of the gear bodies coincide This window shows the variable name of the gear force Working Model 2D treats the pair of gears as a combination of two constraints a gear force and arod The Gear Force variable name is assigned to the gear force constraint while the rod constraint carries the variable name which appears at the top of the Properties window You can refer to these variable names to measure the amount of the gear force or the rod force For example in the case of the Properties window as shown in Figure 4 42 Constraint 16 f y represents the force exerted from one gear to the other the x component is always zero while Constraint 15 f x Figure 4 43 Coordinates bar for a rod 4 12 Rods 135 represents the x component of the rod force the y component is always zero See Chapter 10 Using Formulas for more details 4 12 Rods A rod applies forces at its endpoints to maintain a fixed length between
329. racy dialog appears Figure 8 23 2 Click the More Choices button 3 Remove all checkmarks from the Warnings check boxes Working Model 2D stores the simulation data in its available memory including the simulation history You can increase the memory space available to an application Please refer to A 1 Making the Best Use of Available Memory When you suspect that the memory may be insufficient to store the entire duration of the simulation you have two options before you start running it Using Scripting to Control Unattended Operations 8 14 Useful Simulation Tips 283 Option 1 Let Working Model 2D stop the simulation as soon as memory runs out and later review the result obtained thus far 1 Choose Preferences in the World menu The Preferences dialog appears Figure 8 7 2 Remove the checkmark from the check box Loop when tape player is full Under this setting Working Model 2D will automatically pause the simulation when memory runs out preserving the simulation history obtained thus far Ifnecessary you can continue the simulation discarding the history See Running a Simulation Beyond What Can Be Recorded on page 260 for details Option 2 Let Working Model 2D continue its simulation lapping around the tape as long as necessary see Loop When the Tape Player is Full on page 258 This option is useful when for example you want to observe the steady state of a dynamic system after a
330. rademark of AutoDesk Incorporated DXF is a trademark of AutoDesk Incorporated All other brand or product names are trademarks or registered trademarks of their respective holders For phone fax numbers mail E mail addresses technical support sales and development please visit http www workingmodel com WM2D V5 Z Z Z DC USR Introduction Operating Concept Simulation Engine Running Scripts with Working Model Basic xvii What is Working Model 2D Working Model 2D combines advanced motion simulation technology with sophisticated editing capabilities to provide a complete professional tool for engineering and animation simulation The dynamic simulation engine models real world Newtonian mechanics on the computer and the simple yet powerful graphical user interface makes it easy to experiment with various engineering designs and scenarios To create a simulation use Working Model s drawing tools or import CAD geometry from a DXF file then connect the bodies with constraints e g motors springs and joints Clicking Run simulates your system Working Model allows you to refine your mechanical design and control properties of objects through sliders Excel and Matlab Engineering measurements are possible with graphs bar charts and numerical displays Designed for both speed and accuracy the Working Model simulation engine calculates the motion of interacting bodies using advanced numerical analysis te
331. ration of the two endpoints of a constraint measured along the line that connects the two endpoints Constraint length is always a positive value Constraint velocity is positive when the length of a constraint is increasing Constraint velocity is negative when the length of a constraint is decreasing For example Figure 4 19 shows a spring that is being stretched by a circular body in motion In this case the constraint velocity measures positive Stretched spring is under tension Rest Length Velocity of the Circle Constraint Velocity Positive Constraint Force Negative In this example Constraint forces are defined as positive when they tend to increase the length of a constraint push outwards You may consider that the constraint force always measures compression For example since the spring shown in Figure 4 19 is under tension which can be considered as negative compression Working Model 2D measures the constraint force as negative Constraint rotation is the difference in rotation between the two bodies connected to the endpoints of the constraint Constraint rotation is always measured in a counter clockwise direction with respect to the object to which the base point is attached The base point of linear constraints is the first point created when sketching the constraint 110 Chapter 4 Constraints Figure 4 20 Constraint torque in the positive direction Constraint To
332. rger spring constant exerts more torque for a given rotation than one with a smaller constant Enter the value for the rotational spring constant next to K in the Properties window You can create a rotational spring damper which combines a rotational spring and a linear rotational damper described in 4 9 Rotational Dampers A rotational spring damper exerts a torque equal to the sum of the torques exerted by the spring component and the damper component The damper component exerts a torque equal to the product of the damper constant and the relative angular velocity between the two bodies attached to the endpoints The default value for the damper constant is zero i e there is no damping component Enter the value for the rotational damper constant next to C in the Properties window 4 9 Rotational Dampers 123 NOTE You cannot model damping in a rotational spring proportional to higher powers of the relative angular velocity of attached bodies Attempts to do so by using separate rotational spring and rotational damper constraints will produce unpredictable results 4 9 Rotational Dampers A rotational damper is composed of two overlapping points and has a built in pin joint Ifa rotational damper is created over a single body the body will be attached to the background beneath it Ifa rotational damper is drawn over the background it will do nothing If a rotational damper is drawn over two bodies it will bind the two b
333. rn initial body overlap Warn redundant constraints Warn inconsistent constraints Custom If any simulation parameters are changed the simulation mode becomes Custom Please continue reading to learn more about each parameter Euler Kutta Merson A 6 Simulation Accuracy Dialog and Simulation Parameters A 15 Integrators Working Model 2D assigns an integrator when you choose either Fast or Accurate mode This section is presented for those who wish to experiment with the benefits of various integration methods The integrator is the mathematical process that continuously integrates bodies accelerations to update their positions and velocities The following integrators are available in Working Model 2D Euler Integration e Kutta Merson Integration In order to illustrate the relative complexity of the two methods let s examine the following first order differential equation y fo and see how each integrator solves it numerically We are interested in solving y 7 or the value of y at the next step given the information Yn and t We will denote the time step as A so A Euler integration is the fastest and simplest but least accurate integrator available for a given time step Euler integration is the default in the Fast simulation mode and should suffice in giving you a rough idea of the motion The Euler method solves the above differential equation in a sin
334. rom the Window menu The Properties window appears to show the object properties including its mass You can click the resize box in the upper right corner of the Properties window to make it larger The entry fields expand at the same time allowing you to enter longer expressions more easily A typical rocket might start with a mass of 10 000 kg excluding fuel and carry 10 000 kg of fuel If the fuel is burned in 100 seconds and at a constant rate then the mass M of the rocket can be described as follows M R 1007 0 lt lt 100 10000 100 If you were running your simulation for less than 100 seconds you could simply enter the following into the mass field of the properties window see Figure 10 2 that defines the rocket s mass 20000 100 time mass Z20000 100 time kg When you run the rocket simulation the rocket will progressively become lighter according to the formula you have entered 332 Chapter 10 Using Formulas Conditional Formulas If you were running your simulation for more than 100 seconds you could accurately combine these two equations into a conditional statement as follows if time lt 100 mass 20000 100 time else mass 10000 You could enter a formula like this using the if function The if function takes three parameters each separated by a comma in the following format if condition return if true return if false The rocket equations are co
335. rques Ea The base point of a rotational constraint is the bottom most point of the constraint when the constraint is sketched You can verify the position of the base point of rotational constraints in the Coordinates bar When a constraint is split the base point will include the constraint icon e g a spring and a curled arrow for a rotational spring as shown in Figure 4 20 Positive torque tends to rotate the top body in the direction of the arrow Base Point attached to the bottom body A constraint torque is defined as positive when it tends to increase the rotation of a constraint push counter clockwise on the body that is not connected to the base point See Figure 4 20 4 4 Ropes As its name suggests a rope applies forces at its endpoints so that the distance between them does not exceed the specified length or the rope length A rope applies no force at all when the distance between the endpoints is less than the rope length Creating a Rope To create a rope 1 Select the Rope tool from the Toolbar 2 Position the mouse pointer where you would like to define the first endpoint The pointer changes from an arrow to a crosshair indicating that you can start drawing Figure 4 21 Coordinates bar for a rope Figure 4 22 Properties window for a rope 4 4 Ropes 111 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second
336. rties bamped Spring r Spring K N m length m current 2 200 m r Damper kL__1 000 n s7 r Active when Always O To change a property of a spring damper 1 Select the spring damper and choose Properties from the Window menu The Properties window appears 2 Choose the property of the spring damper you would like to change You can change the spring constant the rest length of the spring and the damping constant 4 8 Rotational Springs A rotational spring is composed of two overlapping points and has a built in pin joint Ifa rotational spring is created over a single body the body will be attached to the background beneath it Ifa rotational spring is drawn over the background it will do nothing Ifa rotational spring is drawn over two bodies it will attach the two bodies with the built in pin joint Rotational springs exert a torque that depends on the difference in rotations of the two bodies attached to the endpoints For example a coil spring can be simulated by a rotational spring Rotational springs cannot be built by joining two elements but they can be split to edit their component point elements Figure 4 30 Coordinates bar for a rotational spring 4 8 Rotational Springs 121 Creating a Rotational Spring To create a rotational spring 1 Select the Rotational Spring tool from the Toolbar On MacOS systems the Rotational Spring tool is hidden in the Spring pop up palette by
337. rties in the Window menu The Properties window shows the names of the Base Point and the Point such as Point 14 and Point 15 2 Click on the constraint name on top of the Properties window You will see a pop up list of all the objects in the current model 3 Choose the Base Point or Point you want to modify 4 Type the coordinate values to position the points precisely at the desired location Working Model 2D has two distinct sets of expressions designed for global and local coordinates reference point i p Global Coordinates point i offset Local Coordinates Therefore point i offset y refers to the y coordinate of point i with respect to the body to which it is attached The body to which the point is attached can be referred to as point i body returns a body 4 3 General Properties of Constraints 101 Please see Appendix B Formula Language Reference for more details Positioning Constraints Precisely You can precisely position constraints in one of the following ways e Using Object Snap you can automatically attach a constraint at a precise location when you create it e Using Grid Snap you can create a constraint so that it is automatically aligned to the background grid geometry of constraints numerically e Using the Coordinates bar you can quickly view and modify the e Using the Properties window you can directly edit the endpoint coordinates numerically When you
338. s To set the rest length of a spring numerically 1 Double click on a spring The Properties window appears 2 Enter the desired value for rest length 3 Click OK You can graphically set the rest length of a spring using the mouse 116 Chapter 4 Constraints Sketch or resize the spring until it is the desired length The spring s rest length is automatically set to be the distance between the two endpoints Resize the spring while holding down the Option key on MacOS or Control on Windows key The spring s rest length will remain the same while you resize the spring Spring Type You can create inverse square springs along with springs that produce forces proportional to the square cube or reciprocal of their extension A linear spring exerts a force equal to its spring constant multiplied by its extension from rest length This choice is available in the Spring Type pop up as Kx Figure 4 25 Choosing a spring type K x 3 K x 2 Force Lies lt Spring Type Menu length 1 703 m current 1 703 m Active when Always 8 To change the type of spring 1 Select the spring and choose Properties from the Window menu The Properties window appears Click the pop up menu next to Force and drag to select the desired spring type The spring will exert forces as specified by the relationship of Force to distance x that you have chose
339. s This format is useful for transferring data to animation programs that support object motion paths in keyframes MacroMind Three D Animation Wavefront Technologies Advanced Visualizer DXF Lincages Simulation Data 9 2 Choosing an Export Data Type 289 Working Model 2D will export a complete MacroMind Three D script and geometry files These files can be opened directly in MacroMind Three D All motion data will be placed in keyframes and all objects can be generated as extruded 3 D shapes Working Model 2D will export a complete Wavefront animation script and object files These files can be opened directly in Wavefront All motion data will be placed in mov files all object data will be exported as extruded 3 D shapes in obj files and a set file will be generated to tie the information together Import Working Model 2D can import data in the following formats Existing CAD drawings can be imported into Working Model 2D as DXF geometry files The DXF format is popular for transferring data between CAD systems MacOS only Lincages is a linkage synthesis package developed at the University of Minnesota and distributed by Knowledge Revolution Mechanisms designed within Lincages can be imported into Working Model 2D and set in motion 9 2 Choosing an Export Data Type The Working Model 2D export options can be grouped by the type of data they create If you wish to export numerical data from a simulati
340. s can have inconsistent velocities if they are unable to initially move in the direction of their velocity A body that is pinned to the background will have an inconsistent velocity if its initial velocity is directed at the pin joint rather than perpendicular to the pin joint Large correcting forces will be applied to objects that have inconsistent velocities in the initial frames of a simulation Why Some Simulations Slow Down on Certain Frames A simulation may slow down if your model moves into a configuration where many objects are in contact or when objects are colliding rapidly e As collisions become imminent Working Model 2D needs to do more computations to determine appropriate time steps to model collisions as accurately as possible e As accelerations become large Working Model 2D automatically picks smaller integration time steps to ensure simulation accuracy Since the animation step size is constant throughout the simulation a single frame requires more computations resulting in a longer delay between frames Therefore when your model reaches a difficult configuration with many colliding objects colliding or large accelerations Working Model 2D decides to use smaller integration time steps to maintain accuracy resulting in more computations per animation frame Consequently the simulation will appear as if it were slowing down l Integration time step would be constant if you chose Locked time st
341. s checkmark appears to indicates the current tracking rate Every 8 frames Every 16 frames Every 32 frames The options available are Off Every frame Every 2 frames Every 4 frames Every 8 frames Every 16 frames Every 32 frames and Other The Other dialog Other box lets you choose your own custom tracking rate AutoErase Track if active erases tracks whenever the simulation history is erased A checkmark appears before the menu item when it is active Erase Track immediately erases the trace of any tracked simulation 50 Chapter 2 Guide to Tools amp Menus Workspace gt Grid Snap Object Snap System Center of Mass Lock Points L Lock Controls Numbers and Units View Size Background Color New Reference Frame Delete Reference Frame gt v Home 31 Workspace gt Rulers Grid Lines H Y Axes v Coordinates v Toolbar v Status Bar v Scroll Bars v Tape Player Controls Workspace Workspace Submenu MacOS only Retain Meter Values if active retains the history of all meter values obtained from multiple simulation runs A checkmark appears before the menu item when it is active Erase Meter Values erases all meter histories except the one from the most recent simulation Working Model 2D continues to accumulate meter histories if Retain Meter Values is active Accuracy causes the Accuracy dialog to appear allowing you to control whether simulations run more quickl
342. s of the spring and its rest length as shown in Figure 4 24 Both coordinate values are given in reference to the body to which each point is attached Figure 4 24 Coordinates bar for a spring ny Spring Constant Rest Length 4 5 Springs 115 xL 4 500 m yl 2 200 m _xL 1 600 m yl 0100m 1 2 285 m First Point Second Point Rest Length Spring Properties To view and modify the properties of a spring select the spring and select Properties from the Window menu You can change the spring constant and rest length of springs You can also make springs exert forces proportional to the inverse square of their length The spring constant determines how stiff a spring is Springs with a large spring constant stretch less than do springs with a low spring constant given the same load Linear springs exert a force equal to the distance they are stretched from their rest length times their spring constant The spring constant of a spring can be changed using the Properties window Simply double click on the spring or select it and choose Properties from the Window menu The rest length is the length of a spring when it is neither stretched nor compressed When you sketch or drag a spring the rest length is automatically made equal to the current length i e the spring is neither stretched nor compressed You can create springs with rest lengths other than the automatic value current length in two way
343. s the center of mass of all bodies in the group Currently the only defined group is group 0 which is the group that contains all bodies Returns the total kinetic energy of all bodies in the simulation as a number Takes the ID numbers of two bodies x and y and returns the length of the line connecting their centers of mass Takes the ID numbers of two bodies x and y and returns the contact force of the first object acting upon the second The value is returned as a vector section x v time or t self B 7 Predefined Values B 23 Working Model 2D considers the contact force as the sum of the normal force and the collision force Please see A 7 Simulating Collisions for more information Takes the ID number of a body x and a vector quantity y Returns the cross sectional width of the body in the direction of the vector For example section body 1 vector 1 0 will return the vertical cross section width of body 1 This function is used by the air resistance force field to approximate the drag on bodies B 7 Predefined Values Variables There are several predefined variables that you can use in formulas Name Type time or t number self mass other mass ground mass Returns the current time in the simulation Time always begins at 0 0 in frame 0 Returns a body type when placed inside a force field equation When force field equations are evaluated for each body in the simulation self ass
344. s will be displayed by checking boxes in the Components area 2 3 Choose colors from the pop up menus in the Color area Choose whether to draw force vectors nose out or nose in and whether to draw force vectors at the point of application Force vectors are drawn nose out and at the point of application by default 7 5 Text 245 Showing Vectors of Joint Reaction Forces If a pin joint is selected and then Total Force is chosen from the Vectors menu vectors will be shown for each of the two points that constitute the pin joint When the simulation is run two opposite force vectors will originate from the pin joint To show just one vector select only one of the points in the pin joint before choosing Total Force from the Vectors menu as follows 1 Select the pin joint and choose Properties from the Window menu 2 In the Properties window choose one of the points that constitute the pin from the pop up menu at the top of the window Only one of the points that make up the joint will be selected on the workspace 3 Choose Total Force from the Vectors menu When the simulation is run the displayed vector will be the force on only one of the points If you wish to measure the reaction forces quantitatively using meters please refer to Measuring Reaction Forces at Joints on page 154 for details 7 5 Text To label your simulations you can create text captions within a document Text captions are con
345. same time These are the meter choices that logically apply to two bodies After you have selected two bodies choose the Measure menu and you will see a new set of measurement possibilities that apply to two bodies In particular the properties of collision force and friction force apply to a specific pair of bodies To install a collision force or a friction force meter you need to select two bodies The second body selected will be the body on which force is being applied Contact force measures the sum of the collision impact force and of the contact force the force exerted by two bodies on each other when they are in contact You can also create meters for constraints and points Select the object you wish to measure and then choose the desired property from the Measure menu Creating Meters To install a meter 1 Select one body point or constraint object whose properties you wish to measure You can also select two bodies to measure properties that apply to a pair of bodies 2 Choose the property you wish to measure from the Measure menu A meter with a numerical display appears Figure 7 2 Digital graph and bar meters 7 1 Meters 225 To install a contact force or a friction force meter you must select two bodies before you create a meter You can move resize or delete a meter Switching among Digital Graph and Bar Displays Working Model 2D features three types of meters as shown in Figure 7 2 bel
346. see Displaying the Coordinates Bar on page 201 for more information on the Coordinates bar Creating Circles To create a circle 1 2 Click on the Circle tool to select it Position the pointer in an empty area of the background The pointer changes from an arrow to a crosshair indicating that you can start drawing Hold down the mouse button and drag diagonally to create a circle of any size The Coordinates bar shows the current dimensions and position of the object see Figure 3 5 You can edit these values later Release the mouse button 62 Chapter 3 Bodies Figure 3 5 Creating a circle Alternative Way to Create Circles Editing Configuration and Radius Quickly Click here ee 3 The Coordinates bar shows W F and drag to here the current position and dimension ana grag to nere 0 300 m y O200 m 11 200 m 0 000 You can also create a circle in the following fashion 1 2 4 Click the Circle tool to select it Position the pointer in an empty area of the background Click once and drag the mouse Note that the circle is drawn diagonally following your mouse movement When the body reaches the desired size click the mouse button again You do not need to change any options or preferences to use this alternate drawing method Working Model 2D intelligently identifies your actions on the mouse and switches drawing methods You can quickly edit the position orien
347. selected object Selecting any item creates a meter to measure that property The display at left shows the measurable properties for a single body These properties include Position Velocity Acceleration P V A Position Velocity and Acceleration in one meter Center of Mass Position Velocity Acceleration Momentum Angular Momentum Total Force Total Torque Run Editor Optimize Create Constraint Document Model Zoom to Extent Measure Between Points Multiple File Run Flip Polygon Properties Ctri Appearance Ctrl Geometry Ctrl K Cascade Tile Arrange Icons v 1 Untitled 2 2 Working Model 2D Menus 55 Gravity Force Electrostatic Force Air Force Force Field Kinetic Energy and Gravity Potential Selecting other objects will give you various measurement options When two bodies are selected the Measure menu changes so that you can measure forces that inherently act between a pair of objects including Contact Force Friction Force and Pair Gravity Force The Script Menu The Script menu allows you to run scripts written in Working Model Basic Run prompts you to choose the script tool file and runs it Editor invokes the Script Editor The Script Editor allows you to write edit and debug scripts and tools If the Script Editor is already open but hidden behind other windows choosing this menu item brings it to the front NOTE The Script Editor is unavailable on MacOS computers
348. set in Preferred Size If the available memory is below Minimum the MacOS will not allow you to launch Working Model 2D The above method will not work if the memory available to the whole MacOS computer is low In this case you can take advantage of virtual memory if desired To turn on virtual memory open the Memory Control Panel Turn on Virtual Memory in the dialog and set the appropriate size as desired You will have to restart your MacOS computer to activate virtual memory In Windows an application can claim whatever memory space is available on demand In addition you can take advantage of virtual memory to make more space than available in your RAM By default virtual memory is enabled in Windows unless otherwise specified by the user if you are getting an insufficient memory warning from Working Model 2D please check to make sure you have not disabled virtual memory Virtual memory makes use of your hard disk for memory transactions As a result the execution speed can decline significantly on both Windows and MacOS computers Scripting Engine and Memory Usage on MacOS Systems The scripting engines are application components necessary for operating Working Model Basic Approximately 1 300 kilobytes 1 3 megabytes of memory is required to run the scripting engines This memory is allocated in addition to the memory size that appears in the Get Info box of the Working Model 2D application Figure A 1 Abou
349. sidered text objects in the Working Model 2D You can edit a text object by selecting all or part of its text on the screen and typing replacement text Object names can also appear on the screen This section explains how to create and edit both kinds of text Using the Text Tool To create a text object 1 Select the Text tool 2 Click on the workspace where you want to begin typing 246 Figure 7 20 Selected text Chapter 7 Simulation Interfaces 3 Enter the text Press Return to end a text line and start a new one Selecting a Text Object To select text in a text object 1 Select the desired text object 2 Select the letter or words you want to edit by dragging through the text This is a object The selected text appears highlighted 3 Double click on a word to select it 4 Click elsewhere in the window to deselect text Deleting a Text Object To delete a text object 1 Choose the Arrow tool in the Toolbar 2 Click the text object to select it 3 Choose Cut or Clear from the Edit menu or press the Delete key on your keyboard Cut text is placed on the Clipboard and can be pasted into the current document or into another document Pressing the Delete key is the same as choosing Clear from the Edit menu thus the cut text cannot be pasted To undo deletion choose Undo from the Edit menu before doing anything else 7 5 Text 247 Inserting New Text You can always add more text to
350. ss will be approximated and that it will not collide with other objects Reshaping Polygons and Polygons and curved bodies can be reshaped with the mouse or through the Curved Bodies Graphically Geometry window This section will cover the mouse driven reshaping while Reshaping Polygons and Curved Bodies Numerically on page 82 of this chapter covers the latter method To graphically reshape polygons and curved bodies 1 Select the polygon or curved body and choose Reshape from the Edit menu The menu item will be enabled only if a reshapable object polygon curved body or curved slot exists All reshapable objects will show square reshape handles on the vertices when they are selected see Figure 3 8 3 2 Body Properties 65 2 Click on and drag a reshape handle Figure 3 8 Reshape mode 3 To drag an object while in Reshape mode click in the body of the object away from a vertex or an edge 4 Exit Reshape mode by deselecting Reshape from the Edit menu or by choosing any tool in the Toolbar To add a vertex 1 Choose Reshape in the Edit menu The menu item toggles the Reshape mode 2 Click on the desired side away from an existing vertex and drag the new vertex to the desired position To delete a vertex 1 Be sure to be in Reshape mode the Reshape menu item in the Edit menu should have a checkmark 2 Select the reshape handle corresponding to the vertex you want to delete The han
351. st and last frame entry If you haven t run your simulation yet the last frame defaults to 100 If you have selected a single frame export type such as DXF there will be no last frame and the first frame will be the current frame 6 Type a name for the file and then click Save A progress dialog appears on the screen and the exported data is saved as a file Settings from the Working Model 2D workspace apply when exporting When exporting meter data the numerical format is taken from the current setting in the Numbers and Units dialog When exporting QuickTime movies and PICT files on MacOS systems the color settings or number of colors are taken from the current monitor settings 9 4 Importing CAD Geometries as DXF files The DXF file format was developed by AutoDesk to exchange information between AutoCAD and other packages DXF files contain geometry information for all objects in a CAD drawing Working Model 2D directly imports DXF CAD files Therefore if you want to simulate a model with object shapes that may be difficult to draw directly in Working Model 2D or if you have CAD data you have always wanted to see in motion you can first design your model using your favorite CAD program export the data toa DXF file and import it into Working Model 2D Since CAD packages deal with drawings and Working Model 2D deals with physical objects not all the information can be transferred seamlessly For example lines in a CAD do
352. sting vertical gravity you are changing the value of g the proportional constant relating the force on the mass center of an object with its mass i e F mg Planetary gravity simulates the true gravitational attraction that exists between all bodies When adjusting planetary gravity you are changing the value of G the universal gravitational constant The forces exerted by gravity between objects such as a person or a book are minuscule because the objects are not massive enough Thus to see the effects of planetary gravity your simulation must have one or more extremely massive objects A good rule of thumb is that the mass of the sun is approximately 1 0 x 10 kg Air Resistance Air resistance is modeled as a force on a moving body opposite to the direction of its motion This force is proportional to the object s cross section in the direction of motion Air resistance in Working Model 2D does not take into account the coefficient of drag of various shapes Rather it uses the cross section of the appropriate object in the direction of motion Thus a 1 meter Figure 6 21 Air Resistance dialog 6 4 Defining World Parameters 209 diameter circle has the same air drag as a square meter on edge To account for an object s cross section modify the air resistance coefficient k as follows For a sphere multiply k by pi r 2 where r is the radius of the sphere For a cylinder multiply k by W width of the cyli
353. sufficient to repel the bodies to simulate the collision Working Model 2D employs an impulse based collision model in which the coefficient of restitution denoted elasticity in the Properties window see Elasticity and Friction on page 68 is used As an example in one dimensional particle mechanics start with two particles of mass m and m7 which are colliding head on with velocities v and v gt respectively Then their velocities after the collision call them v and v2 can be computed from a pair of linear equations as follows note that two unknowns v and v exist in two linearly independent equations 1 1 H i mv m v m v m v conservation of linear momentum V2 TESH definition of the coefficient of restitution Mie Y where e is the coefficient of restitution Working Model 2D is a two dimensional simulator and it uses somewhat more generalized yet similar principles to compute the new velocities of bodies after a collision Figure A 4 Time step size numerical peak value and physical peak value A 7 Simulating Collisions A 21 Computing Collision Forces Since collisions are simulated in discrete time the time history of the forces arising from the collision are affected by the time step Using the notations provided in the previous section How Working Model 2D Simulates Collisions Working Model 2D reports the collision force f acting on the mass m as
354. t Constraint Output Input B 4 Fields B 3 For example body 10 is the ID for body 10 Body is the identifier for bodies such as circles polygons and rectangles Point is the identifier for point objects Point objects are either isolated points or the points which compose the endpoints of a constraint Point 11 is the ID for point 11 See Body Fields on page B 6 for polygon vertices Constraint is the identifier for constraint objects including springs ropes joints and pulleys Output is the identifier for all meters Input is the identifier for all input controls including sliders text boxes and buttons If you use an identifier with an ID for an object that does not exist the result will be a Null object Null objects return 0 0 for all of their properties B 4 Fields Each identifier in the Working Model 2D formula language can have fields You use fields to access the values of basic properties such as position and velocity Fields are specified by a Type followed by a period and a field name To access the moment of a body with an ID of 3 you would enter the formula body 3 moment The value returned from body 3 moment is a number that can be used in any formula Any value that has an x y and rotational component is returned as type vector The vector type has three fields x y and r rotation Fields are a way of accessing smal
355. t This Macintosh dialog A 1 Making the Best Use of Available Memory A 3 Memory which the system is using including approx 1 3MB used by the scripting engines SS About This Macintosh Total Memory 24 576K System Software 6 319K 4 Working Mode12D 6 000K Largest Unused Block 12 216K Memory which Working Model minus the scripting engines is using The memory size for Working Model 2D may be different depending on your setup When you examine the memory status using the About This Macintosh dialog from the Finder see Figure A 1 you will only see the block allocated to Working Model 2D However the memory used up by the scripting engine is accounted as part of the System Software The scripting engines attempt to claim this additional memory when Working Model 2D is launched If the memory is not available Working Model 2D will present a warning dialog indicating that any scripting feature including running pre written scripts will be disabled You can continue to launch and use Working Model 2D but all scripting and script editing functions will be disabled To re activate the scripting engines 1 Quit Working Model 2D 2 Make more memory available by either quitting other applications or use increase virtual memory Please see Increasing the Memory Available to Working Model 2D on page A I for more information 3 Launch Working Model 2D again
356. t alignment near the completion of a design you can decrease the value of Assembly Error The automatic values are calculated based on the size of objects in your model and the velocities of the objects 6 1 Physical Objects and Interface Objects 191 CHAPTER 6 The Workspace In this chapter you will find instructions to e Set viewing options e Use rulers and the grid Define world parameters Define object properties and parameters e Use the status bar to get quick information about objects and tools in the workspace e Change measurement units 6 1 Physical Objects and Interface Objects The simulation world has two layers a back layer and a front layer Physical objects reside on the front layer and interface objects reside on the back layer see Figure 6 1 Physical objects include bodies points and constraints Interface objects include meters controls sliders text boxes buttons and pictures that are not attached to physical objects 192 Chapter 6 The Workspace Figure 6 1 The interface layer and the physical layer Physical layer Interface layer Sc SSeS Since interface objects are on the back layer it is possible to obscure them by positioning physical objects over them In the physical layer a constraint will attach to the top body when positioned on overlapping bodies To make an object the topmost object select the object and then choose Bring To Fron
357. t always uses constraint ID 10002 To measure the force imposed on a body by the linear gravity constraint use the formula B 22 Appendix B Formula Language Reference constraintforce x y z frame frictionforce x y groupcofm x kinetic length x y normalforce x y constraintforce 10002 3 y In this case the y suffix is used to get the value of force in the y up and down direction Takes the ID number of a constraint x and the ID numbers of two bodies y and z Returns the amount of force being applied by the constraint between the two bodies This function only returns values for forces which are applied to each pair of bodies planetary gravity electrostatics and custom force fields The ID numbers for these constraints are constant and are described in the next section The gravity constraint always uses constraint ID 10002 To measure the force of gravity between two specific bodies in a planetary system use the formula constraintforce 10002 3 5 x As with point to point constraints the x value of the vector measures the force applied along the line that connects the center of mass of the two bodies Returns the current frame number The initial conditions are defined as being frame zero Takes the ID numbers of two bodies x and y and returns the friction force of the first object acting upon the second The value is returned as a vector Takes the ID number of a group x and return
358. t from the Object menu 6 2 Viewing Options Working Model 2D provides a practically infinite workspace that is larger than what can be displayed on the screen at one time The area occupied by the workspace is called the world What you see on the screen is only a small part of the world This part is called the view See Figure 6 2 Figure 6 2 What you see on the screen versus the working area 6 2 Viewing Options 193 The view what you see ina window Untitled 1 E The world the area over which you can place the view gt 1049 m gt Moving the View Across the World You can move the view to different areas of the world by using the horizontal and vertical scroll bars Figure 6 3 shows the window controls scroll boxes and arrows 194 Chapter 6 The Workspace Figure 6 3 Window controls Vertical Scroll Arrows Vertical Scroll Box Horizontal Scroll Arrows Coordinates bar Horizontal Scroll Box y 0 900 42600 m m S TT 19 fa Click one of the four scroll arrows to pan the view in the direction you choose or drag a scroll box to jump to a new view position The scroll bars automatically adjust to encompass all the objects you have created within the world You can continue to use the scroll bars until your objects are just off the screen To scroll further first use the Zoom tool to zoom out Zooming Using the Zoom
359. t greater than 1 QuickTime movies carry information on how quickly they should be played back 10 frames per second should provide sufficiently smooth animation The size of the document window determines the size of the exported QuickTime movie The settings for your monitor determine the bit depth of the QuickTime movie If you have a color MacOS computer setting your monitor s bit depth to 4 in the Control panel will result in the best performance for Working Model 2D while maintaining a full range of available colors QuickTime movies require a large amount of space on your hard disk approximately 10K bytes per frame As a result a 100 frame movie may approach 1000K which is larger than the size of a 800K floppy disk The size of a QuickTime movie is directly related to the size of the image being exported and the monitor s color setting You can create QuickTime movies that play simulations in real time by matching the playback rate to the time step used in simulation 1 Pick a playback rate for the QuickTime movie that your computer can support A good starting point is 10 frames per second 2 In the Accuracy dialog box set the frame rate to match this value 306 Chapter 9 Importing and Exporting Files and Data Figure 9 8 Video for Windows export options If the playback rate is 10 frames per second the simulation frame rate should be 10 frame per second The time step should be 1 10 of a second 3 Adjust th
360. t that contains a numerical keyframe for each object in a simulation Each frame of Working Model 2D simulation is translated into a Wavefront Three D keyframe Motion data from each object 316 Chapter 9 Importing and Exporting Files and Data Figure 9 13 Wavefront export options is placed in the x and y positional keyframes and the z axis rotational keyframes The z positional and x and y rotational keyframes are set to the value 0 0 Working Model 2D creates mov files containing positional and rotational data from each object in a simulation Working Model 2D also creates a geometry obj file for each object in the simulation These are placed in the same folder as the motion script and are correctly referenced by name from the script Working Model 2D can create flat or extruded 3 D shapes when creating the obj files To export complete Wavefront animations 1 Create or open a Working Model 2D simulation 2 Choose Export from the File menu The Export dialog box appears see Figure 9 1 for general information on the Export dialog 3 Set the export type to Wavefront 4 Set Export Options as necessary You can choose to export all objects or just those that are selected 5 Click OK A set and several mov and obj files one per object are created and placed in the same folder Export WaveFront W Export every a a frames every 0 010 s Export data from every object selected objects only
361. table Error These error criteria are based on two parameters both can be customized relative error denoted and absolute error denoted e Relative Acceptable Error Relative error is a positive number used to relate the relative acceptable error to Y the estimate of the absolute value of Y the variable being integrated The Relative Acceptable Error is defined as Relative Acceptable Error Y The value of e is chosen to give a specific number of significant digits of accuracy A useful rule is to set e 10 where n is the desired number of significant digits for Y The value of n can be set in the Accuracy dialog as Significant Digits see A 6 Simulation Accuracy Dialog and Simulation Parameters The upper limit on n depends on the precision of the numbers used for calculations For extended double precision 80 bit numbers as in Working Model 2D n should not be greater than 20 The relative error criterion works best when the value of Y retains the same order of magnitude during the integration Ifthe value of Y varies over many orders of magnitude especially if Y changes sign or approaches 0 the relative error criterion above would cause the simulation to slow down dramatically For example suppose Y takes on values between 1000 and 1000 and e is set to 10 8 significant digits When Y 1000 the relative acceptable error is 10 e Y However when Y 001 the relat
362. tation and radius of the circle as follows 1 Select the circle if it is not already selected Ifyou have just drawn the object it is selected already Click the field you would like to edit and type the number desired see Figure 3 6 for available parameters Press the Enter or Return key The object will immediately reflect the changes entered Figure 3 6 Coordinates display for a circle A Note about Curved Bodies 3 1 Creating Bodies 63 BE x position x position radius orientation x 1 500 m y 0 400 m rL 1100m 0 000 b We i la Creating Polygons and Curved Bodies Both polygons and curved bodies are created by defining multiple points in the background For polygons these points form the vertices corners of the object for curved bodies these points control the shape of the curve Since the way a curved body is defined by its control points is similar to the way a polygon is defined by its vertices these two types of objects are fundamentally related In fact Working Model 2D treats curved bodies as a subclass of polygons with an additional curved Geometry parameter selected see Converting Between Polygons and Curved Bodies on page 80 Due to this similarity curved bodies are listed in the Status bar and in all selection menus as polygons To draw a polygon or curved body 1 Click the Polygon or the Curved Body tool to select it On MacOS systems the Curved Body
363. te Taking Advantage of Automatic Features Always start in Accurate mode when building a new model Accurate mode is the default setting for a new document and it sets the internal step size to variable This enable the automatic time step control in Working Model 2D and gives accurate and stable results Accuracy is set in the Accuracy dialog under the World menu Any warning messages that are displayed at the beginning of a simulation should not ignored The user should identify the source of the problem and correct it A common message regards overlapping bodies If you see the message you should first identify which bodies are overlapping and colliding and turn off collisions between them or adjust the parts for proper clearance If you have trouble identifying undesired collisions select all objects via Select All in the Edit menu turn on contact force vectors Define gt Vectors gt Contact Force and watch for unexpected force vectors as the simulation runs C 6 Appendix C Useful Tips and Shortcuts Selecting Connected Objects The pop up menu at the top of the different utility windows Properties Appearance Geometry is a useful way to select objects in your simulation You will notice that some of the entries Points Bodies Constraints appear highlighted preceded by a on Windows systems and in bold type on MacOS systems These entries are related in some way to the current selection If you select a b
364. tem Current Length Elasticity ca Figure 4 37 Gears relate behaviors of two bodies 4 11 Gears 127 This is the length of a line connecting each point in the pulley system If the pulley is slack the current length is less than the length of the pulley Elasticity defines how objects will behave if the pulley system goes quickly from a slack to a taut configuration For more information on elasticity see Rope Properties on page 111 4 11 Gears The Gear tool provides a constraint between two bodies so that their rotations are dependent on each other Gears also have a built in rod that can be useful when you are simulating planetary gears the rod is active by default but can be turned off if you so prefer The section Principle of Simulating Gears on page 131 provides more discussion on how gears are simulated in Working Model 2D Figure 4 37 shows a typical use of gears in Working Model 2D where two disks of different radii are in contact One disk is driven by a motor where the other is attached to the background with a pin joint In this case the gear ratio is computed as the ratio of the two radii See Gear Properties on page 133 for more discussions on the gear ratio and other properties Creating a Gear To create a gear 1 Create two bodies that will be constrained with gears 2 Select the Gear tool in the Toolbar 128 Chapter 4 Constraints External Gears Internal Gear
365. ter of body 3 are both of type vector You cannot enter these formulas in a text field because they are not numbers To access individual components of these vectors you must designate whether you want the x y or rotational components To get a number enter the following equation instead body 3 v x x velocity of mass center of body 3 B 6 Appendix B Formula Language Reference p v a mass moment charge staticfric kineticfric elasticity cofm body 3 v x represents the x velocity of the mass center of body 3 which is a number not a vector The subfield r returns the rotational component of any vector Body Fields These are the current values of position velocity and acceleration Each of these fields returns a value of type vector Thus to use any of these field you need to add one of the vector fields x y r body 1 p x x position of mass center of body 1 body 3 v y y velocity of mass center of body 3 body 37 a r angular acceleration of body 37 These are the current values of the various properties body 3 charge charge of body 3 body 14 mass mass of body 14 This field returns the kinematic properties of the center of mass of a body The expression body 3 cofm is the same type as points so it has all the fields available to a point see Point Fields on page B 7 For example the expression body 3 cofm p x returns the x coordinate of the c
366. ter the joint is created On MacOS systems the Slot Joint tools are accessed through the Slot Joint pop up palette Constraint Tools Constraint tools are the collection of Working Model 2D tools to create various types of constraints See Chapter 4 Constraints for more information on each constraint H The Damper tool creates a link which resists changes in compression or extension For example a damper simulates a shock absorber of an automobile suspension Dampers can be attached between one body and the background or between two bodies the endpoints of the damper are the attachment points 2 1 The Working Model 2D Toolbars 45 The Rotational Damper tool creates a pin joint that resists changes in rotation Like dampers rotational dampers can connect two bodies or a body and the background the endpoints of the spring are the attachment points For example a rotational damper simulates the resistance experienced by a propeller rotating in a viscous medium On MacOS systems the Damper and Rotational Damper tools are accessed through the Damper pop up palette The Spring tool creates a link which resists stretching or compression Springs can connect two bodies or a body and the background the endpoints of the spring are the attachment points The Rotational Spring tool creates a pin joint which resists rotation For example a rotational spring simulates a coil spring Like springs rotational springs can
367. ters because SI unit has meters as a default distance unit on the Working Model 2D document Lengths for other properties velocity and acceleration are computed in the same fashion To adjust the vector display scale factor 1 Choose Vector Lengths from the Define menu A dialog box appears as shown in Figure 7 18 Vector Lengths Eg Velocity Acceleration Force efe 5 bers Cancel 3 a 5 re Short fo 200 fo 130 fo 130 244 Chapter 7 Simulation Interfaces Figure 7 19 Vector Display dialog 2 3 Use the sliders or enter a scale factor to adjust vector lengths for velocity force and acceleration vectors Click OK to save the changes Adjusting Vector Display Options Vectors can be displayed with their x y and total components Velocity acceleration and force vectors can be displayed in different colors Force vectors can be displayed at their point of application or at the center of mass of the body they act upon To adjust vector display options 1 Choose Vector Display from the Vectors menu A dialog box appears as shown in Figure 7 19 Vector Display x m Components Color IV Magnitude i Velocity i gt V Name Ea Acceleration O Cancel Line Thickness gt Force i B r Draw force vectors e a a A o nose out b nose in o at point of at center of application mass Choose which vector component
368. tes their collision In order to prevent two bodies from interpenetrating Working Model 2D applies a repulsive contact force to each object when the bodies overlap by more than this value This scheme ensures that the overlap will never exceed the value specified in Overlap Error See A 7 Simulating Collisions for more discussion Assembly error is used to bound the numerical error in the Join operation performed by the Smart Editor For example when you join a pair of point elements to form a pin joint Working Model 2D iteratively computes the configuration until the result converges within the Assembly Error value NOTE Joints are more closely monitored for error correction during the simulation run Maintaining the pin joint constraint is a fairly simple process and in variable step mode Working Model 2D corrects errors as soon as they are eminent In fixed time step you may observe that the joints wobble slightly Working Model 2D is trying to correct the position of a pin joint because the simulation result after one frame may place the pin joint slightly offset due to a numerical error The value given in the Significant Digits box corresponds to the number of digits that are accurate during numerical integrations The number given in the Significant Digits field sets the relative error 10 see A 5 How Working Model 2D Bounds Errors for details Inaccurate Integration Initial Body Overlap Redundant Cons
369. than squares and rectangles Define each vertex with a single click Double click to signal the final vertex The polygon will automatically close connecting the first vertex with the final vertex You can also close the polygon by pressing the space bar which will connect the last defined vertex with the first Polygons can be converted into arbitrary curved bodies by checking Curved sides in the Geometry window The vertices of the polygon then become the control points of the new curved body The Curved Body tool is used to create arbitrary curved bodies from a series of smoothly interpolated splined control points Define each control point of the curved body with a single click and double click the final point or hit space to close the curved body 42 Join Splite Chapter 2 Guide to Tools amp Menus Curved bodies can be converted into polygons by unchecking Curved sides in the Geometry window The control points of the curved body then become the vertices of the new polygon On MacOS systems the Polygon and Curved Body tools are accessed through the Polygon pop up palette The Anchor tool locks the motion of bodies Anchored bodies will not move unless an equation is entered to define their position Join Split Control The Join button forms a joint from two elements For example you can select two point elements created using the Point tool as shown below and click the Join button to form a pin
370. the the rod length Creating a Rod To create a rod 1 Select the Rod tool from the Toolbar 2 Position the mouse pointer at where you would like to define the first endpoint The pointer changes from an arrow to a crosshair indicating that you can start drawing 3 Hold down the mouse button to create the first endpoint 4 Drag the mouse to the desired location of the second endpoint Release the mouse button to create the second endpoint The endpoints will automatically attach to the uppermost body directly beneath them If no body exists under an endpoint it will be attached to the background The Coordinates bar shows the coordinates for the two endpoints of the rod and its length as shown in Figure 4 43 Both coordinate values are given in reference to the body to which each point is attached x 4 500 m y _2 200 m x 1 600 m y 0 100 m 1L _2 285 m T First Point Second Point Length 136 Chapter 4 Constraints Figure 4 44 Properties window with a rod selected Length Rod Properties Rods exert whatever force is necessary to keep their endpoints a fixed distance apart To change the properties of a rod 1 Select the rod and choose Properties from the Window menu length 1 924 Active when Always 2 This is the current length of the rod If you specify the length as a numeric constant the rod will be modified to the specified length immediately T
371. the current values for the difference in position velocity and acceleration between the two points of the constraint Each of these fields returns a value of type vector These values measure in the constraint s reference frame The x value is measured along the line connecting the two points of a point to point constraint To find out how fast the length of a spring is changing the difference in velocity between the two endpoints of the spring you enter the following formula constraint 3 dv x Each of these fields returns point that serves as an endpoint of the constraint The p1 field returns the point element that was first created See Point Fields on page B 7 for associated fields force y1 y2 y3 y4 B 5 Operators B 9 The force field returns the vector representing the constraint force The field is equivalent to constraint force n see Simulation Functions on page B 21 Output Fields This is the value displayed on the x axis or the abscissa of an output graph output 6 x value displayed on x axis of output 6 These are the values displayed on the y axis of an output graph output 6 y1 value displayed on y1 axis of output 6 output 6 y2 value displayed on y2 axis of output 6 output 6 y3 value displayed on y3 axis of output 6 output 6 y4 value displayed on y4 axis of output 6 B 5 Operators Operators include all of the common algebraic symbols gt The
372. the entire simulation the computer might unnecessarily spend a long time to compute an acceptable solution to the problem The default option in Working Model 2D automatically adjusts the time step size during the course of a simulation A 5 How Working Model 2D Bounds Errors A 9 Variable Time Step A variable time step integrator is useful in getting accurate results relatively quickly When acceleration changes rapidly during a portion of a simulation the integrator internally reduces the integration time step When possible the integrator will increase the integration time step to improve computational performance In variable time step mode Working Model 2D estimates a numerical error at every integration step A 5 How Working Model 2D Bounds Errors discusses how the error checking is done and if the error exceeds a certain tolerance the current integration time step which is equal to the animation step in the beginning is considered to be too large for the particular frame In such cases Working Model 2D cuts the time step in half and attempts to compute a new result with the smaller time step This result is subject to the same error checking Working Model 2D recursively repeats the process until the discrepancy falls within the tolerance and the remainder of the animation frame is computed using these smaller integration time steps After the frame is finished however Working Model 2D resets the integration time st
373. the external application See below for examples of such commands 6 Run the simulation e Ifthe external application is used as an output of a Working Model 2D meter object data is sent to the external application at every frame of simulation e Ifthe external application is used as an input to a Working Model 2D control object data will be fetched from the external application at every frame You can execute commands that are specific to the external application linked to Working Model 2D For example you can execute MATLAB commands or Excel macros by typing them in Initialize and Execute text boxes before you start a simulation The following are example commands In MATLAB you can type the function calls into Initialize and Execute command boxes Initialize u 0 324 Chapter 9 Importing and Exporting Files and Data A Sketch for Designing a Control System Execute u f x y In Excel you can type Excel macro language into the command boxes On Windows the commands must be enclosed by a pair of box brackets as shown below the brackets are not necessary for MacOS Initialize FORMULA R 1 C R2C3 Execute RUN MACRO1 where MACRO1 is the name of a macro command you recorded for example Please consult Excel s Function Reference manual for details Commands typed in the Initialize box will be executed when the simulation starts before Working Model 2D performs any comput
374. the object to control the configuration of the object 1 Select the Anchor tool in the Toolbar 2 Click on a body An Anchor will appear on the body 3 Select the body with the Arrow tool 4 Choose Properties from the Window menu The Properties window will appear 5 Type a formula in the x y and or rot position fields The body will move according to the formula To make a body move to the right at a constant velocity you could type time 2 3 in the x position field When you run the simulation the body will start at x 2 3 and then move to the right If you type a formula in any of the three velocity fields the values in the position fields will only be used as initial conditions For example if V time and x 3 0 time the center of mass of the object will start at x 3 and then accelerate to the right At time 1 it will have a velocity of 1 in the x direction 10 7 Specifying Body Path by Velocity You can also prescribe the velocity of a body throughout the simulation with an Anchor 1 Select the Anchor tool in the Toolbar 2 Click on a body 10 8 Defining Frames of Reference 339 An anchor will appear on the body 3 Select the body with the Arrow tool 4 Choose Properties from the Window menu The Properties window will appear 5 Type a formula in the Vx Vy or V field To make the center of mass of an object move to the right with constant acceleration you could type time in the
375. the object and choosing Properties from the Window menu 220 Chapter 6 The Workspace Figure 6 27 Properties window for a rectangle Figure 6 28 Appearance window Appearance Window E Body 1 Rectangle Rectangle x 1 400 m y 0 550 m Jo co0 is Ve Jo000 m s Vy Jo c00 m s vo Jo 000 ts material Standard mass Bo o kg stat fric Jo300 kin fric Jo300 elastic ps charge 1 000e 004 C density 1 000 kg m 2 Planar hd moment fi 952 kg m 2 Doing so displays the Properties window that describes the object Figure 6 27 You can then make changes within the window Since the Properties window is a floating window you can move it anywhere you like on the screen The window remains in front even while you are running a simulation You can move a utility window by positioning the pointer on its title bar and dragging it to another location You can make the Properties window wider by clicking in the zoom box on the top right corner or by dragging the bottom right corner This is helpful when entering longer equations Utility windows enable you to quickly change parameters of many different objects You can change more than one object of the same type at the same time Select the objects you wish to change and then enter the desired value in a field of a utility window All objects will be changed at the same time Color Pattern Body 1 Recta w K Show Fill Rectangle o E
376. the selected bodies Figure 3 24 Figure 3 24 Collision submenu three cases 3 6 Controlling Collisions among Bodies 89 Join Split H Mowe To Front F Send To Back 6 v Collide Do Not Collide All selected bodies None of the selected Some bodies collide could collide with bodies will collide with and others do not another another Join Split Mowe To Front F Send To Back 6 Collide v Do Not Collide Join Split Mowe To Front F Send To Back 6 Collide Do Not Collide The checkmark if any beside the two menu items indicates whether the selected objects can collide Three possible cases are as follows e Ifthe checkmark is located beside Collide the selected set of bodies can collide with one another That is any two bodies among the selected set will collide with each other when they come in contact e Ifthe checkmark is located beside Do Not Collide the selected set of bodies cannot collide with one another they will penetrate one another Note that any two bodies among the selected set will penetrate each other when they come in contact e A dash appears on both Collide and Do Not Collide when more than two bodies are selected and the collision property is not uniform for all bodies some bodies collide and others do not For example if you selected the three bodies shown in Figure 3 23 the Object menu will show two dashes To identify
377. the x and y components of the force acting on the center of mass of each body respectively Tis the torque acting on each body 336 Chapter 10 Using Formulas Fields Acting on Pairs of Bodies To model the gravitational attraction between each pair of bodies you can select pair wise forces The directions of F F and T correspond to the reference frame created by the connecting line between each successive pair of bodies Forces in the x direction are parallel to the connecting line and forces in the y direction are perpendicular to the connecting line To model gravity in planetary systems the following equation could be used FX 6 67e 11 self mass other mass sqr self p other p Fy 0 T 0 This is the complete gravitational force definition A force corresponding to Gmm ee t will be applied to each pair of bodies in the simulator r Note that constants are entered in scientific notation so the universal gravitational constant G 6 67x10 is entered in Working Model 2D as 6 67e 11 For more information see Appendix B Formula Language Reference 10 5 Customizing Meters Meters measure properties defined by formulas Whenever a meter is created formula language descriptions are assigned to the meter Suppose you created a position meter for a body You can view the formulas used by a meter in the Properties window as shown in Figure 10 5 below Figure 10 5 Formulas
378. themselves Instead of analytical methods Working Model 2D uses numerical methods to allow the solution of the motion of mechanical systems which are governed by differential equations arising from mechanics principles In 2 D these principles can be expressed in simple equations as F ma Force mass acceleration T IQ Torque moment angular acceleration pa dt instantaneous acceleration time derivative of v _ ax dt instantaneous velocity time derivative of x v do dt instantaneous angular acceleration time derivative of a Working Model 2D uses these equations in its solution of dynamics problems The solution is carried out by a process known as numerical integration l As a matter of fact no analytical solutions exist for 2 bodies either unless they are perfect spheres A 3 Numerical Methods A 7 l dv 7 For example integrating both sides of the equation a results in dt v faat vo which may be approximated as v 4 dt Vo The accuracy of this approximation improves with smaller yt called time step see A 4 Time Step and Performance for more discussion The heart of numerical integration lies in approximating the problem by subdividing the problem into small discrete time steps and incrementally computing the result at each time step More specifically Working Model 2D finds the current acceleration of an object and uses this acceleratio
379. tial pairs of point coordinates Figure 3 22 below shows a sample Microsoft Excel worksheet holding coordinate pairs for six control points 2 683 152 987 3 034 169 616 1 630 77 828 1 477 29 820 2 032 100 187 0 688 158 682 2 Copy the selected data to the Clipboard using the Copy function of the source application 3 5 Anchoring Bodies 87 3 Switch to Working Model 2D and create a polygon or curved body Choose Geometry from the Window menu The vertices of the polygon are not important as they will be overwritten with the new data that is pasted 4 Inthe Geometry window select whether you want the data to be interpreted as World or Shape coordinates by clicking on the appropriate radio button This step is very important Mismatching the coordinate system will lead to an incorrect rendering of the object 5 Click the Paste button in the Geometry window The data points are automatically interpreted as vertex coordinates of the new polygon or curved body 3 5 Anchoring Bodies Use the Anchor tool to limit the motion of a body After selecting the Anchor tool click inside a body to anchor it You can also hide the anchor see Showing and Hiding Constraints on page 96 You may also find the anchor tool useful while you join objects Simply attach an anchor to a body which you do not wish to move when joining objects To remove an anchor simply select the anchor and delete it You can als
380. to the body to which the point is attached You can edit these values at all times The bottom set of is given in global coordinates If local coordinates are defined using geometry based formulas you cannot edit global coordinates since formulas are evaluated with higher priority than any global coordinate specification In the case of a motor that attaches a circular body to the background the base point of the motor has coordinates measured in the World frame whereas the Point has coordinates measured with respect to the center of the circle You can modify these values directly to locate the constraint precisely For example e by modifying the Base Point coordinates you can precisely specify the location of the motor s attachment point with respect to the background the disk and the motor will move together or e by modifying the Point coordinates you can precisely specify the location of the motor s attachment to the disk the disk alone will move Figure 4 9 illustrates this example with a motor 100 Chapter 4 Constraints Figure 4 9 Base Point and Point of a rotational constraint Coordinates Descriptions with Formula Language Point is attached to the circle and has coordinates 1 0 0 0 Base Point is attached to the background and has coordinates 6 0 4 0 To position these constraints precisely using the Properties window 1 Select the rotational constraint and choose Prope
381. tom force field You will see these ID numbers in the formulas used in meters to measure forces produced by these constraints These ID numbers are as follows Force Field Reserved ID gravity 10002 electrostatics 10004 air resistance 10006 custom force field 10008 If you create a meter to measure the force of gravity on a body you will see a formula such as constraintforce 10002 3 y This formula gives the y component of the force applied by constraint 10002 on body 3 The value 10002 is automatically inserted in the formula for this meter as the constraint ID for the gravity force C 1 APPENDIX C Useful Tips and Shortcuts This appendix contains a variety of useful tips that will help you be more effective when using Working Model 2D C 1 Using Modifier Keys The following list explains modifier keys that you can use when editing objects Using the Tab key Use the tab key to select the first value in the Coordinates bar without having to click the field You can also use the tab key to move from one field to the next in the Coordinates bar Holding the shift key down while using the tab key allows you to skip fields backwards MacOS Using the Shift key To select more than one item hold down the Shift key while clicking the items you want Clicking on an already selected object while holding down the Shift key deselects the object Using the Option key To maintain the rest length of a constraint while r
382. tool is hidden in the Polygon Curved Body pop up palette by default Click and hold on the Polygon tool to bring the Curved Body tool in view and select it 2 Position the pointer in an empty area of the background The pointer changes from an arrow to a crosshair indicating that you can start drawing 3 Click once to set the first vertex of the body You can use the values shown in the Coordinates bar to identify the global coordinates of the point The first vertex serves as the first control point in the case of a curved body 4 Move the pointer and click each time you want to create a new vertex Note that the Coordinates bar shows the relative displacement of the mouse pointer from the last vertex created Figure 3 7 64 Chapter 3 Bodies Figure 3 7 Creating polygons or curved bodies Working Model 2D will automatically construct the polygon or curved body as you create each vertex Click on the first vertex or double click the final point to complete the polygon or curved body Alternatively press the space bar to finish after you click the last vertex If you have the Geometry window open the polygon or curved body will display a crosshair titled FOR its frame of reference See Frame of Reference FOR on page 67 for details If you construct a polygon or curved body with crossed lines Working Model 2D will display a dialog warning that the body s moment mass and center of ma
383. tor produces a torque rather than a linear force You can specify the motor constraint in one of the four terms torque rotation velocity and acceleration A torque motor applies a torque of equal magnitude in opposite directions on the bodies attached to the motor A rotation motor exerts whatever torque is necessary to maintain a particular angle between the bodies attached to the motor If you specify the rotation as a numeric constant the actuator will be modified to the specified orientation immediately The Smart Editor see Chapter 5 The Smart Editor will automatically modify the rest of the model to accommodate the specification If you used a formula expression to specify the rotation the formula will be immediately evaluated as t 0 and the motor rotation will be modified accordingly Again the Smart Editor will automatically modify the rest of the model to accommodate the specification A velocity motor exerts whatever torque is necessary to maintain the specified relative angular velocity between the bodies attached to the motor An acceleration motor exerts whatever torque is necessary to maintain the specified relative angular acceleration between the bodies attached to the motor To change the properties of a motor 1 Select the motor and choose Properties from the Window menu Figure 4 58 Properties window with a motor selected Pin Joints and Rigid Joints 4 18 Joints 149 Base Point Po
384. torial you will use the Working Model 2D Smart Editor to create and edit a mechanism When you drag the mechanism with the mouse it moves like a real mechanism The Smart Editor enforces constraints while you edit To construct a linkage consisting of three bars 1 Create a new Working Model 2D document by selecting New from the File menu Close all open documents prior to starting this exercise 2 Double click the Rectangle tool in the Toolbar Double clicking allows you to use a tool successively without re selecting the tool after each use On MacOS systems double clicking on a tool turns its icon dark grey 3 Sketch a rectangle similar to the one in Figure 1 15 4 Sketch two vertical rectangles below the horizontal rectangle While you draw the additional rectangles a small X symbol appears as you move the mouse pointer closer to the midpoints and corners of the existing rectangle This symbol indicates that the Object Snap feature is active see Figure 1 16 18 Chapter 1 A Guided Tour Figure 1 16 Aligning rectangles based on Snap Points Figure 1 17 The layout of a four bar linkage Small X appears as you bring and your drawing starts right the mouse pointer to a Snap Point the first time When you start to create a rectangle while a Snap Point symbol is visible the drawing is automatically aligned to that Snap Point As shown in Figure 1 16 you can start creating a recta
385. traints Inconsistent Constraints Detecting Overlaps A 7 Simulating Collisions A 19 Warnings When a warning occurs the simulation pauses and presents a dialog The simulation can then be stopped or continued Warns when bodies have a velocity or an acceleration large enough to violate the given tolerance specified in the simulation see A 5 How Working Model 2D Bounds Errors This warning can be overridden at run time but the remainder of the simulation may be inaccurate and or unstable Warns when two or more bodies overlap by more than the overlap tolerance see Simulation Error Tolerances on page A 17 at the initial condition and the bodies are not connected by joints or designated as Do Not Collide When two overlapping bodies collide they may cause physical instability in the simulation See Preventing Unstable Simulations on page A 22 for more information Warns when there are more constraints than necessary to constrain a specific object s motion For example a body with several pin joints between it and the background has redundant constraints Warns when the constraints in the model become physically inconsistent e g when an object driven by a constant velocity motor hits a second anchored body This warning can be overridden to continue the simulation if desired but the results of the simulation results may be spurious thereafter A 7 Simulating Collisions This section provides a su
386. treat them as a rigid unit so that no alteration in their relative positions or rotations will occur Rule 4 Collisions are ignored during editing Rule 5 No joint will rotate unless some constraint forces it to do so during editing Rule 6 If a body is resized all constraint endpoints attached to the body remain fixed with respect to the background The only exception is when parametrics are used 182 Chapter 5 The Smart Editor A Robot Leg Example Consider the example of a robot leg a collection of rectangles attached together by pin joints with a single pin joint attaching it to the background See Figure 5 11 The thigh of the leg is the white block and it is the only body attached to the background Figure 5 11 A robot leg 4 Click and drag the thigh the white block The gray blocks will move as a rigid unit rotating the joint between the thigh the white block and the background Figure 5 12 illustrates the situation Figure 5 12 Dragging the thigh q 2 Grabbing one of the gray blocks will cause the joints to pivot and the leg to change shape 5 3 Understanding the Smart Editor 183 Grabbing and dragging the foot Figure 5 13 or the shin Figure 5 14 will cause the joints to articulate and the blocks to move relative to one another Figure 5 13 Dragging the foot Figure 5 14 Dragging the shin
387. u are using Excel you can specify the cell by typing R1C3 to indicate the cell located at row 1 column 3 In MATLAB you can simply type the name of the variable exactly as it appears MATLAB like x initial For Meters observe that all the meter fields like y1 y2 and y3 appear separately You can specify variable names or cell names for all these output channels individually 3 Click the Connect radio button for the particular input or output The RiCj cell specification format may not apply to non U S versions of Excel Please consult the localized documentation of Excel for details Figure 9 18 Connecting Disconnecting individual inputs outputs Executing Remote Commands 9 16 Exchanging Data in Real Time with External Applications 323 By default all inputs and outputs are disconnected Working Model 2D does not establish the connection with the cell or variable unless you choose Connect Again you can Connect or Disconnect each input output individually as shown in Figure 9 18 Document Document Outputs Outputs Connect O Connect h oO Disconnect Disconnect Yartable Variable Initialize Initialize The field y2 of output 3 is connected while the field y3 is not 4 Repeat the steps 1 2 and 3 for all the inputs and outputs that you want to exchange data with the external application 5 If desired specify the Initialize and Execute commands appropriate for
388. u must establish a logical link between Controls Meters and particular cells in Excel or variables in MATLAB In the Properties window for the interface object select an input or output from the list l On MATLAB always type engine instead of a filename 2 The application is launched upon pressing the Enter key after you specify the document name If you save the simulation file with DDE links and re open it later Working Model 2D will not launch the application automatically 322 Chapter 9 Importing and Exporting Files and Data Figure 9 17 Selecting output objects from the list 2 Figure 9 17 shows the list of all Meters when you click on the pulldown menu The same applies for the Control objects as well ropertie External Docume v Wis i Properties im Exierna DOCume wW ws ws2 ws2 Outputs Click on the pulldown box Gutputl4 u2 N Output 4 y3 Connect Output S y1 Disconnect Output S y2 Variable R201 Sutputis u3 aa s Output 5 u4 Initialize _____ and the list of meter mane Execute Execute f r Past outputs appears re _input 3 _ oy Linput 3 _ or Connect Connect D Disconnect D Disconnect Variable RICI Variable Timeout 5 000 s Timeout s For each selected Meter or Control object click the Connect radio button and type in the variable name appropriate for the external application For example if yo
389. u will now add menu buttons to create a demonstration for use by others who are not familiar with Working Model 2D MacOS 1 Choose New Menu Button from the Define menu A dialog box appears asking you to choose the menu command that you want the new button to perform 2 Choose Run from the World menu The button appears with the name Run Clicking on this button is the same as choosing Run from the Run menu 3 Click the Run button to watch the simulation 4 Reset the simulation 5 Choose New Menu Button from the Define menu 6 Choose Reset from the World menu You now have a document with two menu buttons Drag the menu buttons and the velocity control so that your screen looks like Figure 1 34 Windows 1 Choose New Menu Button from the Define menu A dialog box appears asking you to choose the menu command that you want the new button to perform A list of all menu commands and actions is displayed alphabetically 30 Figure 1 34 Menu buttons Chapter 1 A Guided Tour Choose Run from the list a The button appears with the name Run Clicking on this button is the same as choosing Run from the World menu Click the Run button to watch the simulation Reset the simulation Choose New Menu Button from the Define menu Choose Reset from the list You now have a document with two menu buttons Drag the menu buttons and the velocity control so that your screen looks like F
390. uage Scripts serve as an extremely powerful tool to expand the capabilities of Working Model 2D To run a script 1 Choose Run in the Script menu 262 Chapter 8 Running Simulations Figure 8 9 Scripts added to Working Model 2D menu A file browsing dialog appears 2 Find the tool file or the file containing the desired script 3 Click OK Adding Scripts and Tools to the Working Mode 2D Menu You can add frequently used tools and scripts to the Working Model 2D menu and invoke them as if they were another new feature Figure 8 9 Script Run Editor Optimize Create Constraint Document Model Please refer to Working Model Basic User s Manual for instructions on how to add scripts and tools to the Script menu Writing and Editing Scripts On Windows and PowerPC based MacOS systems you can write debug and edit your own scripts and tools These features are not available for 680x0 based MacOS systems Please refer to the Working Model Basic User s Manual enclosed in the product package for more information 8 7 Simulation Modes Simulations can be run in either Edit mode or Player mode Edit Mode Edit mode is Working Model 2D s default mode The full range of menus and toolbars is available for editing and running simulations in Edit mode Figure 8 10 Edit mode 8 7 Simulation Modes 263 Working Model Untitled1 Jo x ey Eie Edit World View Object Define Measure
391. ue object applies a torque on a single body To change the properties of a torque 1 Select the torque and choose Properties from the Window menu 144 Chapter 4 Constraints Figure 4 54 Properties window with a torque selected Torque Properties ix fr Constraint 8 Torque Torque value fi 000 N m r Base Point Point Active when VV Always This is the value of the torque applied to the body Positive torque is defined as counterclockwise 4 16 Actuators An actuator is a multi purpose constraint which exerts whatever force necessary to maintain its constraint specifications You can specify its property in one of four ways force length velocity or acceleration You can specify the magnitude of the constraint using a constant or a formula see Chapter 10 Using Formulas for examples and Appendix A Formula Language Reference for more information The actuator extends or contracts in order to maintain the given constraint condition For example if an actuator is providing a constant force to a body sliding on a horizontal keyed slot the body will experience a linear motion with a constant acceleration Then the actuator stretches indefinitely to follow the moving body and keeps applying the force Creating an Actuator To create an actuator 1 Select the Actuator tool from the Toolbar 2 Position the mouse pointer where you would like to define the
392. umes the value of the current body on which the force field is being applied For example the equation for a linear gravitational field is Fy self mass 9 81 A force is applied to each body in the simulation The value of self assumes the value of the specific body onto which force is being applied Thus in this case each body has a force applied equal to 9 81 times its own mass When force fields are evaluated for each pair of bodies pair wise fields the value of self assumes the body of the first body in each pair B 24 other ground Appendix B Formula Language Reference Returns a body type when placed inside a force field equation When force field equations are evaluated for each pair of bodies in the simulation pair wise fields other assumes the value of the second body of each pair For example the force field equation for planetary gravity is self mass 6 67e 11 sqr self p other p other mass Gmm 7 r or more commonly This equation is applied to each pair of bodies in the simulation As the equation is applied to each pair of bodies self assumes the value of the first body and other assumes the value of the second in the pair Returns a body type for the background This is essentially a body at location 0 0 that never moves Constants Four ID numbers are reserved for the global force fields of gravity electrostatics air resistance and the cus
393. uming that the first row of the table data corresponds to the current frame of simulation since Start Here resets both the frame number and time clock to zero 7 3 Menu Buttons A menu button enables you to add common commands directly to the workspace Clicking on a menu button is exactly the same as selecting the corresponding command from a menu To create a menu button 7 3 Menu Buttons 239 MacOS 1 Choose New Menu Button from the Define menu A dialog box appears asking you to choose the menu command that you want the new button to perform Figure 7 15 New Menu Button dialog New Menu Button r Select the menu item that you want this button to perform Close 2 Choose a command from a Working Model 2D menu The new button appears with the name of the menu item you chose Clicking this new button is the same as choosing the named command from the menu 3 Click OK The button will perform its menu command when clicked Windows 1 Choose New Menu Button from the Define menu A dialog box appears asking you to choose the menu command that you want the new button to perform A list of all menu commands and actions is displayed alphabetically 240 Chapter 7 Simulation Interfaces Figure 7 16 New Menu Button dialog New Menu Button x Select the menu item that you want this EOR button to perform Cancel i Accuracy Air Resistance Appearance AutoErase Track Backgrou
394. urate the simulation Getting High Simulation Accuracy The method used to increase simulation accuracy is similar to that used with finite element analysis packages Run your simulation several times at increasing accuracies until the results begin to asymptotically converge There are two ways to increase accuracy With the Fast method fixed time step decrease the size of the time step With the Accurate method variable time step decrease the value of the Integrator Error term A 24 Appendix A Technical Information The best terms to use as a check for accuracy are the positions and velocities of bodies that are integral to a system and subject to large velocities When simulating a vehicle suspension system use one of the fast moving suspension components to check for accuracy When simulating a swinging chain use one of the outermost links To check for accuracy with a specific component create position and velocity meters for the component Record the meter values at a specific time near the end of the simulation Reset the simulation and decrease the time step by half if using a fixed time step method or decrease the Integrator Error by half if using a variable time step method Run the simulation again and see if the metered values change significantly By running with increasing accuracy you should see any value that you measure converge from simulation to simulation If you do not see convergence in a measured simulat
395. ure fixes the joint p relative to the rectangles A and B The pin joint p will still act as a pin joint but you will not be able to drag it While you try to drag the rectangle B you could accidentally end up moving the pin joint p Lock Points only prohibits mouse dragging of points You can still enter numerical coordinates in the Properties window to reposition points Lock Controls 5 3 Understanding the Smart Editor 181 Lock Controls also found in the View menu is similar to Lock Points but affects controls meters inputs and menu buttons rather than points and the endpoints of constraints This option prevents mouse drags from changing a control s position 5 3 Understanding the Smart Editor The rules that the Smart Editor uses in moving objects on the Workspace are simple and consistent The easiest way to understand the Smart Editor is to play with it These rules are an attempt to codify behavior that is intuitive and consistent with everyday experience Rule 1 No constraint is broken during editing If you drag a rectangle that is joined to a circle the circle must follow along Rule 2 Endpoints of constraints cannot move on the objects they are attached to during editing Points that define a joint do not move relative to the object s they connect to Joints must remain in place Rule 3 If a collection of objects is simultaneously selected a drag or rotate operation will
396. ve which may be slightly different from what you expected 4 19 Slot Joints 173 You can generally work around this problem by turning on the Interpolated option from Working Model 2D when you use Copy Table By copying interpolated points you are exporting more data points per curve allowing another CAD CAM program to mimic the curve you expected more closely 174 Chapter 5 The Smart Editor CHAPTER 5 The Smart Editor Figure 5 1 Working Model 2D element types In this Chapter you will find steps to e Construct joints from points and slots e Drag and rotate bodies while preserving the constraints between them e Use the Lock Points and Lock Controls options to prevent accidental changes to a mechanism 5 1 Joining Elements and Splitting Constraints Pin joints rigid joints and slot joints are constructed of component elements These components include points square points and slots a Point 0 Square Point Slot A Pin Joint is composed of two point elements Two bodies connected by a pin joint are free to rotate relative to each other and cannot be dragged apart A Rigid Joint is composed of two square point elements The two bodies connected by a rigid joint are fixed with respect to one another They cannot be dragged apart and they cannot rotate relative to one another BS mr Join Figure 5 2 Working Model 2D joint types Join 5 1 Joining Elements and Splitting Constraints
397. ved slot joint shows the slot base point and the slot pin coordinates the point at which the body is attached to the slot Both values are based on local coordinates x _0 600 m y _0 050 m x _0 750 m y _ 0 700 m Pep Mi l Slot Base Point Slot Pin Coordinates Curved slots can be reshaped with the mouse or through the Geometry window This section will cover the mouse driven reshaping while Reshaping a Curved Slot Numerically on page 167 of this chapter covers the latter method To reshape a curved slot 1 Choose Reshape from the Edit menu The menu item will be enabled only if a polygon curved body or curved slot objects that can be reshaped exists 2 Select a curved slot The curved slot shows reshape handles at all of its control points as shown in Figure 4 72 4 19 Slot Joints 159 Figure 4 72 Curved slot in Reshape mode 3 Click and drag a reshape handle This will move one of the control points 4 Exit Reshape mode by deselecting Reshape from the Edit menu or by selecting any other tool in the Toolbar You must return to edit mode to drag the curved slot with the mouse To add a control point 1 Be sure to be in Reshape mode the Reshape menu item in the Edit menu should have a checkmark 2 Click on the slot away from an existing control point and drag the new control point to the desired position To delete a control point 1 Be sure to be i
398. vious control point 4 19 Slot Joints 157 To create a closed curved slot joint using the Closed Curved Slot Joint tool directly 1 Create a body that will move along the slot 2 Select the appropriate tool and click once on the body The slot pin will be attached to the object This point also becomes the first control point of the curved slot 3 Click to create as many control points as you like and double click to signal the last control point and finish drawing the slot Alternatively press the space bar to complete the slot after you have clicked to create the last control point Note that the Coordinates bar shows displacement from the previous control point as shown in Figure 4 70 Figure 4 69 below shows a simple example of a body meant to move along an open curved track 1 Click here first and l ae Jocke 9 Double click at the last point 2 Click a sequence of control points x 6 000 ft y 2 000 ft Z 6 325 ft L 18 43 2 x and y offsets distance direction 158 Chapter 4 Constraints Figure 4 71 Coordinates bar for a curved slot joint Reshaping a Curved Slot When the Curved Slot Joint tool is selected Working Model 2D linearly extrapolates the portions of the slot beyond the end control points When the Closed Curved Slot Joint tool is selected Working Model 2D automatically closes the curve between the end control points The Coordinates bar for a cur
399. while making sure that all the constraints are satisfied With its systematic approach Working Model 2D can model a wide variety of problems Numerical methods is a huge area of ongoing research in science and engineering Vast amounts of literature are available on this topic Interested readers are strongly encouraged to refer to more advanced literature The A 9 Technical References may serve as a beginning for interested readers In describing numerical methods let s take the example of a ball traveling in projectile motion For simplicity consider gravity as the only force acting on the ball An analytical solution for the x and y position of the mass center a ball seen in most elementary physics texts is x gt Xo T vt 12 y aa t58 x0 where g 9 81 m sec With these formulas one can find the position of the ball at any moment in time by simply plugging in the correct initial values x9 Yo Vap Ve L Also called symbolic method A 6 Appendix A Technical Information Numerical Integration If projectile motion were the only type of problem Working Model 2D needed to solve this would also be an acceptable way to proceed on the computer However for most physical problems it is impossible to find exact solutions like those for projectile motion For example no analytical solution exists for the equations of motion for three particles or stars all acting under gravitational forces among
400. with a condition that governs the force and or torque that acts upon these points 4 2 Types of Constraints There are four classes of constraints in Working Model 2D e Linear Constraints e Rotational Constraints e Forces and Torques l A pulley system is an exception since it has nodes in addition to end points See 4 10 Pulleys for details 4 2 Types of Constraints 91 e Joints Linear Constraints Linear constraints have two end points and apply force along the line connecting their endpoints Linear constraints include Springs Dampers Ropes Rods Separators Actuators and Pulleys You can construct them by clicking the appropriate tool in the Toolbar and then dragging the constraint onto the workspace Forces produced by these constraints have the equal magnitude and act upon the bodies in opposite directions at either endpoint Rotational Constraints Rotational constraints apply a twisting force torque between two objects Rotational constraints include Motors Gears Rotational Springs and Rotational Dampers All rotational constraints except gears include a pin joint Rotational constraints must be created directly by using the appropriate tool You cannot create a rotational constraint by joining primitive elements Once created rotational constraints can be split and edited as separate points Forces and Torques Forces exert a linear force on a body at a single point Torques exert a twist
401. y or more accurately Pause Control causes the Pause Control dialog to appear allowing you to create conditions for your simulations to loop reset and pause Preferences causes the Preferences dialog to appear allowing you to change various program settings to suit the way you use Working Model 2D The View Menu Workspace provides controls over the appearance of various aspects of the Working Model 2D workspace On MacOS systems the Workspace menu item presents a submenu you can either toggle options in the submenu or set multiple options by selecting the Workspace dialog from the submenu On Windows systems there is no submenu of individual options the Workspace menu item leads directly to a dialog with enhanced toolbar options see below The Workspace menu MacOS and the Workspace dialog Windows provide the following options Rulers shows or hides rulers Grid Lines shows or hides grid lines X Y Axes shows or hides the x y axes Coordinates shows or hides the Coordinates bar at the bottom of the active simulation window 2 2 Working Model 2D Menus 51 Status Bar shows or hides the Status bar across the top MacOS or bottom Windows of the simulation window Scroll Bars shows or hides the scroll bars Tape Player Controls shows or hides the Tape player controls on the bottom of the active simulation window Toolbar MacOS shows or hides the Toolbar along the left side of the active simulatio

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