Promech Manual
Contents
1. Figure 5 Screen display generated by program in Section V Section VI Error messages If any rules are broken an error message is generated by the subroutine which detects the fault This consists of the subroutine s name together with a short diagnostic and the program then usually halts A typical error message might be BODY OUT OF SEQUENCE which would tell the user that one of the calls to subroutine BODY had not been made in the order shown in Section IL The full list of diagnostics is as follows BAD ALIGNMENT The two parts of a joint are so far out of alignment that it is not clear which way they should fit e g the axis of a pin is perpendicular to the axis of the hole it is to fit into CONSTRAINTS OR BODY POSITIONS BADLY SPECIFIED FEMALE TAG INVALID AXIS INVALID BODY INVALID TAG INVALID TAG TYPE The mechanism may be overconstrained in one area and underconstrained in another or the initial positions of the bodies may have caused the assembly process to stall e g a pin may be lying exactly perpendicular to the hole it fits into ROTATE and MOVE can only operate on pins The axis for BODROT must lie in the range 1 3 A body number quoted in the call to the subroutine is greater than the number of bodies so far defined or less than 1 In the case of subroutine ROTATE body no 1 is a2. since body 1 is the reference frame If the given reference direction is not perpendicular to the axis direction the component which is perpendicular will be used instead Body IBOD must exist when ADDTAG is called CALL ADDMAS UBOD RM GX GY GZ XX YY ZZ XY YZ ZX gives body IB an additional mass of RM with its centre of gravity at GX GY GZ in local body co ordinates and with moments and products of inertia Ixx Iyy Izz Ixy lyz and Izy CALL BDASK UIBOD VV VA returns the current angular velocity vector VV and angular acceleration vector VA of body IBOD CALL BODMAS IBOD RM GX GY GZ XX YY ZZ XY YZ ZX specifies the mass RM of body IB its centre of gravity GX GY GZ in local body co ordinates and the moments and products of inertia Ixx lyy Izz Ixy lyz and Izy CALL BODMOV IBOD X Y Z Moves the body IBOD through the vector X Y Z in the fixed reference frame Bodies should be in approximately the correct position before the mechanism is interrogated Figure 4 Definition vectors for shafts and holes CALL BODROT IBOD IAX ANG rotates body IBOD through an angle ANG radians about the axis IAX of the fixed reference frame 1 X 2 Y 3 Z The position of the body s origin does not change Bodies should be in approximately the correct position before the mechanism is interrogated CALL BODY ITYPE S1 S2 S3 specifies a new body of type ITYPE see Fig 2 with dimensions S1 S2 and S3 where appropriate If ITYPE 0 the
3. body is a tagless and featureless blob The body is initially positioned with its origin and axes coincident with those of the fixed reference frame Bodies are given unique numbers starting from 1 which is the fixed reference frame CALL DRAWMECH produces a schematic drawing of the mechanism in its current position see Fig 5 CALL FORCE ITAG IBOD FX FY FZ CX CY CZ applies a force FX FY FZ and couple CX CY CZ to tag ITAG on body IBOD This force remains acting on the tag until it is altered or set to zero CALL FCASKUTAG IBOD VF VC CALL GRCLOSE CALL GRSET CALL GRUSER returns the force VF plus the couple VC acting on the tag ITAG of body IBOD in local body co ordinates The line of action of the force is through the tag location quoted in ADDTAG The force and couple include forces from any other body jointed to this tag and any external forces specified by FORCE closes down the graphics environment and restores the normal behaviour of the screen or window On a Windows 9x NT machine it may also be necessary to type Alt Enter from the keyboard to restore the window size sets up the Promech graphics environment Promech does this automatically when it needs to draw something but this subroutine is available in case your program needs to use the graphics environment before Promech does prevents Promech from choosing the scale of the drawing and from clearing the drawing area before drawing a picture Th
4. CALL ROTATE 1 2 0 1 0 C LOOP FOR ONE REVOLUTION OF THE JOINT DO 20 I 0 179 CALL TSET FLOAT I 3 14159 90 C DRAW PICTURE OF MECHANISM T 20 CALL DRAWMECH CALL GRCLOSE STOP END Section V An Advanced Example A more advanced version of the program from Section IV is shown below It illustrates how Promech can be used in conjunction with the system s native graphics routines to produce more advanced displays Statements in lower case are calls to a proprietary DOS graphics package details on request and not to Promech routines C SAMPLE CODE FOR UNIVERSAL JOINT C Implementation specific graphics calls shown in lower case C GET NGLE FOR JOINT AND INITIALISE PROMECH IMENSION VV 3 VA 3 RITE Joint angle EAD A COS A 57 2958 SIN A 57 2958 CALL MECHINIT C TAGS FOR BODY 1 FRAME CALL ADDTAG 4 1 12 0 0 Sh Dag Or Ore Pea CALL ADDTAG 4 1 12 PCL 2S 7 Oe CR Spisy S7 CrO C BODY 2 1ST FORK CALL BODY 3 4 6 6 C BODY 3 CROSS CALL BODY 4 5 5 0 nawzo H C BODY 4 2ND FORK CALL BODY 3 4 6 6 C JOINTS BETWEEN BODIES CALL JOINT 1 1 1 2 1 1 CALL JOINT 2 1 1 4 0 0 CALL JOINT 2 2 1 3 0 0 CALL JOINT 3 2 2 3 0 0 CALL JOINT 2 4 3 3 0 0 CALL JOINT 3 4 4 3 0 0 C POSITION
5. PROMECH II USER S MANUAL This package provides facilities for the description and analysis of many three dimensional and planar mechanisms A kinematic model of the mechanism can be drawn and the velocity and acceleration of any part of it can be determined throughout its cycle of movement Loadings on joints caused by the accelerations within the mechanism can also be calculated The package is written throughout in Fortran 77 and is readily available to interested parties A L Johnson Cambridge University Engineering Department Trumpington Street Cambridge U K May 2000 Figure 1 Typical 3 D Mechanism Hooke s Joint Section I Description of the package The package consists of a family of Fortran subroutines designed to calculate the velocity and acceleration and inertia forces of elements in spatial mechanisms By writing a programme which calls these subroutines the user is able to describe the topology of a mechanism to set it in motion and by interrogation to find the subsequent position velocity and acceleration of any part of it With this information the user can proceed to calculate inertia stresses and other data within the main programme Incorporation of the calculation and interrogation sequence into a program loop permits the mechanism to be analysed throughout its entire cycle The mechanisms analysed consist of solid bodies which may be connected to other bodies by means of cylindrical shafts which fit into
6. THE BODIES CALL BODROT 4 1 1 57 CALL BODROT 4 3 A 57 3 14 CALL BODMOV 2 12 0 0 CALL BODMOV 4 12 C 12 S 0 C SET UP VIEWING DIRECTION CALL VIEWROT 3 60 CALL VIEWROT 1 60 C INPUT VELOCITY CALL ROTATE 1 2 0 1 0 C INITIALISE GRAPHICS amp DRAW AXES FOR VELOCITY GRAPH CALL GRSE call write Press any key to stop 21 call pnt 525 0 call lin 525 6 call colour 2 Call pnt G 5257 25 call lin 975 25 call uscl 8 8 call orig 2 3 C INHIBIT AUTOMATIC SCALING OF DRAWING BY PROMECH CALL GRUSER ICOLOUR 12 C ALTER COLOUR FOR VELOCITY PLOT AT START OF EACH LOOP 10 ICOLOUR 16 ICOLOUR C LOOP FOR ONE REVOLUTION OF THE JOIN DO 20 I 0 179 CALL TSET FLOAT I 3 14159 90 C FIND ANGULAR VELOCITY OF OUTPUT BODY 4 CALL BDASK 4 VV VA R SQRT VV 1 2 VV 2 24 VV 3 2 C DRAW SECTION OF LINE FROM PREVIOUS INSTANT TO PRESENT INSTANT call colour icolour call pnt float i 1 400 525 rold 4 if i gt 0 call lin float i 400 525 r 4 ROLD R C CLEAR LEFT HAND HALF OF SCREEN call i10hd 256 6 0 256 4 1 256 23 39 C DRAW PICTURE OF MECHANISM AND TEST FOR USER INTERRUPT CALL DRAWMECH call testkey ib 20 IF IB NE 0 THEN CALL GRCLOSE STOP ENDIF C START ANOTHER LOOP GO TO 10 END
7. cs controls There are a few rules about the order in which these subroutines should be called The following flowchart shows the normal calling sequences INITIALISATION DESCRIPTION SET MOTION ALTER TIME AMEND MOTION KINEMATIC INTERROGATION DRAWING SET AMEND FORCES gt FORCE INTERROGATION Section III The subroutines A full specification of the subroutines is given in alphahabetic order in this section Arguments beginning with I are integer and others are real in accordance with Fortran defaults Those beginning with V are vectors and should be given dimensions of 3 in the calling program All angles are in radians unless otherwise stated Other units are at the user s discretion but must be consistent for instance forces will only be returned in Newtons if lengths are quoted in metres masses in kilograms and time in seconds A mechanism may currently consist of up to 20 bodies each of which may contain up to 10 tags these limits can be increased if required CALL ADDTAG ITYPE IBOD XP YP ZP X1 Y1 Z1 X2 Y2 Z2 adds a tag of type ITYPE to body IBOD at the initial position XP YP ZP in the body s local co ordinates with axis direction X1 Y1 Z1 and initial reference direction X2 Y2 Z2 see Fig 4 All tags shafts or holes on bodies are given unique numbers starting from 1 though the first few are usually predefined according to the type of body see Fig 2 If IBOD 1 a fixed tag is created
8. cylindical holes pockets or slots Any properly constrained mechanism driven by shafts which move axially i e rams and or which rotate about their axis can be analysed A typical mechanism is shown in Figure 1 The sequence of specifications would be as follows Describe bodies Body 1 is the fixed frame There are two deep cylindrical holes in the fixed frame Body 2 is a fork Body 3 is a cross Body 4 is a second fork Describe constraints Body 2 is fitted into one of the fixed holes with axial and rotational constraint Body 2 is fitted onto the cross in two places Body 4 is also fitted onto the cross in two places Body 4 is fitted to the second fixed hole but with no axial or rotational constraint Describe motion The pin on body 1 in the fixed hole has a given angular velocity with respect to the body which causes the body to rotate relative to the frame The positions velocities and accelerations of all the bodies and specified points can now be found using various interrogation routines Following a call to a subroutine which advances the clock the behaviour of the mechanism can be recalculated at another point in its cycle Each new body which is created is given a type as shown in Fig 2 As can be seen these types have various numbers of tags shafts or holes which can be joined to appropriate tags on other bodies Figure 2 Standard body types In addition to its standard tags any body can b
9. e given further tags of the types shown in Fig 3 When a joint is made the two tags are quoted together with information about whether rotation about and movement along the shaft axis is permitted This is equivalent to giving the shaft a circlip and or a keyway as shown in Fig 3 This allows for 16 different kinds of joints each of which imposes a certain number of constraints on the overall mechanism as shown in the cells in Fig 3 For the mechanism to be analysed the total number of constaints must be six times the number of bodies apart from the fixed frame which have been created SHAFTS ALL TYPE 0 Groove for Circlip Keyway 98 fi amp HOLE TYPES ae will Figure 3 Standard tag and joint types showing the number of constraints introduced by each joint Section II Method of operation The subroutines can be called by any program and are accessed by including the Promech III Library when the program is linked or loaded The method by which this is done is implementation dependent External references created by the user such as the names of subroutines and Fortran common areas should not begin with the letters PM A complete program to analyze the mechanism in Figure is given in Section IV The program starts with any interactive driving instructions which the user wishes to insert and continues with a description of the mechanism and then the calculation of a complete cycle at two degree intervals of rotation of
10. is subroutine is only used in advanced graphics applications e g a split screen display see Section V If you call this routine you must ensure that the on screen plotting area is suitable for drawing the mechanism and must clear the screen if necessary between successive drawings CALL JOINTUTAGI1 IBOD1 ITAG2 IBOD2 IALOK ITLOK CALL MECHINIT specifies a joint between tag ITAG1 on body IBOD1 and tag ITAG2 on body IBOD2 One of the tags must be a pin and the other a hole pocket or slot and the tags and bodies must exist when the subroutine is called If ALOK 0 the shaft is given an axial constraint i e a circlip which keeps its position coincident with the baseplane of the hole or slot and if ITLOK 0 it is given a rotational constraint i e a woodruff key which keeps its reference direction in the plane of the hole s reference direction and axis The bodies and tags must already have been specified when JOINT is called initializes the data area or clears all accumulated data about an existing mechanism permitting the main program to define a completely new one without restarting The reference frame body 1 is set up with no tags CALL MOVE ITAG IBOD S DS D2S specifies that tag ITAG on body IBOD is to have its reference point moved through S along its axis with velocity DS and acceleration D2S The tag must be a shaft CALL NOSET inhibits the default automatic scaling by DRAWMECH when the first picture is
11. lso invalid as the reference frame can t rotate A tag number quoted in the call to the subroutine is greater than the number of tags so far defined on the body or less than 1 A call to ADDTAG has been made with an illegal value of ITYPE NO CONVERGENCE ON ASSEMBLY OUT OF SEQUENCE The mechanism cannot be assembled either because the parts do not fit or because the approximate angles of the bodies give an appropriate starting point for the assembly process This can happen on initial assembly or subsequently if the time steps are too large The subroutine has not been called in the sequence suggested in Section II PARALLEL VECTORS The two direction vectors for a tag need not be exactly perpendicular but must not be parallel TAG ALREADY IN USE A tag can only be used for one joint Two coincident tags can however be specified on a body if required e g if two bearings are fitted on a shaft TWO MALE FEMALE TAGS A joint must always consist of a pin and some type of hole or slot TOO MANY BODIES The current limit is 20 including the fixed frame TOO FEW MANY CONSTRAINTS The number of constraints placed on the mechanism by the joints see Fig 3 must be equal to 6 times the number of bodies in the mechanism not including the fixed frame TOO MANY FORCES The current limit is 100 TOO MANY JOINTS The current limit is 100 TOO MANY TAGS ON A BODY The current limit is 10 ZERO LENGTH VECTOR The direction vectors qu
12. n the mechanism is viewed from when MECHDRAW is called Initially the axes of the mechanism reference system are aligned with those of the viewing frame with X pointing to the right Y upwards and Z towards the user Section IV A Simple Example A straightforward sample user program is shown below It describes the mechanism shown in Fig 1 following the sequence specified in Section I The output is an animated version of the left half of Fig 5 showing the joint operating C SAMPLE CODE FOR UNIVERSAL JOINT C GET NGLE FOR JOINT AND INITIALISE PROMECH RITE Joint angle EAD A COS A 57 298 SIN A 57 298 CALL MECHINIT C TAGS FOR BODY 1 FRAME CALL ADDTAG 4 1 12 0 0 Sp Oi us Ol Ley Oe CALL ADDTAG 4 1 12 eC 1285 057 CroO Sya Cr 0s C BODY 2 1ST FORK CALL BODY 3 4 6 6 C BODY 3 CROSS CALL BODY 4 5 5 0 naws DP H C BODY 4 2ND FORK CALL BODY 3 4 6 6 C JOINTS BETWEEN BODIES CAL JOINT 140025148 CALL JOINT 2 1 1 4 0 0 CALL JOINT 2 2 1 3 0 0 CALL JOINT 3 2 2 3 0 0 CALL JOINT 2 4 3 3 0 0 CALL JOINT 3 4 4 3 0 0 C POSITION THE BODIES CALL BODROT 4 1 1 57 CALL BODROT 4 3 A 57 3 14 CALL BODMOV 2 12 0 0 CALL BODMOV 4 12 C 12 S 0 C SET UP VIEWING DIRECTION CALL VIEWROT 3 60 CALL VIEWROT 1 60 C INPUT VELOCITY
13. oted to ADDTAG cannot be zero
14. requested This is sometimes necessary e g if only part of the graphics area is to be used for the kinematic picture as in the sample program CALL PTASK ITAG IBOD VP VV VA CALL RESET returns the current position VP velocity VV and acceleration VA of the tag ITAG on body IBOD resets the mechanism and clock to the condition they were in when the mechanism was first drawn or interrogated CALL ROTATE UTAG IBOD A DA D2A CALL SEEFIT CALL TSET T specifies that tag ITAG on body IBOD is to have its reference direction turned through angle A in radians with respect to its initial direction anticlockwise when the tag s axis is pointing at you with angular velocity DA and angular acceleration D2A The tag must be a shaft causes a sequence of pictures to be drawn as the mechanism is assembled This is particularly helpful if you are getting problems with convergence on initial assembly advances the clock to time T The positions and velocities of all points set by MOVPNT and the angles and angular velocities of all bodies set by ROTATE are altered by an amount corresponding to their quoted velocities and accelerations over the elapsed time interval since the last call to TSET or since T 0 if this is the first call to TSET since MECHINIT CALL VIEWROT IAX ANG rotates the mechanism reference system through an angle ANG in degrees about the axis IAX of a fixed viewing frame 1 X 2 Y 3 Z to determine directio
15. the driving crank Full details of the subroutines are given in Section III below where the subroutines are placed in alphabetical order They can however be usefully grouped as follows Initialization CALL MECHINIT initiates data stores ready for a new mechanism Description CALL BODY specifies a new body CALL ADDTAG adds a tag pin round hole or slot to a body CALL BODROT rotates a body into position for assembly CALL BODMOV moves a body into position for assembly CALL JOINT specifies a joint between two bodies Set or amend motion CALL ROTATE gives a pin rotary motion about its axis CALL MOVE gives a pin linear motion along its axis Forces amp c CALL BODMAS specifies a body s mass and inertias CALL ADDMAS gives a body additional mass and inertias CALL FORCE applies a force to a tag Set time CALL TSET sets the clock Interrogation CALL PTASK finds a point s position velocity amp acceleration CALL BDASK finds a body s position velocity amp acceleration CALL FCASK finds the forces and couples acting on a tag Graphics CALL SEEFIT sets a flag to animate the assembly process CALL VIEWROT sets the viewing direction CALL DRAWMECH draws the mechanism in its current position CALL GRCLOSE closes down graphics after use Resetting CALL RESET resets the mechanism to its initial position Advanced use CALL GRSET sets up the graphics environment if you need to use it before Promech does CALL GRUSER overrides Promech s graphi
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