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IN-PARALLEL PASSIVE COMPLIANT COUPLER FOR ROBOT

1. A B C D E 1 B C D E m1 F A B C D E 2 2 1 A B C D E C E m2 F A B C D E K4 A B C D E K5 m3 F A B C D E K6 m6 A B C D E Lsfor33 0 sqrt K1 L 00151 K2 L 505151 5051 K3 L pOp1 L tOtl L tOtl K5 L 404151 041 K6 L rOrl L r0r1 or Lsfor33 1 sqrt fabs k1 151 o0o1 L 1 A Lsfor33 0 Lsfor33 0 os Lsfor33 2 sqrt fabs k4 m4 L 50585151 5051 D Lsfor33 1 Lsfor33 1 ps Lsfor33 3 sqrt fabs k2 m2 L pOpl L B Lsfor33 2 Lsfor33 2 pt Lsfor33 4 sqrt fabs k5 m5 L tOtl L tOtl E Lsfor33 3 Lsfor33 3 qt Lsfor33 5 sqrt fabs k3 m3 L qOq1 L 4041 C Lsfor33 4 Lsfor33 4 qr Function to perform forward analysis of 33 stewart platform 57 void solve platform int pnum solutions double _2_1 8 4 4 double x 1 double qx 1 double q y 1 double s x 2 double t x 2 double t y 2 34 double L or double L os double L ps double pt double double L int poly solve double root r double root c int d double coeff Inte 2122 double p 1131 1 3 vk 3 _1 0 p x 1 1 0 0 1121 0 0 1 1 1 4 1 2 0 0 vk 0 0 0 vk 1 0 0 vk 2 1 0 double L op L pq L
2. 2 deg 2 for k 0 k lt deg k coef k B k if deg 2 goto solve quad if deg 1 goto solve linear The root to the orig eqn is 1 of the polynomial by 1 7 X X Y Y B k 2 2 0 X B k 1 53 else goto L30 ROK KKK KK k k k k k k k ke ke k ke ke e e e x x Solve quad dis coef 1 coef 1 4 0 coef 2 coef 0 X coef 1 2 0 coef 2 if dis gt 0 0 Y Sqrt dis 2 0 coef 2 root r cnt root r cnt 1 X Y root c cnt root 1 0 0 else Y Sqrt dis 2 0 coef 2 root r cnt root r cnt 1 X root c cnt root c cnt 1 return 1 solve linear root r cnt coef 0 coef 1 root 0 0 return 1 k k k k K k K K K K K K K K K K K K K K KOK KOK KOK KOK K ck kok ck k k k k K k K k K K K K k K K K K K K K KOK K K KOK K KOK K KOK KOK kck k k multiplies two Polynomials a0 al a2 a da b bl b2 b db ab ab0 abl ab2 ab da db KOKCKCKCKCKCKCKCKCkCKCk Ck k k k K k K K k K K K K K K K kCKCk K KOK k kc k Ck KOK ck KOK K KOK KOK ckokck R koe e O void pmult Poly A Poly B Poly int i j da db double a b ab da A deg db B deg a A coef b B coef ab AB gt coef AB deg datdb 150 1 4
3. Fig 6 Section of Captive Ball Joint with Teflon Plates The mechanism in the middle of the leg consists of some thin sheets of spring steel arranged in a serial and parallel way in order to get as much compliance as possible in a small space while maintaining enough lateral stiffness to prevent the leg from buckling figure 7 b The outer four sheets of steel are thinner than the two sheets in the middle of the leg assembly The spring constant of each connector was calculated by assuming that each of the thin sheets of steel behaves as two cantilever beams one beam on either side of the middle parts of the leg assembly in pure bending and then calculating the force contained in each individual sheet given the maximum allowable 14 displacement and adding them together according to the serial parallel way that they are connected figure 7 a Therefore there are eight outer beams and four inner beams Fig 7 Connector Springs Elastic elements of the leg 7 b Compact arrangement of elastic elements The steel sheets have the dimensions given in Table 1 These dimensions are then put into the following equation for the deflection of a beam FP BE 5 200000 6 The outer and inner springs are then combined into total deflection of the connector 80 40 outer 7 total 7 inner 20 0508F 0 0241F 8 total 15 The variable in equ
4. 1 1 bmatrix2 k j 48 printf 7 2f n bans 0 6 void matvecmult6616 double cwrench 6 double 6 6 double ctwist 6 THE 1 0 1 lt 6 1 cwrench i 0 0 for 1 0 1 lt 6 1 for 0 36 j 1 1 5 ctwist j Function to multiply a matrix times a vector and return the answer void vecmult double 1 4 double matrix1 4 4 double vector1 4 int iz for 1 0 1 lt 4 1 1 1 0 for 1 0 1 lt 4 1 for 0 j 4 j ansl i matrixl i jl vector1 j double dotproduct double vector1 3 double vector2 3 double ans 0 ant for 1 0 1 lt 3 i ans vectorl i vector2 i return ans void crossproduct double ans 3 double vector1 3 double vector2 3 ans 0 vectorl 1 vector2 2 vector1 2 vector2 1 ans 1 vectorl 2 vector2 0 vector1 0 vector2 2 ans 2 vectorl 0 vector2 1 vectorl 1 vector2 0 double vecmag double vector 3 double ans 49 ans sqrt vector 0 vector 0 vector 1 vector 1 vector 2 vector 2 return ans int valuenear double val double goal double tol if val gt goal tol amp amp val lt goal ttol return 1 else return 0 int INT 100 char _ 50 void MatSwap double 51 double s2 double temp temp
5. z 1 amp amp cand value 0 31 1 z candidate 0 0 z candidate 1 1 z candidate 1 else if value 1 cand value 1 value 3 lt cand value 2 cand value 0 amp amp amp amp cand value 1 lt BB3 aa2 ccl CC3 aal cc2 lt else if cand value 2 42 1 y candidate 1 zz i z candidate 0 value 2 lt cand value 0 amp amp cand value 3 else if cand value 3 cand value 1 amp amp cand value 2 yy i candidate 0 zz i 7 candidate 1 cand value 3 lt cand value 0 amp amp cand value 2 cand value 1 amp amp cand value 3 yy i candidate 1 zz i z_candidate 1 thetax 2 0 atan xx i thetay 2 0 atan yy il thetaz 2 0 atan zz i sin x sin thetax COS X cos thetax y sin thetay y cos thetay sin 2 sin thetaz COS 2 cos thetaz SX Sx prefold sy cos y prefold Sz sin y sy prefold rx 41 rx prefold 541 cos x ry prefold ry 41 rx prefold 41 cos x ry prefold rz sin x ry prefold tx 41 tx prefold 541 p cos z ty prefold ty 541 tx prefold 41 p cos z ty prefold tz sin z ty prefold Enter origin of 2
6. 1507 3 HOLES 3 2 01261 THROUGH EQUISPACED ON A 1481 HOLES 3 2 01261 THROUGH EQUISPACED ON A 136 8 3 HOLES 3 2 01261 THROUGH EQUISPACED ON 1083 8 0 315 THROUGH 6 HOLES 6 0 236 THROUGH EQUISPACED ON A 60 NOTES UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED ES UNLESS OTHERWISE SPECIIED PROJECT FORCE TORQUE SENSOR C C S 2 SECONDARY DIMENSIONS ARE INCHES DRAWN TOLERANCES ARE DATE 3 19 00 1 3 REMOVE ALL BURRS AND SHARP EDGES FRACTIONS DECIMALS TITLE LOWER PLATFORM PLATE 0 13mm 0 005 0 26mm 0 01 X X X XX 8802 10 42 5 8 0 315 THROUGH 3 HOLES 3 2 0 1261 THROUGH 100 123 937 EQUISPACED UN 32 65 3 HOLES 9 3 2 0126 THROUGH EQUISPACED IN A 9 48 49 3 HOLES 3 2 01261 THROUGH EQUISPACED ON A 6708 HOLES 9 3 2 0126 THROUGH EQUISPACED ON 9002 NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL 1 8 ALUMINUM PLATE DIMENSIONS ARE IN MILLIMETERS DRAWN TYLER 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE PRAWN 5719705 3 REMOVE ALL BURRS AND SHARP EDGES FRACTIONS DECIMALS TITLE UPPER PLATFORM PLATE O 13mm 0 005 X XX X XXX 0 26mm 0 01 X X X XX RWG 5 LIST OF REFERENCES Crane C D and Duffy J 1998 Kinema
7. alic Mesdames 24 CONCLUSIONS FUTURE WORK a 25 APPENDIX A COMPUTER CODE 27 APPENDIX B PART 5 22 59 REFERENCES no aae 88 BIOGRAPHICAL SKETCH siie te 89 iii LIST OF TABLES Table page F Dimensions zo oet 14 2 Desired Load and Compliance Characteristics eene 17 3 Potentiometer Calibration Values 20 4 Wrench Comparison 13818 edel 21 iv LIST OF FIGURES Figure page 1 Passive In Parallel Platform on a Serial Robot 2 6 3 In Parallel Mechanism iat b ce ccu gebe ins 8 4 view of 3 3 Parallel mechanism Structure 10 5 Compliant Platform Simulation Software 12 6 Section of Captive Ball Joint with Teflon Plates I3 Connector Springs EN RENS 14 8 Assembly RRRP Mechanism ER 16 9 Computer Rendering ute tet ami als uot ud 26 Abstract of Thesis Presente
8. s12 41 534 s41 c34 12 41 34 541 534 c23 four bar at point double v 3 qo 3 qpl0 _ 0 v qp 1 1 qpl2 2 v_go 0 q 1 0 qo 1 41411 qo 2 4 1 2 41 dotproduct qo v vecmag v qo vecmag v qp crossproduct pxq qo v 541 pxq 2 vecmag v qo vecmag v qp vk 2 223 c34 534 12 512 L qt L qt 4 1 0 sin acos 234 L 1 pq sin acos c12 Second equation AA2 z 2 x 2 BB2 double AA2 AA2 BB2 CC2 DD2 EE2 al al al al a2 a2 a2 cl 1 2 2 2 1 1 b2 2 for i coef 0 0 Coef coef 0 coef coef 0 0 1 0 1 pmult 512 5125 512 4 0 s12 temp2 b2b2 BB2 CC2 41 c34 1 s34 41 s34 512 534 41 534 cl a2 2 p32 33 34 deg 2 cout cout cout cout al 2 2 C2 a2 a2 deg 2 0 0 1 BB2 0 0 AA2 El 20 0 EE2 0 0 2 0
9. XY SQqEt OX X c VEY x if Fabs dXY XY 0 0000000002 was 0 0000001 ltryt t if ltry 400 was 300 goto L38 else goto flip poly else goto reduce_poly flip_poly Lflipt ltry 0 for 0 k lt deg k Z k coef deg k for k 0 k lt deg coef k Z k if lflip 1 0 189 if 1 11 552 1st 4 goto 135 return 300 A solution was not found for 300 iterations for 4 starting values ROKR KKK KKK k k k k reduce_poly if Fabs Y 0 000006 was 0 0000005 0 0 lt 7 if lflip 1 for k 0 k deg k Z k coef deg k for k 0 k lt deg k coef k Z k den X X Y Y root r cnt 1 X X den root c cnt 1 Y Y den else root r cnt 1 X root c cnt 1 if Y 0 0 Reduce the equation by 52 flip it back one degree C X B deg 0 0 for k deg 1 0 k B k coef k 1 C B ERI o fF Le deg Reduce the degr for k 0 k lt deg k coef k B k if deg 2 goto solve quad else if deg 1 goto solve linear Reduce the equation by the complex conjugates else goto L30 else root r cnt 1 X root Y B deg 2 coef deg B deg 3 coef deg 1 2 0 X B deg 2 for k deg 4 k gt 0 k
10. s1 982 562 temp void Transpose double double int m int n int 1 3 150 i m 1 350 j n 244 j m 1 ar 1 75 KK kCk ck k kc k kokck ck ckok ck ckok ck ke ke e x Function to initialize serial ports void setport int address int set serial port parameters outporth address 3 0x80 line contr reg to take baud settings outportb address baud rate outportb address 3 3 8 bits no parity 1 stop outporth 5 4 0 3 modem control reg std setting if inportb address 5 amp 1 1 inportb address clear RDR K K K K K K K K K K K KOK K KOK K KOK K k KOK K KOK OK KOK K R OK R k KO O int poly_solve double root_r double root_c int d double xcof This routine will evaluate the roots of a polynomial of degree d d must be less than or equal to 36 root r and root c are the real and complex parts of the d solutions to the original equation xcof is an array of coefficients ordered from smallest to largest power xcof 16 x l6 xcof 15 15 xcof 1 x xcof 0 0 50 double coef 37 dis X Y 2 37 XX 40 YY 40 U V dUx den dX XY C B 40 int i k deg cnt int 1852 lfilp ery if d gt 36 return
11. 4X 2 26 0 089 THROUGH 0 310 00531 0 20 ra ra o 2 IN 8 c 2 17 00 0 669 23 00 0 906 38 00 1 496 NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL 0 015 SS SHIM STOCK DRAWN TYLER 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DAE i 12 00 3 mnMnMn 00 3 REMOVE ALL BURRS AND SHARP EDGES FRACTIONS DECIMALS TITLE IDDLE SPRING 0 13mm 0 005 X XX X XXX DWG NO 14 REV 10 0 26mm 0 01 40 00 1 575 400 0157 4X 2 26 0 089 THROUGH pxstooos 4 5 ra o e S 2 J2 2 Sj 17 00 0 669 23 00 0 906 38 00 1 496 NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL 0 010 SS SHIM STOCK DIMENSIONS ARE IN MILLIMETERS DRAWN TYLER 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE 1 15 00 _ j 3 REMOVE ALL BURRS AND SHARP EDGES FRACTIONS DECIMALS OUTSIDE SPRINGS 0 13 0 005 X XX X XXX DWG NO CIMAR 15 PREV lo 1 0 26mm 0 01 5 40 UNC lt 2 CLEAN ENDS THREADING NOTES 1 MATERIAL 5 40 18 8 SS THREADED ROD 2 SECONDARY DIMENSIONS ARE INCHES 3 REMOVE ALL BURRS AND SHARP EDGES 18 8 0 74 UNIVERSITY OF FLORIDA CIMAR PROJECT COMPLIANT F
12. 5 1 90 ONIN 0 13 0 005 X XX X XXX DWG 21 0 26mm 0 01 3X 0 3 26 101281 THROUGH 9 01310 0051 2 8 91 0 3511 THROUGH CSINK 10 70 0 421 X 60 00 FROM OPPOSITE SIDE 0 13 0 005 2150 0 8461 20 0 0 79 12 50 0 4921 250 0 981 3 50 0138 0 00 0 0001 159 0 0631S gt 16 00 0 6301 12 00 0 4721 9 00 0 3541 4 00 0157 0 00 0 0001 OTES UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED CU QUEE UNLESS OTHERWISE SPECIFIED PROJECT COMPLIANT FORCE TORQUE SENSOR C 7 SECONDARY DIMENSIONS ARE INCHES DRAN e RR TOLERANCES ARE DATE 19 00 _ ORDINATE DIMENSIONS ARE BASIC FRACTIONS DECIMALS OW TEFLON PLATE 1 REMOVE ALL BURRS AND SHARP EDGES 0 13mm 0 005 X xX X XXX Duc V xxi DWG NO 22 3X 3 26 0128 THROUGH 0 13 0 0051 8 91 0 3511 THROUGH CSINK 10 70 0 421 X 6000 0 13 0 005 5150 0 846 20 0 10 792 12 50 0 492 850 0 981 ex 350 0138 0 00 0 0001 159 0 063ISTOCK gt 16 00 0 6301 12 00 0 4721 9 00 0 3541 4 00 0 157 0 00 0 0001 OTES UNIVERSITY OF FLORIDA CIMAR ea A s UNLESS _OTHERWSE SPECIFIED PROJECT COMPLIANT FORCE TORQUE SENSOR DRAWN SECONDARY DIMENSIONS ARE INCHES DRAWN TOLERANCES ARE DATE 3 19 00 ORDINATE
13. BB3 BB3 amp templ amp temp2 amp DD CC3 CC3 e2 2 amp templ amp temp2 amp DD EE3 E a2a2 E3 amp templ amp temp2 amp alpha 4 0 AA3 EE3 amp templ AA3 DD3 amp temp2 temp2 amp beta E3 amp templ templ amp beta 4 0 BB3 CC3 amp templ templ amp beta BB3 DD3 amp templ templ amp beta CC3 DD3 amp templ templ amp beta DD3 E amp r amp r hol ho2 alpha amp p32 amp p33 amp 34 amp 35 amp 36 amp ioeqn i 1 lt lt ioeqn coef i lt lt An tempunitval coef 16 0 unitval amp ioeqn pcc ioeqn coef 2 i 2 1 lt lt coef2 i lt lt Nn xsq_c 8 40 int OK OK poly_solve xsq_r xsq_c 8 coef2 if OK 1 cout lt lt nERROR in poly_solve n n exit 9 int num_real 0 double xx 8 8 zz 8 for 150 i 8 i if valuenear xsq c i 0 0 0 0001 amp amp xsq r i gt 0 0 xx num real sqrt fabs xsq r i num 1 pnum solutions num real Find corresponding values for thetay and thetaz double y candidate 2 z candidate 2 double aal bbl aa2 bb2 2 double cc3 dd3 double discr int badone 8 0 0 0 0 0 0 0 0
14. t 1 i 0 t lo l t l1 i TI 56 6111 totaldistance i distance r i distance 5 1 distance t i if totaldistance i totaldistancemin 1 totaldistancemin totaldistance i movexyz 0 1 0 10101 movexyz 1 l max 1 19 1 movexyz 2 r_l max 2 10121 lo 0 1 max 0 lo 1 r_1 max 1 _10 2 1 max 2 1013 1 max 3 s 10101 s 1 max 0 s lo 1 s 1 max 1 s 1012 5 1 max 2 s 1013 s 1 max 3 t 19 0 t 1 max 0 t 10111 t 1 max 1 t 10121 t 1 max 2 t 10131 t 1 max 3 return max k k k k k k k K k K K K k K K K K K K K K K K K K K K KOK K K K K KOK kck ck ck Finds the rotation angles of the platform KOKCKCKCKCKCKCKCKCkCKCkCk k k K K K K K K K K K K K K K K K KOK KOK k kc k Ck KOK ck KOK K ck kok ck k K KO koe e void findangles double T 2 1 8 4 4 double newang 3 int bestanswer int rotx double rotatexyz 3 4 comprotxyz 3 4 ang 3 rotatexyz 1 0 rotatexyz 1 1 rotatexyz 1 2 rotatexyz 1 3 112 ore rotatexyz 2 0 asin T_2_1 bestanswer cos rotatexyz 1 0 D2R R2D rotatexyz 2 1 180 asin T_2_1 bestanswer 0 1 cos rotatexyz 1 0 D2R R2D rotat
15. 4 76 0187 THROUGH 3713 1 462 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 3 REMOVE ALL BURRS AND SHARP EDGES 48 7 11681 1 40 0 055 THROUGH 012 PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE ince COMPLIANT FORCE TORQUE SENSOR TOLERANCES ARE DATE 7 12 99 PREV o 0 26mm 0 01 3 0 02 1 4 76 0187 THROUGH 8 00 0 3151 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 5 REMOVE ALL BURRS AND SHARP EDGES TAPPED 42 56 UNC X 40 016 DEEP 3 43 0135 317 0125 THROUGH PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE ince COMPLIANT FORCE TORQUE SENSOR TOLERANCES ARE DAE 7 12 99 PREV o 0 26mm 0 01 85 56 R0 219 STOCK gt TAPPED 45 40 UNC X 3 0 0 12 DEEP OTES MADE FROM McMASTER CARR PART 9291K33 MATERIAL 302 SS ROCKWELL C 25 to 39 SECONDARY DIMENSIONS ARE INCHES REMOVE ALL BURRS AND SHARP EDGES UNIVERSITY OF FLORIDA CIMAR COMPLIANT FORCE TORQUE SENSOR PROJECT DRAWN C TYLER TOLERANCES ARE DATE 7 12 99 FRACTIONS DECIMALS TITLE BALL 0 13mm 0 005 MAR 6 0 26mm 0 01 _ X X X Xx UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS 91 40 NOTES 1 MATERIAL 0 055 SS WIR
16. 77 7 Knew 4 10 2 Ladc 4 83 0 Knew 5 10 2 Ladc 5 77 7 setjac s jac double wrench 6 wrench2 jac Knew wrench fprintf fpout 8 3f 8 3f 8 3f 8 3f 8 3f 8 3f Wn wrench 0 0 2248 wrench 1 0 2248 wrench 2 0 2248 wrench 3 0 00885 wrench 4 0 00885 wrench 5 0 00885 printf 7f 7 7f 57 7f 7f Nn wrench 0 0 2248 wrench 1 0 2248 wrench 2 0 2248 wrench 3 0 00885 wrench 4 0 00885 wrench 5 0 00885 printf check4 d Mn count if ALTER recve rx msg 0 1 exit 0 Abort if error in received messag printf Err check5 Mn 32 exit 0 Abort if error in received messag ALTER tran ALTER 0 Transmit ALTER data update ALTER data 0 to ALTER data 5 6 axis channel data ALTER data 0 movexyz 0 ALTER data 1 movexyz 1 ALTER data 2 movexyz 2 ALTER data 3 newang 0 3 ALTER data 4 newang 1 3 ALTER data 5 newang 2 3 Function to get th converter card 6 leg lengths from the Ana log to Digital M void get leglengths double Ladc 6 int ad value 6 Ladc 0 83 0 ad value 0 3072 10 55 0 25 Ladc 1 77 7 ad value 1 3072 10 7 0 25 Ladc 2 83 0 ad_value 2 3072 10 13 0 25 Ladc 3 77 7 ad value 3 3072 10 3 0 25 set new leg lengths 3072 Ladc 4 83 0 ad value 4 3072 10 428 0 25 Ladc 5 77 7 ad
17. CSINK 12 70 0 500 X 60 00 0 13 0 005 25 0 0 981 140 0 551 1 59 0 06315 UNIVERSITY OF FLORIDA CIMAR PROJECT COMPLIANT FORCE TORQUE SENSOR DRAWN TOLERANCES ARE DATE 3 19 20 O FRACTIONS DECIMALS TITLE LOW ALUMINUM PLATE 2 CIMAR 27 1 1 1 0 13mm 0 005 X XX X XXX 0 26mm 0 01 HOW CIMAR 27 UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS 8 91 0 351 THROUGH CSINK 9 10 70 0 421 X 6000 FROM OPPOSITE SIDE 940 1310 005 CHAMFER 5 0 0 197 0 00 0 0001 3 00 0 1181 OTES MATERIAL 1 16 TEFLON SHEET SECONDARY DIMENSIONS ARE INCHES ORDINATE DIMENSIONS ARE BASIC REMOVE ALL BURRS AND SHARP EDGES 2x 1100 0 433 20 00 0 7871 3X 326 0128 THROUGH 0 1300 005 23 0 0 911 0 00 0 0001 150 0 059 5 50 102171 18 0 0 71 14 50 0 571 159 0 063JSTOCK gt PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE ince COMPLIANT FORCE TORQUE SENSOR DRAWN C TYLER TOLERANCES ARE DATE 3 19 700 1 FRACTIONS DECIMALS TITLE UPPER TEFLON PLATE 1 28 0 13 0 005 X XX X XXX 0 26mm 0 01 NO CIMAR 28 3X 891 0 351 THROUGH 326 0128 THROUGH CSINK 2 10 70 0 421 X 60 00 0 130 005 IAB 0 1300 005 23 0 0 911 0 00 0 000 150 0 059 550 0 217 C
18. for 1 0 1 lt 3 if rx msg i rx tplate head il error flag 1 calculate checksum for i 23 i rx bytes 3 i chksum t rx msg il rx tplate tail 2 chksum check last 3 bytes against template for 1 0 1 lt 3 1 if rx bytes 3 i rx tplate tail i error flag 1 printf check2 in rx Mn if initflag 0 print_recve rx_msg getch return error flag I function to receive array of bytes from ALTER note byte stuffing void rx int address int no unsigned char ch ant unsigned char byte_last 0 for i 0 i lt no i if i 0 byte_last ch i 1 do while inportb address 5 amp 1 0 amp amp kbhit ch i inportb address printf x ch i Enable this line to display received characters c ASCII character x Hex code if ch i DLE amp amp byte last DLE i printf 1 in rx Mn kck ck kckck ck Function to assemble array of bytes to transmit to ALTER void ALTER tran int data word char initflag int counter tx bytes number of bytes being transmitted unsigned char tx msg 20 DEL DLE STX head of normal message to VAL 0 0 0 0 0 0 0 0 0 0 0 0 0 0 body of n
19. s 2 3 3 oaxs4 0 4 3 oaxs4 1 5 oaxs4 2 0 4 s 0 4 jac 1 4 6111141 2 4 5 2 4 3 4 oaxs5 0 4 4 oaxs5 1 5 4 ogqxs5 2 jac 0 5 s 0 5 jac 1 5 s 1 5 2 5 s 21 5 46 s3 3 s4 3 s5 3 opxs2 3 47 jac 3 5 0 0 jac 4 5 0 0 5 5 0 0 K k K K K K K K K K K kck ck ck KOK Finds the wrench in the platform K Kk K KOK kCk Ck K KOK KOK KOK k kc k Ck KOK KOK KOK KOK KOR ckokck O OK R void wrench2 double 6 6 double Knew 6 double wrench 6 matvecmult 6616 wrench jac Knew Function to multiply two matrices and return the answer void matmult double ans 4 4 double matrix1 4 4 double matrix2 4 4 int i j k 1 0 1 lt 4 i for 750 j 4 j ans i j 0 0 1 0 1 lt 4 i for 750 j 4 j for k 0 k lt 4 k 1 51 1 1 2 j void matmult66 double bans 6 6 double 6 6 double bmatrix2 0 6 Ee e 1 0 1 lt 6 1 for 750 546 j 11111 0 0 for 1 0 1 lt 6 1 for 750 546 j bans i 5
20. which is mapped via 6x6 stiffness matrix K to the twist of the movable platform relative to the ground The six twist co ordinates give the twist 6 D 8x 50 The expression for the global stiffness is given by Griffis and Duffy 1991 as K Lille a ol F 6 Ik a 8 54 4 12 18 Where the columns of the 6x6 matrices j and are line coordinates The column of is the line co ordinate for the line for the 1 leg the i column of Sj is the line coordinate of the derivative with respect to the appropriate 0 defines the elevation angle of the plane of the triangle which is formed by the end points of the i connector with the adjacent connector that shares the base edge from the XY plane is the ratio of free length to the new length of the i leg The i column of is the line coordinate of the derivative 7 with respect to the th appropriate The defines the oriented angle of the connector measured from the base edge v and v are 6x6 matrix moment vectors and are explained in Griffis and Duffy 1991 From equation 10 the wrench acting on the top platform can be calculated from the six individual leg forces Equations 11 and 12 can then be used to determine what infinitesimal twist of the top platform with respect to the base is required in order to achieve
21. 0 for 140 1 4 i coef i xcof i deg while coef deg 0 0 deg The leading coefficient was zero if deg 1 return 1 The polynomial must be at least of degree 1 0 cnt keeps track of the number of roots found if deg 1 goto solve linear if deg 2 goto solve quad KK k k k k k k k k ke k ke e e e e x x Set initial values ROKR KKK KK k X k k k k k ke ke k k e e e e x x L30 lst 0 lst counts the number of different starting values lflip i 0 lflip determines whether the inverse polynomial is being considered X 0 00608 Y 0 2939 1354 X0 X X o b 0 Y Y 2 0 X0 ltry 0 ltry counts the of interations for a starting value lstt L38 XX 0 1 0 YY 0 0 0 for i deg i E valuate x 16 x 15 etc where x is complex XX i X XX i 1 Y YY i 1 YY i X YY i 1 Y XX i 1 line 40 51 for 1 1 i deg i Evaluate the polynomial U coef i XX i V coef i YY i 0 0 0 0 for 1 1 i deg 1 dUx i coef i XX i 1 dUy i coef i YY i 1 line 60 den dUx dUx dUy dUy V dUy U dUx den dY U dUy V dUx den X dX Next try for root if Fabs X 40 0 dXY Sqrt dX dX
22. 0 0 5 DD1 0 0 1 2 272 602 x 2 DDZ Z se 2 E2 c41 s34 541 34 541 34 Form up the i o equation Poly al bl templ blbl DD 2 c2 2 2 0 5 DD2 1 lt 3 lt lt al lt lt a2 lt lt cl lt lt a2 amp al c2 amp cl cl amp a2 c2 amp al 2 2 amp c2 a2 amp a2 coef coef coef coef i i i i i a2 c2 1 2 2 2 2 N Ne Ne Ne Ne Ne Ne 541 34 7 36 12 41 34 541 534 12 41 34 541 534 12 41 34 541 534 12 41 34 541 534 1 2 2222 p35 p36 1 2 2 2 lt lt lt lt lt lt lt lt qr L rt h crt 2 oq L oq L or L or 2 L qt L qt L pt L pt 2 2 1 1 alpha al a2 e c2 coef coef coef alal H H H H OAL qt Lh cqr 7 051 qr L oq O L pq L qt EE2 Glel beta rhol b1l deg 1 lt lt lt lt lt lt lt lt 0 a2a2 rho2 lt gt gt gt 223 223 223 223 ioeqn b2 deg 1 mul mul mul mul mul mul CO 0 0 O scale ul VIO al 1 bl b2 bl a2cl m t t
23. 4 4 int num solutions leg lengths i 5 7 double 2 3 3 FILE fpout fpout fopen out 6l dat w k K K K k K K K K K K k K KOK K K KOK KOK KOK KOK ALTER 9 C This program runs External ALTER in ag absolute mode using VAL program ALTERCUM and makes use of an external potentiometer connected to a DT8214 ADC whose base address is set at 0 220 single channel is used to drive the selected axis of the robot Set up to transmit with line ALTER 0 23 as follows The decimal mask value ALTER input data enabled 16 transmit matrix back to host 4 ALTER input data is in World coordinates 2 ALTER input data is cumulative 1 See Table 3 1 Part 3 of VAL manual es Uses 1 PC and the ALTER port 7123 on the VAL controller and uses an external ascii file try X5 dat with path modification data to modify X 5 Y coordinates to draw a small circle in the X Y plane Before running this program you must ensure that the robot has been calibrated the arm power is on and the arm is at the PSTART location and away from any obstacles Use program TERMINAL C to do this When ALTER is running hit any key to abort R Bicker August 1999 KOK KKK KK KK I unsigned char tran ch
24. 5000 samples from each potentiometer while the platform was in its home unloaded position and writing them directly to a file The readings were taken in groups of 500 samples 10 times for each potentiometer in order to get a wide range of data In between each data acquisition the top plate of the platform was moved rotated and then allowed to return to its home position This was done to identify the dead zones of the potentiometers The maximum unassembled sample range of the potentiometers is from 2048 to 4096 counts corresponding to 300 degrees of rotation In order to utilize the full range of sampling capability of the potentiometers the voltage sent to the potentiometers had to be increased inversely proportional to the amount of the rotation range being used When the potentiometers are in the platform they can only rotate 30 which is one fifth of the total range Therefore the potentiometers were given 25V of power to utilize their entire sample range The averages of all the data taken are listed in Table 3 along with their standard deviations The value of the standard deviation for each potentiometer was used to set up the range of values considered to be zero for each potentiometer This range was calculated 21 22 by setting any sample taken that was within the standard deviation to zero The length of the platform connectors can change 8mm overall The change in length was divided by the Ta
25. DIMENSIONS ARE BASIC FRACTIONS pecmals THLE LOW TEFLON PLATE 2 REMOVE ALL BURRS AND SHARP EDGES 0 13mm 0 005 DWC 23 0 26mm 0 01 X X X XX 3X 326 101281 THROUGH 0 13 0 0051 11 00 0 433 THROUGH CSINK 9 12 70 0 500 X 60 00 10 1300 005 2150 0 846 20 0 0 79 12 50 0 492 250 0 981 2X 3 50 0138 0 00 0 0001 159 0 0631S gt 16 00 0 6301 12 00 0 4721 9 00 0 3541 4 00 0157 0 00 0 000 OTES UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED PROJECT FORCE TORQUE SENSOR MATERIAL 1 16 ALUMINUM BAR DIMENSIONS ARE IN MILLIMETERS DRAWN C TYLER SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE 3 19 00 1 ORDINATE DIMENSIONS ARE BASIC FRACTIONS DECIMALS TITLE LOW ALUMINUM PLATE 1 REMOVE ALL BURRS AND SHARP EDGES 0 13mm 0 005 X XX X XXX DLE NO LOW ALUMINUM PLATE 1 0 26mm 0 01 REV 1 ex 18 00 0 7091 12 00 0 4721 3 00 0 118 0 00 0 0001 3X 326 101281 THROUGH 0 00 10 000 9101 300 005 Jal 3 50 0 138 8 91 0 351 THROUGH CSINK 1070 0 421 X 60 00 8 50 0 335 FROM OPPOSITE SIDE 0 13 0 005 25 0 0 98 12 50 0 492 140 0 55 19 50 0 7681 159 0 0631S gt NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL 1 16 TEF
26. PC then to the PUMA700 and finally back to the as shown in figure 2 PECCO 3 ES JN WS Card Serial Ports Fig 2 System Loop The objective of this thesis was to design a small passive compliant coupler based on an in parallel mechanism for force control The desired load supporting ranges and compliance characteristics are given in Table 1 The resolution of the platform in measuring forces and torques are also listed in the table The values shown in the table are with respect to a right handed co ordinate system xyz defined at the center of the bottom plate such that z is parallel to Z and x passes through a point O see fig 3 Table 1 Desired Load and Compliance Characteristics Sensing Axis Ranges Compliance Resolution Fx 25 4 mm 0 25 Fy 25 4 mm 0 25 Fz 60 N 8 0 25 N Mx 500 N mm 18 2 5 N mm My 500 N mm 18 2 5 N mm Mz 1000 N mm 18 2 5 N mm The desired size of the platform was less than four inches tall and base diameter of about six inches so that it would be a good size to fit onto the end of the PUMA700 robot arm The actual platform is only 3 5 inches tall and has a base diameter of 6 75 inches The platform had to be light enough to not greatly impact the performance of the 700 which can support a 50 pound load duri
27. The approach taken to solve this problem was a graphical one A program was written using a Microsoft Windows interface with OpenGL 3d graphics being displayed in that interface The program displays a 3d model of the platform which changes as data is altered through various user input toggles and sliders on the interface The program was setup so that the user can change both the side length of the base triangle which would in turn change the top triangle and height dimensions and the separation distance of the ball joints The program also allows the user to modify the pose of the top plate of the platform by setting the value of the x y and z translations and any combination of rotations about any axis in the x y plane that passes through the center of the top plate This important fact allows the user to see if the platform components will interfere with each other inside of the platforms usable workspace The parts of the platform that were dimensionally fixed were the size of all the parts of each of the legs except for the lengths of the parts that connect the spherical balls to the middle section of the legs In this manner the overall lengths of the legs were also adjusted as changes were made to the 12 platform dimensions There numerical outputs on the program interface that display the length of each leg that can be used for the final design length of each leg once the other dimensions are satisfactorily selected These leg len
28. XX X XXX 0 26mm 0 01 XX X XX HE CIMAR 19 UNLESS OTHERWISE SPECIFIED PROJECT DIMENSIONS ARE IN MILLIMETERS 10 0 0 39 THROUGH 13 5 0 53 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 3 REMOVE ALL BURRS AND SHARP EDGES 3X TAPPED 42 56 UNC X 5 0 0 20 DEEP EX 17 50 0 69 11 50 0 45 e 30 0 10 19 50 0 77 12 50 0 49 8 50 0 33 3 50 0 14 10 0 0 39 20 00 0 79 2X TAPPED 85 40 UNC X 4 0 0 16 DEEP r 3 00 0 12 4 00 0 16 10 00 0 39 PROJECT UNIVERSITY OF FLORIDA UNLESS ee E COMPLIANT FORCE TORQUE SENSOR DRAWN TYLER TOLERANCES ARE DATE 5 16 00 1 FRACTIONS DECIMALS TITLE LOW ANGLE MOUNT 2 CIMAR 202 0 13mm 0 005 X XX X XXX 0 26mm 0 01 XX X XX HE CIMAR 20 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 3X TAPPED 82 56 UNC X 5 0 0 20 DEEP 2 84 0 11 1184 0 47 3 90 0 14 12 50 0 49 16 50 0 65 21 0 08 TAPPED 2X 45 40 UNC X 4 0 0 16 DEEP 15 00 0 591 3 00 0 12 5 00 0 20 10 00 0 39 10 0 0 39 THROUGH CHAMFER 4 0 0 16 18 0 0 71 0 59 PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR DIMENSIONS ARE IN MILLIMETERS TOLERANCES ARE DRAWN 00 _____ _ _ s 3 REMOVE ALL BURRS AND SHARP EDGES ANCES AR RENNES HAE
29. double value 4 double ang cos fold angles Get coordinates of points r s and t in the 1st coord system get the coordinates in the 15 system then fold the triangles get point s coordinates before folding double sx prefold sy prefold double sx sy 52 cos ang op L os L os 1 ps L ps 2 0 L op L os ang acos cos ang prefold L os cos ang Sy prefold L os sin ang get point r in xtra coordinate system before folding double rx prefold ry prefold double rx ry rz cos ang or L or L oq L oq qr 2 0 L or L ang acos cos ang rx prefold L or cos ang ry prefold L or sin ang get point t in xtra2 coordinate system before folding double tx prefold ty prefold double tx ty tz cos ang L pt L pt L pq L pq L qt L qt 2 0 L pt L pq ang acos cos ang tx prefold L pt cos ang ty prefold L pt sin ang double thetax thetay thetaz double sin x cos x sin y cos y Sin 7 z double xvec 3 yvec 3 zvec 3 tempvec 3 vector xvec 3L yvec 3L zvec 3L tempvec 3L 41 for 1 0 1 lt pnum solutions 1 aal al eval xx i cout lt lt naal lt lt aal bl eval xx il cout lt lt 1 lt lt 1 cl eval xx i cout l
30. for a compact design For these reasons the parallel mechanism is a good candidate to use in a serial manner with a serial robot without changing the workspace of the serial robot the robot s normal operating procedures The small size will allow the parallel mechanism to be attached as the end effector of the robot arm and the lightweight nature of the mechanism will not adversely affect the robot arm performance A drawing of a passive in parallel platform connected at the end of a serial robot is shown in figure 1 Fig 1 Passive In Parallel Platform on a Serial Robot There are advantages to using a passive compliant structure to control force and displacement simultaneously as opposed to active compliant force control methods When the lengths of the connectors of the parallel platform are adjusted using servos a linear relationship between the force and displacement can be computed Sugar and Kumar 1998 This active method does not allow for the simultaneous control of both force and displacement There are other methods to control forces by controlling positions or controlling positions and forces together such as compliant control compliance and force control and hybrid control These methods require more complicated means of control than the passive compliance control On the other hand passive compliance motion control can accommodate the misalignments that exist between the robot manipulator and the object it is manipula
31. int no unsigned char ch xnt for 1 0 1 lt 10 1 do while inportb address 5 amp 0x20 0 printf x ch i Activate line to display character string outportb address ch i printf in K K K K K K K KOK K K KOK K K KOK K KOK K KOK K KO kk Function to tranmit string of characters via VAL terminal UA void transmit unsigned char string int base int count int i for i 0 i lt count i 58 outporth base 1 delay 5 KOK KKK KK KR I A I kkk k kkk kkk k kc k k kck k kck ck kckck kkk k kk Sampling function using Data Translation DT 8214 card Number of channels to convert are selected using CHAN k k k K K K K K KOK K KOK K K K KOK k KOK KOK KOR KOK K K KOK KOK KOK OK K void sample int value int chan int i for i 0 i lt chan i i start conversion on selected channel do while inp BASE ADC amp 0x80 0 then wait until conversion done value i inp BASE 1 16 41 gt gt 4 Justify 8 format adc value printf 7d value i printf Mn APPENDIX PCCFC PART LIST The following is a list of all the drawing numbers material descriptions and quantities needed To machine all of the
32. of an in parallel passive compliant force torque sensor can improve the capabilities of a serial manipulator by allowing for the control of position and contact force This is done by taking readings from the force torque sensor in the form of analog voltage data from six rotary potentiometers The data is then transformed into the lengths of the six platform connectors The data is then used to compute the pose of the top plate of the platform with respect to the bottom plate and then to modify the path for the serial robot to follow The goal of this modification is to allow the serial robot manipulator to maintain a desired force and contact orientation with objects in the workspace In order to get six degrees of control the force torque sensor must have the geometry such that we can compute the twist it is experiencing as a result of the serial robot movement Further to control the torque being generated through the sensor by the serial robot the stiffness properties of the sensor device must be known With the twist and stiffness known the wrench being applied to the sensor can be computed Griffis and Duffy 1991 The desire to have six degrees of freedom leads to the use of an in parallel mechanism The in parallel mechanism has a high load bearing capacity and the geometric properties of load distribution This is due to the fact that the connectors sustain the load in a parallel fashion Further the geometry of the parallel mechanism allows
33. oq Lop 2 1 sqrt p 1 0 p 1101 p 1 1 p 1111 p 1121 11 vecmag a 1 sqrt q_1 0 q_1 0 1 1 q 1 1 1 2 q 1 SEIN 5 sart abs T p 1 0 1 0 p 110 4 1101 _1 1 4 1 1 p 1 1 4 1111 1121 1121 1121 q 1121 1 4 1 double 8 2131 2131 s 2 0 x 2 s s 2 2 0 0 t 2 0 t x 2 t 2 1 t y 2 401 05 double L rs L rt L st rs vecmag s 2 sqrt s 2 0 s 2 0 2 1 s 2 1 Lrt sqrt t 2 0 t 2101 2 1 t 211 t 2 2 t 21 rai L st sart abs a ZLO D E2210 S82 207 t 2 D0 s_2 1 _2 1 8_2 1 t 2111 52121 double 41 841 c34 534 12 812 223 double 41 o 541 double 41 541 double pxq 3 cross product of p 1 and q 1 four bar at point 5 41 41 dotproduct p 1 4 1 L op L oq crossproduct 1 4 1 541 541 pxq 2 L op L oq vk 2 c23 1 or L os L os rs L rs 2 0 L or L os c34 L os L os L op L op L ps L ps 2 0 L os L op 534 sin acos c34 35 12 L oq L oq or L or L qr L qr 2 0 L oq L or 512 sin acos c12 First equation 1 y 2 x 2 x 2
34. parts for one PCCFC platform Not included in this list are all of the fasteners and 6 potentiometers Part Material Quantity Assembly of parts cimar 1 4 5 7 8 5 6 35380427 or 2 bearings per assembly 12 total 1 Al 6061 or comparable 6 Cimar 2 Al 6061 or comparable 6 Cimar_3 Al 6061 or comparable 6 4 Al 6061 comparable 5 Al 6061 comparable 6 Cimar_6 302 SS ball 12 Cimar_7 0 055 SS wire 6 Cimar 8 0 055 SS wire 6 Cimar 9 5 40 SS threaded rod 6 Cimar 14 0 015 SS shim stock 12 15 0 010 SS shim stock 24 17 5 40 SS threaded rod 6 18 Al 6061 or comparable 36 19 Al 6061 or comparable 3 20 Al 6061 or comparable 3 21 Al 6061 or comparable 6 Cimar_22 1 16 Teflon sheet 3 Cimar_23 1 16 Teflon sheet 3 Cimar_24 1 16 Al 6061 or comparable 3 Cimar_25 1 16 Teflon sheet 3 Cimar_26 1 16 Teflon sheet 3 Cimar_27 1 16 Al 6061 or comparable 3 Cimar_28 1 16 Teflon sheet 6 Cimar_29 1 16 Teflon sheet 6 Cimar_30 1 16 Al 6061 or comparable 6 Cimar_31 1 8 Al 6061 1 Cimar_32 1 8 Al_6061 1 59 NOTES 1 ALL JOINTS ARE PRESS FIT 2 SECONDARY DIMENSIONS ARE INCHES me 012 CIMAR_1 CIMAR 5 PART 3435380427 CIMAR 8 4 CIMAR 7 MSC PART 3435380427 PRO
35. software then took that wrench and applied an opposite scaled twist to the robot end effector The result is a sort of joystick application that allows the user to move the robot end effector anywhere in the workspace The next step would be to mount the on the PUMA700 and develop some tasks for the robot to perform using it s new capabilities Design of the Platform The six degree of freedom in parallel mechanism has six connectors they are connected through spherical joint balls in a pair wise manner at the top and at the base The top and bottom surfaces are planar for the sake of simplicity The in parallel mechanism in its best form should be fully triangulated to form a 3 3 octahedron A schematic sketch of the in parallel mechanism is given in figure 3 This simple kinematic structure is complex to design One because of the problem of designing concentric R lt Fig 3 3 3 In Parallel Mechanism joint balls and the other is due to the mechanical interference of closely arranged legs Concentric ball joints could have been used in this application however they would have required a large amount of development and design time to produce The problems of using concentric joint balls were overcome by separating the center of the joint balls by a small distance as to avoid possible interference problems The overall size of the platform was adjusted as needed to avoid connector to connector and connector to platform interf
36. to decide which position solution set is closest to the prior position of the platform int solve_bestsolution doub movexyz 3 double r_1 8 4 double int pnum_solutions le s 1 8 4 double t_1 8 4 int i max double distance r 8 distance 5 8 distance t 8 totaldistance 8 totaldistancemin static double 10 4 1 30 75 53 26 61 44 1 0 static double s 10 4 1 61 5 0 0 61 44 1 0 static double t 10 4 1 92 25 53 26 61 44 1 0 totaldistancemin 10000 0 for 1 0 i pnum solutions i cout lt lt 1 lt lt l i 0 lt lt lt lt ss IL 27 lt lt lt lt 1 1 3 lt lt Nn cout lt lt 5 1 lt lt s 1 1 0 lt lt lt lt 5 1111111 lt lt lt lt s 1 i 2 lt lt lt lt 5 1111 lt lt An cout lt lt tll lt lt C 01 lt lt ILLE La E TIL lt lt 44 distance r i sqrt fabs r 1 i 0 r_lo 0 r_1 i 0 r 00112 1111 20111 r_1 i 2 10 121 1 il 2 19 2 distance s i sqrt 5 111110 s 1o 0 s 1 i 0 s lo 0 s 1 i 1 1o 1 s 1 i 1 s 10111 s_1 i 2 1o 2 s 1 il 2 19 2 distance t i sqrt fabs t 1 i 0 t 1o 0
37. y 2 DD1 x EEL 0 double AA1 CCl DD1 EEL 1 512 541 34 41 534 12 41 34 541 534 c23 1 12 cA1 s34 541 34 c12 c41 c34 s41 s34 c23 CCI 512 c41 s34 541 34 12 41 34 541 534 c23 4 0 512 534 EE1 s12 41 534 541 34 cl2 c41 c34 s41 s34 c23 four bar at point P double v po 3 01 01 v 11 4 1111 1111 21 1121 v po 0 p 1 0 v po 1 p 1 1 v po 2 p 1 2 c41 dotproduct v pq v po vecmag v po vecmag v pq crossproduct pxq pq v 41 pxq 2 vecmag v po vecmag v pq vk 2 41 p c41 541 541 23 pt L pt L ps L ps st L st 2 0 L ps c34 L pq L pq L pt L pt L qt L qt 2 0 L pq L pt 534 sin acos c34 12 L op L op L ps L ps L os L os 2 0 L op L ps 512 sin acos c12 Third equation AA3 y 2 z 2 BB3 y 2 CC3 z 2 DD3 y z EE3 0 double AA3 BB3 CC3 DD3 512 541 34 41 534 12 41 34 541 534 c23 512 c41 s34 541 34 12 41 34 541 534 c23 512 41 534 541 34 12 41 344541 534 c23 DD3 4 0 512 s34
38. 0 0 D2R location of along y axis S x 2 61 5 location of s along x axis 228 30 45 location of t along x axis t y 2 61 5 sin 60 0 D2R location of t along y axis L or Lsfor33 0 L os Lsfor33 5 L ps Lsfor33 4 33 leg lengths L pt Lsfor33 3 L qt Lsfor33 2 L qr Lsfor33 1 solve platform amp num solutions T 2 1 p x 1 1 1 SX 25 2 1 7 2 Lor L os L ps L pt L qt L qr int i j k bestanswer double 1 8 4 s 1 81 4 t_1 8 4 double vr2 4 vs2 4 vt2 4 for 150 i num solutions i 31 990 s l il j 0 0 t 11111351 0 0 vr2 0 0 0 vr2 1 0 0 vr2 2 0 0 vr2 3 1 0 vs2 0 s x 2 vs2 1 0 0 vs2 2 0 0 vs2 3 1 0 vt2 0 t x 2 vt2 1 EOY 0 0 vt2 3 18501 for 1 0 i num solutions i for 750 j 4 3 for 0 k lt 4 k 22 174 34 2 s 1111131 T 2 1 1 3 vs2 k t 11411121 T 2 llil j3 Ik vt2 k bestanswer solve bestsolution num solutions r 1 s 1 t 1 movexyz int rotx if r l bestanswer 3 t 1 bestanswer 3 0 0 rotx 1 else rotx 1 findangles T 2 1 newang bestanswer rotx double 6 6 6 Knew 0 10 2 Ladc 0 83 0 Knew 1 10 2 Ladc 1 77 7 Knew 2 10 2 Ladc 2 83 0 Knew 3 10 2 Ladc 3
39. 041 i 1 0 150 i lt da i 750 lt jtt 1 a i b j k k k k K K K K K k K K K K K K K K K K K KOK K K K K KOK ck KOK ck subtract two Polys I k K K k K CK Ck K K Ck K K K K kCk k k K K Ck KOK ck KOK kokck kO void psub Poly A Poly B Poly A B Ant aig 28 double a A coef b B coef B coef if A deg gt B deg db A deg ds B deg 150 i lt db 144 atf 1 lt a b i a i blil else a b i 1 else db B deg ds A deg for 150 i lt db i if i lt ds a b i a i blil else a b i blil A_B gt deg db KKK k 1 k k k k k k K K K K K K K K KOK K K K K KOK K K KOK K K K K KOK K K kck k kck ck KI adds two Polys ba b a KOKCKCKCKCKCKCKCKCk k K K K K K K K K Ck Ck kCKCk K KOK k KOK ck kok ck ckokck R OK ke O void padd Poly A Poly B Poly A_B int 22 48 sdb double a A coef b B coef a_b A_B gt coef if A deg gt B deg db A deg ds B deg for i 0 i lt db i if 1 48 a b i a i b i else a b i 1 else db B deg 55 ds A deg 150 i lt db i 4 if 1 48 a b i a i 01117 else a b i b i A B deg db k k k k K K KOK K K
40. 2 E3 amp temp2 23 amp temp2 23 amp temp2 E3 amp temp2 2 0 AA3 DD3 blb2 amp temp2 lt lt clc2 coef 6 lt lt clc2 coef 1 lt lt Nas lt lt pl coef 1 lt lt amp temp2 amp templ amp templ amp templ amp templ amp templ amp templ amp templ lt lt lt lt lt lt lt lt pl coef 2 lt lt psub DD temp2 amp DD 2 0 BB3 CC3 clc2 amp temp2 pscale 1 2 pmult templ psub DD temp2 amp DD 4 0 BB3 CC3 b2b2 amp temp2 pscale alcl pmult templ padd DD temp2 amp DD 4 0 BB3 CC3 blbl amp temp2 pscale a2c2 pmult templ padd DD temp2 amp DD pscale blbl pmult templ 8 0 BB3 CC3 b2b2 amp temp2 psub DD temp2 amp DD 2 0 BB3 EE3 2 1 amp temp2 pscale 1 2 pmult templ padd DD temp2 amp DD 4 0 BB3 E b1b1 E3 amp temp2 pscale a2a2 pmult temp1 psub DD temp2 amp DD 2 0 BB3 DD3 blb2 amp temp2 pscale 2 1 pmult templ psub DD temp2 amp DD 2 0 CC3 E a2c2 E3 amp temp2 pscale alal pmult templ padd DD temp2 amp DD 4 0 CC3 E b2b2 23 amp temp2 pscale alal pmult templ p
41. E 2 SECONDARY DIMENSIONS ARE INCHES 5 REMOVE ALL BURRS AND SHARP EDGES 9 0 0 35 UNIVERSITY OF FLORIDA CIMAR COMPLIANT FORCE TORQUE SENSOR PROJECT DRAWN C TYLER DATE 7 13 99 LOW ___________________ 0 13 0 005 X XX X XXX DLE NO EL PREV lO UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS TOLERANCES ARE FRACTIONS DECIMALS 0 26mm 0 01 91 40 NOTES 1 MATERIAL 0 055 SS WIRE 2 SECONDARY DIMENSIONS ARE INCHES 5 REMOVE ALL BURRS AND SHARP EDGES 70 0 28 UNIVERSITY OF FLORIDA CIMAR COMPLIANT FORCE TORQUE SENSOR PROJECT DRAWN C TYLER TOLERANCES ARE DATE 15 UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS 7992 02 2 12 FRACTIONS DECIMALS TITLE SHAFT 2 0 13mm 0 005 X XX X XXX TILE UPPER 2 PREV lO 0 26mm 0 01 5 40 UNC lt 2 CLEAN ENDS FOR THREADING NOTES 1 MATERIAL 5 40 18 8 SS THREADED ROD 2 SECONDARY DIMENSIONS ARE INCHES 3 REMOVE ALL BURRS AND SHARP EDGES 16 3 0 641 UNIVERSITY OF FLORIDA CIMAR PROJECT COMPLIANT FORCE TORQUE SENSOR DRAWN C TYLER DECIMALS 2 0 SHORT THREADS 0 13mm 0 005 TILE NO SHORT 2 HREADS PREV UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS 0 26mm 0 01 0 0 1 57
42. HAMFER 5 0 0 197 18 0 0 71 1450 0 571 159 0 0631S gt 0 00 0 0001 3 00 0 181 eX 11 00 0 433 20 00 0 787 NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL 1 16 TEFLON SHEET DIMENSIONS ARE IN MILLIMETERS FDRAWN DRAWN C TYLER 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE 37 19 00 7 3 ORDINATE DIMENSIONS ARE BASIC FRACTIONS DEcMALS TITLE TEFLON PLATE 2 O 4 REMOVE ALL BURRS AND SHARP EDGES 0 13mm 0 005 Tel E TEFLON PLATE 2 0 26mm 0 01 3x 11 00 0 433 THROUGH 2 3 26 101283 THROUGH CSINK 2 12 70 0 5001 X 60 00 0 1320 0053 8 0 13 0 0051 23 0 0 911 0 00 0 000 150 0 059 2X 5 50 0217 CHAMFER 5 0 0 1971 18 0 0 71 14 90 0 571 gt A 159 0 063JSTOCK gt 0 00 0 0001 3 00 0 1181 11 00 10 4331 20 00 0 7871 NOTES UNIVERSITY OF FLORIDA CIMAR E E UNLESS OTHERWISE SPECIFIED PROJECT COMPLIANT FORCE TORQUE SENSOR DRAWN TYLER 2 SECONDARY DIMENSIONS ARE INCHES H7 DATE 19 00 11 3 ORDINATE DIMENSIONS ARE BASIC FRACTONS DECMALS THLE UPPER ALUMINUM PLATE 0 4 REMOVE ALL BURRS AND SHARP EDGES 0 15 0 005 DLE NO UPPER ALUMINUM PLATE 0 26mm 0 01 0170 26 693 3 HOLES 2 3 2 0126 THROUGH EQUISPACED
43. IN PARALLEL COMPLIANT COUPLER FOR ROBOT FORCE CONTROL By CHAD M TYLER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2000 ACKNOWLEDGMENTS The author greatly acknowledges the support of the Center for Intelligent Machines and Robotics at the University of Florida for providing a Research Assistantship as well as the facility and equipment to carry out this work The Department of Energy is also gratefully acknowledged for its support via grant through the University Research Program in Robotics ii TABLE OF CONTENTS page ACKNOWLEDGMENT S ii LIST OF TABLES iv EIST OF EIGURES ve E vi 1 SYSTEM PERFORMANCE SPECIFICATIONS AND DESIGN 5 Platform and Robot Performance 5 Design of the Platform DC a R 8 Kinematic Model of the Platform 4 trt ett bare eae qti eat Saeed 17 Software 18 EXPERIMENTAL RESULTS a tens 21 Potentiometer Calibration e ed 21 Torque ipeo e uot 22 JoysuckoNppliedlol
44. JECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE neues COMPLIANT FORCE TORQUE SENSOR DRAWN TYLER TOLERANCES ARE DATE 45 99 2 2 FRACTIONS DECIMALS TITLE BEARINGS PIVOT ASSEMBLY CIMARASM 1 1 0 13mm 0 005 X XX X XXX 0 26mm 0 01 X X X XX BWG NO CIMARASN T TAPPED 45 40 UNC X 30 012 DEEP FROM OPPOSITE SIDE 9 01310 0051 ex 8 0 0 311 100 0 391 4X TAPPED 42 56 UNC X 40 016 DEEP 6 0 130 0053 ex 2 0 0 081 eX 140 0 55 2 140 0 055 X 30 012 DEEP 8 0 0 311 40 0162 44 0 13 0 0057 8 0 0 0 001 6 0 0 24 8 5 0 33 10 0 43 E m 0 631 2 0 0 08 2 0 0081 TYP 2 0 0 08 TYP NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL ALUMINUM DIMENSIONS ARE IN MILLIMETERS DRAWN C TYLER 2 SECONDARY DIMENSIONS ARE INCHES DATE 7 9 TOLERANCES ARE DATE 9 au I 3 ORDINATE DIMENSIONS ARE BASIC US pecus HAE AWGLOCK 4 REMOVE ALL BURRS AND SHARP EDGES 0 13mm 0 005 DWG NO 1 PREV 7 0 26mm 0 01 3X 8 00 0 315 3X 200 0 079 0 00 0 0001 0 00 0 000 ex 2 00 0 079 ex 8 00 0 3151 N 1 3 2 gt eu 8 0 40 0161 2 5 0 22 10 5 10 411 16 0 10 631 OTES MATERIAL ALUMINUM SECONDARY DIMENSIONS ARE INCHES ORDINATE DI
45. K K KOK K KOK K K K K kck ck ck scales a Poly KOXCKCKCKCKCKCKCKCk k K K K K K K k KOK K K KOK k kc k Ck KOK KOK KOK ck kok ck ckokck K koe void pscale Poly A double s a double a A coef i A deg 144 11 150 1 AS deg A deg Poly AS as AS coef I I ckokck sk ke e function to receive ALTER message initial amp steady state message determined by initflag ie initflag 1 means initial message Returns value of error flag toi 27 For further information on ALTER communications see Part 3 of VAL user manual int ALTER recve unsigned char msg char initflag int rx bytes no of bytes actually received from VAL i unsigned char chksum 0 error_flag 0 check sum byte signals error in received data DL rx_tplate_head 3 DEL E STX 1st 3 bytes of healthy received message rx tplate tail 3 DLE ETX 0 penumltimate 2 bytes of healthy rx message if initflag 1 rx bytes 8 Initial message from ALTER is only 8 bytes long else rx bytes 36 Subsequent message length determined by ALTER mode as set in VAL ALTER program rx BASE ALTER rx bytes rx msg get message from ALTER check 1st 3 bytes against template 56
46. LON SHEET DIMENSIONS ARE IN MILLIMETERS DRAWN vx 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE 3 ORDINATE DIMENSIONS ARE BASIC FRACTIONS DECIMALS TITLE LOW TEFLON PLATE 3 4 REMOVE ALL BURRS AND SHARP EDGES 0 15mm 0 005 DWG NO 25 0 26mm 0 01 REV 1 ex 18 00 0 7091 12 00 0 4721 3 00 0 118 0 00 0 0001 3X 3 26 101281 THROUGH 9 0 13 0 00516 12 50 0 492 250 0 981 0 00 10 0001 3 50 0 1381 2 8 91 0 351 THROUGH 8 50 10 335 CSINK 10 70 0 421 X 60 00 0 13 0 005 14 0 10 55 19 50 0 7681 159 0 0631S gt OTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR MATERIAL 1 16 TEFLON BAR DIMENSIONS ARE IN MLLMETERS DRAN e eR SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE ORDINATE DIMENSIONS ARE BASIC FRACTIONS DECIMALS TITLE LOW TEFLON PLATE 4 REMOVE ALL BURRS AND SHARP EDGES 0 13 0 0057 X XX X XXX DWG 26 0 26mm 0 01 3 50 0138 8 50 0 335 12 50 0 492 19 50 0 7681 OTES MATERIAL 1 16 ALUMINUM BAR SECONDARY DIMENSIONS ARE INCHES ORDINATE DIMENSIONS ARE BASIC REMOVE ALL BURRS AND SHARP EDGES 18 00 0 7091 ex 00 0 478 12 3 00 0 118 0 00 0 0001 3X 2 3 26 0128 THROUGH 013 0 005 11 00 0 4331 THROUGH
47. MENSIONS ARE BASIC REMOVE ALL BURRS AND SHARP EDGES 6X TAPPED 42 56 UNC X 40 0 16 DEEP 0 13 L0 005A BC 6 0 0 24 85 0 331 V 145 0 57 Rd 100 0 391 UNIVERSITY OF FLORIDA COMPLIANT FORCE TORQUE SENSOR DRAWN C TYLER 7 12 UNLESS OTHERWISE SPECIFIED PROJECT DIMENSIONS ARE IN MILLIMETERS TOLERANCES ARE DATE 799 FRACTIONS DECIMALS TITLE MIDBLOCK 0 13mm 0 005 FOE NO T REA IRE 10 0 26mm 0 01 TAPPED 45 40 UNC X 30 012 DEEP 0 13 L0 005 1A BC 3X 2 50 0 098 0 00 0 0001 S e 5 2 e Cu 8 00 0 315 2X CHAMFER 2 0 08 12 50 0 492 0 00 10 000 gt 10 0 0 39 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 5 ORDINATE DIMENSIONS ARE BASIC 4 REMOVE ALL BURRS AND SHARP EDGES ex TAPPED 42 56 UNC X 40 0 16 DEEP FROM OPPOSITE SIDE 0 13 0 005 3 6 61 0 260 800 0 79 6 35 0 250 THROUGH 2 0 EN PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR DIMENSIONS ARE IN MILLIMETERS DRAWN C NLER TOLERANCES ARE DATE 7 12 99 O FRACTIONS DECIMALS TITLE UPBLOCK 0 13 0 005 0 26mm 0 01
48. OK K KOK kck ck K KOK ck KOK ck Set up the Jacobian for the platform KOKCKCKCKCKCKCkCKCkCKCk k kCKCk K K K K K K K K KOK KOK K Ck KOK KOK KOK ck K KOK ckokck K OK e setjac double 5 3 6 double 6 6 1 cos rotatexyz 1 0 D2R R2D 1 cos rotatexyz 1 0 D2R R2D cos rotatexyz 1 0 D2R R2D 1 rotatexyz 1 0 D2R R2D double op 3 3 s2 3 opxs3 3 oqxs4 3 oqxs5 3 op 0 123 0 op 1 0 0 op 2 0 0 oq 0 61 5 1 123 0 sin 60 0 D2R oq 2 0 0 s2 0 s 0 1 s2 1 s 1 1 52 2 s 2 1 s3 0 s 0 2 s3 1 s 1 2 s3 2 s 2 2 s4 0 s 0 3 s4 1 s 1 3 s4 2 s 2 3 s5 0 s 0 4 55 1 s 1 4 s5 2 s 2 4 crossproduct opxs2 0p s2 crossproduct opxs3 op s3 crossproduct 54 03 54 crossproduct 55 03 55 0 0 s 0 0 jac 1 0 5 1 0 2 0 s 2 0 jac 3 0 0 0 jac 4 0 0 0 jac 5 0 0 0 jac 0 1 s 0 1 jac 1 1 s 1 1 2 1 s 21 1 jac 3 1 opxs2 0 jac 4 1 opxs2 1 jac 5 1 opxs2 2 jac 0 2 s 0 2 1 2 5 1 2 2 2 s 2 2 3 2 opxs3 0 4 2 opxs3 1 5 2 opxs3 2 jac 0 3 s 0 3 jac 1 3 s 1 3 jac 2 3
49. ORCE TORQUE SENSOR DRAWN C TYLER TOLERANCES ARE DATE 8 00 4 FRACTIONS 5 TITLE LONG THREADS 0 13 0 005 X XX X XXX DWG NO CIMAR 17 PREV 1 UNLESS OTHERWISE SPECIFIED DIMENSIONS ARE IN MILLIMETERS 0 26mm 0 01 14 50 0 57 TAPPED 2X 42 56 UNC X 4 0 0 16 DEEP BOTH SIDES 4 00 0 16 NOTES PROJECT UNIVERSITY OF FLORIDA CIMAR UNLESS OTHERWISE SPECIFIED COMPLIANT FORCE TORQUE SENSOR 1 MATERIAL ALUMINUM DIMENSIONS ARE IN MILLIMETERS DRAWN C TYLER 2 SECONDARY DIMENSIONS ARE INCHES TOLERANCES ARE DATE 4 4 3 REMOVE ALL BURRS AND SHARP EDGES ANCES AR bes ee 0 13 0 005 X XX X XXX DWG NO CIMAR 18 REV 10 0 26mm 0 01 15 67 0 62 1 67 0 46 8 67 0 34 3 67 0 14 21 50 0 85 12 50 0 49 2X 3 50 0 14 TAPPED 2X 5 40 UNC X 4 0 0 16 DEEP 25 0 0 98 NOTES 1 MATERIAL ALUMINUM 2 SECONDARY DIMENSIONS ARE INCHES 5 REMOVE ALL BURRS AND SHARP EDGES 22 00 0 87 3 00 0 12 10 0 0 39 THROUGH 3X TAPPED 2 56 UNC X 5 0 0 20 DEEP 15 0 0 59 L 4 0 0 16 6 3 0 25 0 7 0 031 1 18 8 0 74 211 18 0 0271 8 00 0 31 4 00 016 UNIVERSITY OF FLORIDA CIMAR COMPLIANT FORCE TORQUE SENSOR DRAWN C M TYLER TOLERANCES ARE DATE 5 16 00 1 FRACTIONS DECIMALS TITLE LOW ANGLE MOUNT 1 19 0 13mm 0 005 X
50. ality Index criteria Lee et al 1998 The Quality index QD is defined by the following dimensionless expression 2 1 Det where is the determinant of the Jacobean The 6 by 6 matrix formed by the line co ordinates of the 6 legs gives the Jacobean matrix of the mechanism The normalized determinant of the Jacobean DetJ at the central position and when both base and platform are parallel as shown in figure 4 is given by Fig4 Top view of 3 3 Parallel mechanism structure 343a b I ab b 2 4 h Where a and are the sides of the equilateral triangle of the platform and the base respectively h is the height of the platform measured from center of the base plate to the center of platform along z axis see figure 3 The above expression is optimized to find 11 the expression for maximum The maximum QI occurs when either of the following two parametric relationships is satisfied b 2a 3 26 h b With these maximized values in mind the platform was designed so the length of a side of the bottom triangle is equal to twice that of the top triangle and the height at the home unloaded position is equal to the length of a side of the top triangle Given those geometric ratios there was still the matter of deciding what the size of the bottom triangle would be and also what the separation distance of the ball joints would be
51. ar1 30 ch unsigned char rx msg 19 int ALTER data 6 08 00 70 07 03 37 int count 0 loopcount 0 int ad_value CHAN 16 bit ALTER data ER Bytes received from ALT Initialize bot setport BASE ALT setport BASE TER ER 0 3 0x0c strcpy tran charl ex al tercum transmit tran 1 BASE T a VAL ERM CR outportb BASE T delay 1 hould now printf ALTI printf check if ALTER recve rx 50 1 message delay 1 printf check 3 Mn ALTER tran ALTER data l1 message delay 1 while kbhit continuous count tt printf count sample ad_value CHAN get leglengths Ladc ad value L oo Ladc 0 L ss Ladc 1 L pp Ladc 2 Ltt Ladas L qq Ladc 4 L rr Ladc 5 Solve georedux L oo L ss L pp 30 h serial ports baud rate set at 38400 baud rate set at 9600 Tranmit string via terminal RM 11 to execute ALTER program in Send Carriage return running n Check initial ALTER 1 exit 0 abort if error in received messag Transmit initial PC loop communication with ALTER 554 n count L_tt L_qq L_rr Lsfor33 1 123 0 location of p along 15 015 7 location of along x axis 1 123 0 sin 6
52. arried out theoretical investigations of the behavior of the Stewart platform sensor Svinin and Uchiyama 1995 have considered the optimality of the condition number of the force transformation matrix The optimum condition number criterion has to be exercised with utmost care Though the optimum configuration appears to present an isotropic solution the neighborhood solutions configurations may deteriorate very fast and could be close to singularity Therefore the condition number criteria can be at best limited to stiff Stewart Platform Sensors Dasgupta et al 1994 Bhaumick et al 1997 where change in structural configurations is not anticipated and the condition number remains the same Lee et al 1996 defined the problem of closeness to a singularity measure by defining what is known as Quality Index for planer in parallel devices Lee et al 1998 extended the definition of Quality Index to spatial 3 3 in parallel devices The quality index is the ratio of the absolute value of the determinant of the Jacobean of the platform in some arbitrary position to the maximum absolute value of the determinant that is possible for the same in parallel mechanism However there is no proper mathematical basis to compare the performance of the two in parallel systems as yet The practical implementation of the parallel device based on theoretical studies present numerous problems Hunt and McAree 1998 present an in depth implication of such const
53. ation 8 has units of Newtons has units of millimeters The relationship between the spring constant of the outer and inner springs and the force and deflection is known so the overall spring constants were computed as outer inner connector OK outer inner 2K 9 where 41 5 19 7N mm outer Thus the calculated overall spring constant for each connector was determined to be Keonnector 20 2N mm This value was used to compute the stiffness matrix for the platform in order to do the wrench calculations Table 2 Steel Sheet Dimensions Position Height Width Bendable Length Quantity Outside 0 010 0 254mm 4mm 11 0 mm 8 Inside 0 015 0 381mm 5mm 11 0 mm 4 Attached to the body of the leg is a RRRP R represents a revolute joint and P represents a prismatic joint planar mechanism where the spring section serves as a compliant variable length link figure 8 The motion of the 3 link mechanism is used to rotate the shaft of a rotary potentiometer that is mounted into one of the pieces of the middle section of the leg The potentiometer has 5Vdc output which be used to 16 produce a range of values for the rotation that can be then be transformed into change in the overall length of the leg utilizing the given geometry of the 3 link mechanism The compliance of the leg allows it to change length up to 4mm This amount of length change t
54. ble 3 Potentiometer Calibration Values Pot Average Standard Measurement Percent of Resolution Reading Deviation Range mm count 1 91 9 314 2048 1024 15 0 0039 2 128 1 35 3 2048 1 7 0 0039 3 116 4 34 0 2048 1 6 0 0039 4 54 9 50 5 2048 24 0 0039 5 280 7 34 4 2048 1 7 0 0039 6 247 8 47 2 2048 2 3 0 0039 measurement range to get the resolution of each connector The resolution of each connectors 15 0 0039mm count The main reasons for the large standard deviations of the potentiometer data are considerable amount of friction Inside the potentiometer and slipping between the potentiometer shaft and the RRRP mechanism The difficulty of which to get very accurate measurements from the potentiometers in this sort of platform configuration is a definite reason to pursue use of other types of sensing devices in future platform devices Force Torque Measurements In order to test out the platform software wrench calculations weights were placed on the top plate of the platform and readings were taken using the PCCFC software The weights were placed directly over the center of the top plate The coordinate system used to calculate the wrench has it s origin at one corner of the bottom 29 plate refer to Figure 3 Therefore a mass placed on the center of the top plate generates force mainly in the direction of the Z axis and torques over the X Y plain The wrench data taken for several different loads
55. d at the National High Magnetic Field Laboratory in Tallahassee Florida as a Mechanical Engineer on the 900 MHz NMR Magnet Project until the end of 1998 He will receive his Master of Science in Mechanical Engineering from the University of Florida in August of 2000 89 certify that I have read this study and that my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Master of Engineering Carl D Crane III Chairman Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Master of Engineering Joseph Duffy Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Master of Engineering John Ziegert Professor of Mechanical Engineering This thesis was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Master of Engineering August 2000 M J Ohanian Dean College of Engineering Winfred M Phillips Dean Graduate School
56. d to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ROBOT FORCE CONTROL USING AN IN PARALLEL PASSIVE COMPLIANT COUPLER By CHAD M TYLER AUGUST 2000 Chairman Dr Carl D Crane III Major Department Mechanical Engineering This thesis presents the design of a Passive Compliant Coupler for Force Control PCCFC as well as the method for controlling the contact force and orientation of a robot manipulator with the coupler To accomplish these tasks a compliant parallel platform was designed and built and then connected through both physical hardware and computer software to a Puma industrial robot The platform consists of six connectors that are linearly compliant structures of known spring rate with a mechanism in each that allows its change in length to be measured A forward displacement analysis is performed using the connector length values This analysis provides the position and orientation of the top platform with respect to the base Line coordinates can be computed for each connector from these values The wrench being applied to the platform is then computed using the their line coordinates and connector lengths This wrench is then used to modify the robot end effector position vi and orientation in order to get a force and orientation combination acceptable to the particular task being performed vii 1 INTRODUCTION The use
57. e 11 Use the pose to calculate the twist and wrench of the top platform 12 Calculate the error wrench the difference between the desired wrench and the measure wrench 13 Determine the infinitesimal twist to move in order to reduce the error wrench 14 Scale the translation and rotation data according to the wrench 15 Send the transformation data to the robot through the alter port Repeat starting at step 5 20 The process to calculate the stiffness matrix and wrench in the platform was outlined in the preceding section The geometric reduction was done using an algorithm explained in Griffis 1993 There were two corrections to the equations listed in this Patent publication Equation 33 on page 27 should read as o0r1 0 1 K3 p0p1 In Equations 35 on page 28 the 3 and 4 equations should read as follows pOt1 k2 m2 p0p1 1 401 k5 m5 t0t1 E p0t1 The computer code equivalent of the reduction equations are listed in the computer code listing in Appendix A in the function solve georedux The forward analysis was done using the function solve platform also listed in the computer code listing in Appendix A The algorithm for this forward solution was taken from Griffis and Duffy 1989 3 EXPERIMENTAL RESULTS Potentiometer Calibration The potentiometers were calibrated after final assembly of the platform This was done by taking
58. empl pmult templ el cl al 10 15 1925 b2 amp alcl amp clcl amp alal amp b1b1 50202 amp b1b2 lt Ne Ne Ne Ne Ne 2 0 AA3 BB3 clc2 2 amp 1 amp templ 37 amp templ cout cout cou a2cl coef cou Cou lt lt lt lt An BB3 An a2cl coef 0 2 lt lt lt lt a2cl coef 6 templ coef 0 2 lt lt lt lt lt lt a2cl coef 1 lt lt templ coef 6 lt lt lt lt Np ms lt lt templ coef 1 lt lt lt lt clc2 templ coef lt lt clc2 coef 0 2 lt lt t lt lt pl coef 0 coef cou lt lt pl coef 6 pscale 1 1 pmult temp2 psub templ pscale alcl pmult templ padd DD pscale c2c2 pmult templ psub DD pscale 1 2 pmult templ psub DD pscale alcl pmult templ padd DD pscale a2c2 pmult templ padd DD pscale blbl pmult templ psub DD pscale clc2 pmult templ temp2 temp2 temp2 temp2 temp2 temp2 lt lt ms 4 0 AA3 BB3 b2b2 temp2 amp temp2 amp DD 2 0 AA3 CC3 e2c2 amp DD amp temp2 4 0 AA3 CC3 bibl 2 0 AA3 E 2 4 0 b2b2 4 0 AA3 E bibl 8 0 AA3 E b2b2 amp DD amp DD amp DD amp DD amp DD amp temp
59. erences To overcome the interference of connectors various ways of locating a leg along intended line coordinates were considered One way was to separate the balls by moving them an equal distance away from and towards the center of the platform A second way was to keep one ball joint at the optimal location and moving the other ball joint either towards or away from the center of the platform In this case the joint ball pairs were separated by locating one at the optimal position at each corner of the top and bottom platform and then moving the other joint balls in a counter clockwise fashion along the sides of the triangles that connect the optimal positions The legs were connected from the outside to inside and inside to outside positions going from the bottom to the top platform The distance between the centers of each pair of ball joints was dependent on maintaining enough clearance between ball joints once the entire platform was built so that the legs could have a range of motion suitable to the platforms intended workspace The distance between the ball joints was not the only factor to consider to configure the platform for optimum range of motion The actual size of the bottom and top platform triangles had to be decided along with the separation or height of the top plate with respect to the bottom plate 10 The structure and the relative dimensions of the platform mechanism were obtained by applying the optimal Qu
60. exyz 2 2 acos T_2_1 bestanswer 0 0 cos rotatexyz 1 0 D2R R2D rotatexyz 2 3 360 acos T 2 l bestanswer 0 0 cos rotatexyz 1 0 D2R R2D 45 rotatexyz 0 0 _2_1 bestanswer 1 rotatexyz 0 1 _2_1 bestanswer 1 rotatexyz 0 2 2 2 112 180 asin T 112 acos 2 l bestanswer rotatexyz 0 3 acos T_2_1 bestanswer 112 360 112 for int 0 143 itt for int j 0 j 4 j if 2 1 3 lt 0 0 comprotxyz i j 360 rotatexyz il jl else comprotxyz i j rotatexyz il jl for i 0 i 3 i if valuenear comprotxyz i 0 2 1 1 0 0 ang i 2 1 0 else if valuenear comprotxyz i 0 comprotxyz i 2 0 ang i rotatexyz i 0 else if valuenear comprotxyz il 0 comprotxyz i 3 0 ang i rotatexyz i 0 else if valuenear comprotxyz i 1 comprotxyz i 2 0 ang i 2 1 1 else if valuenear 1 1 2 1 3 0 1 2 1 1 else if valuenear comprotxyz il 2 comprotxyz i 3 0 1 rotatexyz i 2 0 ang 0 newang 0 1 ang 1 1 2 60 ang 2 2 K k K K K K K K K K K K K K K K KOK KOK KOK K K
61. gram computes the geometric reduction of the special 66 parallel platform to the 33 and then performs a forward analysis on the 33 platform leg lengths t he program then calculates he wrench in the platform include stdio h include conio h include lt dos h gt include lt stdlib h gt include math h include lt string h gt define BASE ADC 0x220 base address of DT8214 ADC card define CHAN 6 number of channels to convert define BASE ALTER 0x3f8 base address of ALTER serial port define BASE TERM Ox2f8 base address of terminal serial port define CR 13 carriage return define DEL Oxff control characters define DLE 0x90 endif endif define TRUE define FALS define STX 0x82 define ETX 0x83 1 0 ifndef D2R define D2R 0 01745329 ifndef R2D define R2D 57 29577951 define Sqrt x sqrt double x define Fabs x fabs double x typedef struct Polyy int deg double coef 37 double eval double x Poly double Poly eval double x inte i 27 28 double result coef 0 double val if deg gt 0 result coef 1 x for 152 i deg itt val pow x double i result val coef i return result void pmult Poly a Poly b Poly c void psub Poly a Poly b Poly c void padd Poly a Po
62. gths were also used to test the forward analysis program since this was a quick way to get six leg lengths for the platform in different poses The program allows the user to quickly adjust the important Compliant Platform Kinematic Simulation Modell Platform Controls Blinkers Negative e 2909 4 77 0418 Positive BEI 63 72 848 Wave Fac Porter u 80 3478 761 389 Leg Lengths Rotate Force Pointer TranslateX 4 Translate Z Joint Seperation 20 Fig 5 Compliant Platform Simulation Software dimensional parameters of the platform and to immediately get a visual display of what the platform will look like in a wide range of poses see Figure 5 The use of the program led to the following dimensions of the platform b 123 0 mm 61 5 mm ball joint separation distance 14 0 mm long leg length 2 83 0 mm short leg length 2 77 7 mm 13 Each of the six legs is serial SPS spherical prismatic spherical chain The leg has a ball at either end that is held captive by a socket on the platform The socket is a captive arrangement of thin Teflon plates surrounded by aluminum plates both with counterbored holes in them that encapsulate each of the joint balls on two sharp edges and allow for a large range of motion figure 6 This construction was used to get a low friction and predictable spherical joint
63. is given in Table 4 along with theoretical values of the forces and torques that would be generated by the given load and geometry Table 4 Wrench Measurement Data Load Wrench software Theoretical Direct Error 158 Component lbs and in lbs lbs and in Ibs 0 114 0 0 0 114 Fy 3 518 0 0 3 518 14 Fz 15 984 14 0 1 984 Mx 11 724 19 6 7 88 My 38 386 33 9 4 486 Mz 12 542 0 0 12 542 Fx 0 295 0 0 0 295 0 318 0 0 0 318 10 Fz 10 703 10 0 0 703 Mx 13 539 14 0 0 461 My 25 404 24 2 1 204 Mz 3 160 0 0 3 16 Fx 0 784 0 0 0 784 0 638 0 0 0 638 5 Fz 4 248 5 0 0 752 Mx 3 950 7 0 3 05 My 12 16 12 1 0 06 Mz 4 218 0 0 4 218 The wrench measurement data shows a good correlation between the theoretical force being placed in the Z direction and the platforms wrench output of that force Forces along the X and Y axis did not change much as expected under the vertical load The moments produced by the weights about the X and Y axis corresponds closely to the theoretical values The worst part of the data 15 the large measurement discrepancies in the data of the moment about the Z axis as compared to the theoretical values 24 Joystick Application The software listed in Appendix A was written to communicate with a PUMA700 industrial robot in real time The software controls the movement of the robot by sending it value
64. ly b Poly c void pscale Poly a double 5 Poly as void sample int int ADC sampling function void setport int address int baud initialise serial port int ALTER recve unsigned char rx msg char initflag receive ALTE void ALTER tran transmit ALTER message f R message int data word char initflag void rx int address int no unsigned char ch receive array over serial port void tx int address int no unsigned char ch transmit array over serial port void transmit unsigned char string transmit to VAL terminal void get leglengths void solve georedux double 6 int base int ad value double o0o1 double L_s0s1 doub double q0qi double r0rl double Lsfor33 6 int count 61 le 0 1 double void solve platform int pnum solutions double T_2_1 8 4 4 double p x 1 double x 1 double double s x 2 double t x 2 double t y 2 double L or double L os double L ps double pt double double qr int solve bestsolution int pnum solutions double r 1 8 4 double s 1 8 4 double t 1 8 4 double movexyz 3 void matmult double ans 4 4 double matrix1 4 4 double matrix2 4 4 void matmult66 double bans 6 6 double bmatrixl 6 6 double bmatrix2 6 6 void matvecmult6616 double cwrench 6 double cmat 6 6 double ctwi
65. nd coord system as seen 1st _2_1 1 0 3 rx T 2 1 1 1 3 T 2 14141121131 rz T 2 1 i 3 3 1 0 Enter x axis of 2nd coord system as seen in 1st xvec 0 sx rx xvec 1 sy ry xvec 2 sz rz double tempmag tempmag vecmag 122210 xvec 0 tempmag xvec 1 tempmag xvec 2 tempmag xvec 01101 0 11101 xvec 1 21 0 2 31 0 0 0 lt lt L 43 Enter z axis of 2nd coord system as seen in 1st tempvec 0 tx rx tempvec 1 ty Ty tempvec 2 tz zvec xvec tempvec crossproduct zvec xvec tempvec tempmag vecmag zvec zvec 0 zvec 0 tempmag zvec 1 zvec 1 tempmag zvec 2 zvec 2 tempmag zvec zvec T 2111110112 zvec 0 T 2 1 i 1 2 zvec 1 T 2 1 i 21 2 zvec 2 31 21 0 20 5 Enter y axis of 2nd coord system as seen in 156 crossproduct yvec zvec xvec tempmag vecmag yvec yvec 0 yvec 0 tempmag yvec 1 yvec 1 tempmag yvec 2 yvec 2 tempmag yvec zvec xvec yvec T 21111101111 yvec 0 T 2 14411111111 1 T 2 111411121111 2 T 2 1 i 3 1 0 0 7 Function
66. ng normal operation The final platform weight was between one and two pounds More importantly than the actual values for the load supporting and compliance characteristics of the platform is that the platform can actually improve the capabilities of the PUMA700 which will be shown in chapter 3 of this thesis Several experiments were done prior to getting to the point of controlling the robot in real time with the PCCFC mounted on the PUMA700 end effector The first of these experiments was a sampling of the potentiometer outputs The data was collected with the platform under zero load conditions several times to get a range of values The values were then used to calibrate the individual potentiometers and eventually set the zero value for each potentiometer in the control program The second experiment was a wrench calibration of the PCCFC using weights of known mass The weights were place on the top plate of the PCCFC and then data was taken using the PCCFC software The wrench generated in the platform was then compared to the theoretical values for the force and torques that the weights would apply over the given geometry This allowed the platform to be calibrated for output of the wrench data The third experiment was very similar to the final system the difference being that the PCCFC was mounted to table rather than the PUM A700 end effector With the PCCFC mounted to table a wrench was applied to the top platform The computer
67. ormal message to VAL DLE ETX 0 tail of normal message to VAL chksum check sum byte see if initial or normal message transmission is required 57 if initflag 1 If initial message from PC only send 7 bytes tx_msg 3 0 tx_msg 4 DLE tx_msg 5 ETX tx_msg 6 0 tx_bytes 7 else Normal message from PC length depends on no of coordinates sent see VAL user mannual tx_bytes 20 tx msg 4 Ox3f ALTER select bits for 6 axis operation all 6 bits construct normal message first construct bytes containing ALTER data for 1 0 1 lt 5 1 tx_msg 2 1i 5 data word il tx msg 2 i 6 data word i 8 the body of the message should be checked for byte stuffing during construction but previous problems observed with the PC version have shown that it is better to just ensure that a DLE byte cannot be sent by sending DLE 1 instead chksum 0 for 1 3 1 lt 16 1 if tx_msg i DLE tx_msg i t chksum tx msg i tx msg 19 chksum now send it if initflag 0 print_tran tx_msg getch tx BASE ALTER tx bytes tx msg KKK KK k k k k k K K k K K K k K K K K K K K K K OK K KOK KOK K k KOK ck k kc k k kc k k KOK ck kckck ck ckckck ck kk sy Function to transmit array of bytes to ALTER void tx int address
68. raints and realistic design ideas 2 SYSTEM PERFORMANCE SPECIFICATIONS AND DESIGN Platform and Robot Performance Tasks The goal of this project was to develop a system that uses real time data from the PCCFC to modify the movements of a PUMA700 industrial robot This was done using 5V potentiometers as the output devices from the PCCFC that send their data to an ADC card that was installed in an IBM PC running MS DOS The PC is also connected via two serial ports to the PUMA700 One of these ports allows the PC to take over control of the robot terminal program used to initialize the robot and transmit commands back and forth The other terminal is attached to the robots alter port This port s function is to allow the PC to send path modification data to the robot in real time The PC is also used to run the software necessary to receive the real time data from the PCCFC transform it to usable connector length values and then perform a forward analysis of the in order to obtain the wrench that is acting on the PCCFC This wrench is then used to calculate a modification to the robot end effector pose which is then transmitted via the serial connection to the PUMA700 data being transmitted contains six numerical values which represent the x y and z translations and the rotations about those three axis of the top plate with respect to the bottom plate Therefore a loop is created starting from the PCCFC on to the
69. ranslates to 30 of rotation of the potentiometer shaft The calculated change in length can be added to the original length of the leg and therefore the platform will produce six leg length values in real time BMM Fig 8 Leg Assembly RRRP Mechanism The detailed design of the PCCFC was done in AutoDesk Mechanical Desktop Detailed part drawings of all of the parts needed to manufacture the platform are included in Appendix B Also included at the beginning of Appendix B is a list of all those drawings and the quantities and material type of each part needed 17 Kinematic Model of the Platform To make a static force analysis an external wrench W Fx Fz My Mz a force acting through the origin together with a general couple M is applied to the movable platform The external wrench is in static equilibrium with the six leg forces the equation representing this is given by 4 6 W Y 75 10 i l where f amp the magnitudes of the axial reaction forces experienced by the legs and are the line co ordinates of the legs The system of forces remains in static equilibrium as the moveable platform twists relative to ground To account for the twist the external wrench changes as the platform moves The mapping of the change in wrench to the twist of the platform is given by SW 1 160 11 where 8W f m is the change in wrench
70. s for the twist that 15 placed on the top plate of the PCCFC result of this is the ability to move and orient the end effector of the robot in 6 degrees of freedom in a much faster and more natural way than previously possible using either a computer terminal or the PUMA700 Teach Pendant The compliant nature of the PCCFC coupled with the ability to do a forward analysis using its connector lengths makes this application possible 4 CONCLUSIONS FUTURE WORK This thesis has presented the design of an In parallel passive compliant force torque sensor and it s ability to be used to control an industrial robot During the design of the platform many of the important design issues associated with parallel platforms have been addressed There is the compact arrangement of elastic elements in the platform connectors that allow a large compliance in a small space The use of 3D visualization during the design process was introduced to further assist in making the platform as compact as possible The need for a ball joint that had very low friction while maintaining strength under dynamic loads led to the design of the captive Teflon ball joints Measuring the change in length of the connectors was accomplished using rotary potentiometers and 3 link mechanism computer rendering of the final design of the is presented in figure 9 The ability of the platform to measure a wrench in a compliant manner is crucial to the f
71. some infinitesimal change in the wrench applied to the top platform A simpler form of equation 3 which was used in the PCCFC software is SW 1 13 where is the platform jacobian a 6X6 matrix with the spring constants of each connector along the diagonal and is the change in length of each connector This equation is valid near the home position of the platform Software Algorithm The software to perform the tasks outlined in the above section was written using a Borland C compiler in an MS DOS environment For this example consider the case 19 where the in parallel platform is attached to the end effector of the PUMA robot Also assume that the top of the platform is rigidly connected to ground user will specify a desired wrench that is to be experienced by the top platform The objective is to determine how to move the PUMA end effector in order to realize this wrench The flow of the software is as follows 1 Initialize the robot 2 Send starting message to the robot 3 Receive starting message reply from robot 4 Begin running in absolute alter mode 5 Obtain 6 potentiometer readings and transform them to 6 leg lengths 6 Reduce the special 6 6 geometry to the 3 3 geometry 7 Calculate the equivalent 3 3 leg lengths 8 Send the 3 3 leg lengths to the forward analysis program 9 Compute all real solutions for the platform pose 10 Select best pose solution according to which is closest to previous pos
72. st 6 vecmult double ans1 4 ble vector1 3 void double dotproduct dou void crossproduct double ans 3 double vecmag double vector 3 int valuenear double x double goal double matrix1 4 4 double vector1 4 double vector2 3 double vector1 3 double vector2 3 double tol void Inverse double matdata int numcol double det double invary void MatSwap double 51 double s2 void Transpose double a double b int m int n void findangles double T 2 1 8 4 4 int rotx void findwrench double 6 6 double jactp 6 6 double newang 3 int bestanswer double k 6 6 29 double wrench 6 void wrench2 double jac 6 6 double Knew 6 void setjac double s 3 6 double 6 6 double wrench 6 void main base points are lst coordinate system on x axis is upper platform points 2nd coordinate system on x axis t is in xy input items double 1 q_x_l double s x 2 t x 2 double L or L os L ps and q origin is at o plane are r 5 and t origin is at r 5 is plane p is 4 L virtual 33 double movexyz 3 double newang 3 leg lengths pt L qt t L oo L ss L pp t L 44 33 L rr reassigned 66 leg lengths 1 2 L L double Ladc 6 Lsfor33 6 virtual output items double _2_1 8
73. sub DD temp2 amp DD 2 0 CC3 DD3 blb2 amp temp2 pscale 1 2 pmult templ psub DD temp2 amp DD 2 0 D blb2 amp temp2 pscale 1 2 pmult templ psub DD temp2 amp DD DD3 D elc2 D3 amp temp2 pscale 1 2 pmult templ psub DD temp2 amp DD 38 amp templ amp templ amp templ amp templ amp templ amp templ amp templ amp templ amp templ amp templ amp templ amp templ pscale pmult templ psub DD pscale a2a2 pmult templ psub DD pscale alal pmult templ psub DD pscale alal pmult templ psub DD 5152 clc2 pscal pscal pscale 1 2 pscale blb2 pscale a2cl pscale alc2 psub beta 0101 b 2 2 psu psu pmult alpha pmult beta pmult rhol pscale p33 pmult p35 psub p32 for 1 0 cout lt lt double unitval unitval ioegn tempunitval Iy pscale ioeqn double coef2 9 for 1 8 1 gt 0 2 1 cout lt lt double xsq r 8 temp2 temp2 temp2 temp2 templ padd beta psub beta psub beta alcl a2c2 beta rho2 4 0 p34 p36 0137 tempunitval 39 AA3 AA3 2 2 amp templ amp temp2 amp DD
74. t lt 1 lt lt 1 2 2 1 1 cout lt lt naa2 lt lt 2 bb2 2 1 cout lt lt nbb2 lt lt bb2 2 c2 eval xx i cout lt lt 2 lt lt cc2 discr 4 0 bbl bb1 4 0 aal ccl if discr 0 badone i TRUE cout lt lt bady lt lt discr lt continue y candidate 0 2 0 bb1 sqrt di y candidate 1 2 0 1 sqrt discr 4 0 bb2 bb2 4 0 aa2 cc2 if discr lt 0 badone i TRUE cout lt lt badz discr continue z candidate 0 z candidate 1 2 0 bb2 sqrt di 2 0 bb2 sqrt di aa3 4 0 AA3 bb1 bb2 DD3 aal aa2 bb3 2 0 AA3 bb1 cc2 2 0 BB3 aa2 cc3 2 0 AA3 bb2 ccl 2 0 CC3 aal AA3 ccl cc2 EE3 aal aa2 cand value 0 fabs aa3 y candidate bb3 y candidate 0 cc3 cand value 1 fabs aa3 y candidate bb3 y candidate 1 cc3 cand value 2 fabs aa3 y candidate bb3 y candidate 0 cc3 cand value 3 fabs aa3 y candidate bb3 y candidate 1 cc3 if cand value 0 cand value 1 cand value 2 amp amp cand value 0 cand valu candidate 0 z candidate 0 lt endl scr 2 0 aal scr 2 0 aal lt endl scr 2 0 aa2 scr 2 0 aa2 bbl bb2 0 z candidate 0 z candidate 0 z candidate 0 z candidate 1
75. tic analysis of robot manipulators Duffy J 1996 Statics and Kinematics with Applications to Robotics Dwarakanath T A Crane C D Duffy 7 and Tyler 2000 In parallel passive compliant coupler for robot force control DETC2000 MECH 14114 Griffis M 1993 Method and apparatus for controlling geometrically simple parallel mechanisms with distinctive connections United States Patent 5 179 525 Griffis M and Duffy J 1989 A Forward Displacement Analysis of a Class of Stewart Platforms Journal of Robotic Systems Vol 6 no 6 pp 703 720 Griffis M and Duffy J 1991 Kinestatic Control A Novel Theory for Simultaneously Regulating Force and Displacement Trans ASME Journal of Mechanical Design vol 113 pp 508 515 Hunt K H and McAree P R 1998 The octahedral manipulator geometry and mobility International Journal of Robotic Research Vol 17 no 8 pp 868 885 Lee J Duffy J and Hunt K H 1998 A Practical quality index based on the octahedral manipulator International Journal of Robotic Research Vol 17 no 10 pp 1081 1090 Sugar T and Kumar V 1998 Design and control of a compliant parallel manipulator for a mobile platform published on CDROM 98 DETC MECH 5863 Atlanta Georgia USA 88 BIOGRAPHICAL SKETCH Chad Tyler received a Bachelor of Science in Mechanical Engineering from The Florida State University in the spring of 1997 Following that he worke
76. ting due to geometrical uncertainties and manufacturing tolerance of the parts Passive compliance is therefore qualified to sustain the required contact force between two interacting surfaces and most importantly would assist in the smooth transition of forces from the no contact mode region to contact with the environment The simple and real time response of passive control avoids the complex controller and sophisticated instrumentation required in some industrial applications The in parallel mechanism offers a straightforward and easy method to reconstruct the wrench applied on one of the plates from calculated connector forces therefore the Passive Compliant Coupler for Force Control PCCFC can provide force feedback control of the robot It is different from commercially available Remote Center Compliance RCC devices that are open loop systems and not meant to sense the applied wrench and hence cannot provide force feedback control of the robot Gaillet and Reboulet 1983 developed the first sensor of this kind based on the octahedral structure of the Stewart platform Nguyen et al 1991 reported the development of a Stewart platform based sensor with LVDT s mounted along the legs for wrench measurement in the presence of a passive compliance Bhaumick et al 1997 reported the development of a stiff force torque sensor based on the Stewart Platform with shape optimization of the legs to minimize the Noise to Signal ratio Various authors c
77. uture use of such a device The compliance will allow the platform to be used as a compliant wrist element on a serial robot This will allow the robot to encounter obstacles in its workspace without immediately damaging those objects The platforms wrench output could be used to maintain a desired wrench on such an object This can be done by modifying the code in Appendix A so that it uses the wrench calculations to modify the twist data that is sent to the 700 in a way that will maintain the desired wrench The code will also have to be altered to include instructions for the desired robot 25 26 task currently the code only modifies the position of the robot from whatever position it starts out at when the program is run If the platform is used in this manner it will improve the capabilities of the serial robot Fig 9 PCCFC Computer Rendering In summary the primary objective of designing and fabricating an in parallel platform that met the performance criteria listed in Table 2 was attained This design is documented in detail in Appendix B In addition the methodology is presented as to how the device could be used in the future as an attachment at the end of an industrial robot in order to control contact forces This implementation represents the significant work to be accomplished in the future APPENDIX A COMPUTER CODE Program PCCFC Software Programmers Chad Tyler Date June 30 2000 This pro
78. value 5 3072 10 19 0 25 Function to reduce th th special 66 platform geometry to the 33 geometry in order to calculat to the solve_platform 33 1 4 1 function to do forward analysis void solve georedux double 001 40001 5051 ngths to send double double L_t0t1 double L_q0q1 double L_rOrl double Lsfor33 6 double 0 0 o0s0 p0q0 p0t0 q000 q0r0 50 0 t0q0 r000 rlsSl sitt sTply tlrl tlqi oldsl pltl qlrl C D E kl 5 ko KO Kl K2 K4 K5 K6 ml m2 m3 m4 m6 0 0 123 0080 109 p0q0 123 poto 109 4000 123 020 109 50 0 14 0 0 14 0 0 14 risi 61 5 rlol 47 5 51 1 61 5 slpl 47 5 33 tiri 61 5 141 47 5 olsl 14 14 91 1 14 0151 101 1 1 81 1 C 1 1 1 1 D 50 0 0050 t0q0 p0t0 F q0r0 r000 olsl rilol 0151 0151 k2 pltl slpl 1 1 1 1 qlril tiql qlril qlrl k4 50 0 050 50 0 50 0 k5 t0q0 pOtO t0q0 t0q0 r0o0 q0r0 q0r0 q0r0 ml 181 101 m2 1 1 51 1 m3 amp 1 1 1 1 m4 0 0 050 m5 p0q0 p0t0 m6 q000 r000 C k5 C E k2 B C E k4 B C D E k1 F

IN-PARALLEL PASSIVE COMPLIANT COUPLER FOR ROBOT

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