Solving the forward kinematics of a planar three-legged platform with holonomic higher pairs

Journal of Mechanical Design, Transactions of the ASME

Volumn 121, Issue 2, 1999, Pages 212-219

  Hayes, M J D ^a   Husty, M L ^b,c   Zsombor Murray, P J ^c,d  

^a Centre for Intelligent Machines   (United States)

^b UNIVERSITY OF LEOBEN   (Austria)

^c MCGILL UNIVERSITY   (Canada)

^d GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

HOLONOMIC HIGHER PAIRS; PLANAR THREE-LEGGED PLATFORMS;

END EFFECTORS; KINEMATICS; MOBILE ROBOTS; MOTION CONTROL; MOTION PLANNING; PROBLEM SOLVING; ROBOTICS;

MACHINE DESIGN;

EID: 0032663746     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2829446     Document Type: Article

References (78)

1. Agrawal, S. K., and Pandravada, R., 1992, “Inverse Kinematic Solutions of a Rolling Disk Between Two Planar Manipulators,” Robotics, Spatial Mechanisms, and Mechanical Systems, ASME, DE-Vol. 45, pp. 473-478.
2. Agrawal, S. K., and Pandravada, R., 1993, “Kinematics and Workspace of a Rolling Disk Between Planar Manipulators,” Proc. Am. Control Conf., San Francisco, CA, pp. 741-745.
3. Angeles, J., 1997, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer-Verlag, New York, N.Y., p. 318.
4. Blaschke, W., 1911, “Euklidische Kinematik und nichteuklidischc Geometric,” Zeitschr. Math. Phys., Vol. 60, pp. 61-91 and 203-204.
5. Bottema, O., and Roth, B., 1990, Theoretical Kinematics, (originally published in 1979 by North-Holland Publishing Co., Amsterdam, as Vol. 24 of North-Holland Series in Applied Mathematics and Mechanics) Dover Publications, Inc, New York, N.Y.
6. Chen, W., and Kumar, V., 1995, “Workspace of Planar Cooperating Robots with Rolling Contacts,” Advanced Robotics, The Int’l J. of the Robotics Soc. of Japan, Vol. 9, No. 5, pp. 483-504.
7. Cole, A., Hauser, J., and Sastry, S., 1988, “Kinematics and Control of Multifingered Hands with Rolling Contact,” Proc. of IEEE Int. Conf. on Rob. and Aut., pp. 228-233.
8. Coxeter, H. S. M., 1969, Introduction to Geometry, second edition, John Wiiey & Sons, inc., Toronto, Ont., Canada.
9. De Sa, S., 1979, “Classification and Properties of Planar Motion Using Kinematic Mappings,” Dissertation, Stanford University, Stanford, CA.
10. De Sa, S., Roth, B., 1981, “Kinematic Mappings. Part 1: Classification of Algebraic Motions in the Plane,” ASME, J. of Mech. Design, Vol. 103, pp. 585-591.
11. Gosselin, C., 1988, “Kinematic Analysis, Optimization and Programming of Parallel Robotic Manipulators,” Ph.D. thesis, Dept, of Mech. Eng., McGill University, Montréal, Que, Canada.
12. Gosselin, C., and Sefrioui, J., 1991, “Polynomial Solutions for the Direct Kinematics Problem of Planar Parallel Three-Degree-of-Freedom Parallel Manipulators,” Proc. 5th int. Conf. on Adv. Rob. (ICAR), Pisa, Italy, pp. 1124-1129.
13. Gough, V. E., 1956, “Discussion in London: Automobile Stability, Control, and Tyre Performance,” Proc. Automobile Division, Institution of Mech. Engrs., pp. 392-394.
14. Grünwald, J., 1911, “Ein Abbildungsprinzip, welches die ebene Geometrie und Kinematik mit der räumlichen Geometrie verknüpft,” Sitzber. Ak. Wiss. Wien, Vol. 120, pp. 677-741.
15. Hayes, M. J. D., Zsombor-Murray, P. J., 1996a, “A Planar Parallel Manipulator with Holonomie Higher Pairs: Inverse Kinematics,” Proc, CSME Forum 1996, Symposium on the Theory of Machines and Mechanisms, Hamilton, Ont., Canada, pp. 109-116.
16. Hayes, M. J. D., Zsombor-Murray, P., 1996b, “Kinematic Mapping of 3legged Planar Platforms With Holonomie Higher Pairs,” Recent Advances in Robotic Kinematics, eds. Lenarčič, J., Parenti-Castelli, V., Kluwer Academic Publishers, Dordrecht, pp. 421-430.
17. Hayes, M. J. D., and Zsombor-Murray, P., 1998, “Inverse Kinematics of a Planar Manipulator with Holonomie Higher Pairs,” Recent Advances in Robotic Kinematics, eds. Lenarčič, Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 59-68.
18. Hui, R., and Goldenberg, A. A., 1989, “Formulation of the Hybrid Control Architecture Using the Constrained Manipulator Model-Application to Rolling Manipulation of a Rigid Object Using a Dextrous Robotic Hand,” Second Workshop on Military Robotic Applications, Kingston, Ont., Canada, pp. 316-323.
19. Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford, England.
20. Hunt, K. H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot Arms,” ASME J. of Mech., Trans, and Automation in Design, Vol. 105, No. 4, pp. 705-712.
21. Husty, M. L., 1995, “Kinematic Mapping of Planar Three-Legged Platforms,” Proc. 15th Canadian Congress of Applied Mechanics, CANCAM 1995, Vol. 2, pp. 876-877.
22. Husty, M. L., 1996a, “On The Workspace of Planar Three-legged Platforms,” Proc. World Automation Conf, 6th Int. Symposium on Rob. and Manuf. (ISRAM 1996), Montpellier, France, Vol. 3, pp. 339-344.
23. Husty, M. L., 1996b, “An Algorithm for Solving the Direct Kinematics of General Stewart-Gough Platforms,” Mechanism and Machine Theory, Vol. 31, No. 4, pp. 365-379.
24. Merlet, J-P., 1996, “Direct Kinematics of Planar Parallel Manipulators,” IEEE Int. Conf. on Robotics and Automation, Minneapolis, MN, pp. 3744-3749.
25. Merlet, J-P., 1998, “Determination of the Presence of Singularities in 6-D Workspace of a Gough Parallel Manipulator,” Advances in Robot Kinematics: Analysis and Control, eds. Lenarčič, J., Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 39-48.
26. Mimura, N., and Funahashi, Y, 1992, “Kinematics of Planar Multiiin-gered Robot Hand with Displacement of Contact Points,” JSME International Journal, Series 3, Vol. 35, No. 3, pp. 462-469.
27. Murray, A. P., Pierrot, F., 1998, “N-Position Synthesis of Parallel Planar RPR Platforms,” Advances in Robot Kinematics: Analysis and Control, eds. Lenarčič, J., Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 69-78.
28. Nielsen, J., and Roth, B., 1996, “The Direct Kinematics of the General 6-5 Stewart-Gough Mechanism,” Recent Advances in Robotic Kinematics, eds. Lenarčič, J., Parenti-Castelli, V., Kluwer Academic Publishers, Dordrecht, pp. 716.
29. Pennock, G. R., and Kassner, D. J., 1992, “Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 114, No. 1, pp. 87-95.
30. Pennock, G. R., and Kassner, D. J., 1993, “The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 115, pp. 269-276.
31. Ravani, B., 1982, “Kinematic Mappings as Applied to Motion Approximation and Mechanism Synthesis,” Dissertation, Stanford University, Stanford, CA
32. Ravani, B., and Roth, B., 1983, “Motion Synthesis Using Kinematic Mappings,” ASME Journal of Mechanisms, Transmissions, & Automation in Design, Vol. 105, pp. 460-467.
33. Rooney, J., and Earle, C. F., 1983, “Manipulator Postures and Kinematics Assembly Configurations,” 6th World Congress on Theory of Machines and Mechanisms, New Delhi, pp. 1014-1020.
34. Salisbury, J. K., and Roth, B., 1983, “Kinematic and Force Analysis of Articulated Mechanical Hands,” ASME Journal of Mechanical Transmissions and Automation in Design, Vol. 105, pp. 35-41.
35. Salmon, G., 1885, Lessons Introductory to the Modern Higher Algebra, fourth edition, Hodges, Foster, and Figgis, Dublin, Ireland.
36. Shirkhodaie, A. H., and Soni, A. H., 1987, “Forward and inverse Synthesis for a Robot with Three Degrees of Freedom,” 19th Summer Computation Simulation Conference, Montreal, Quebec, Canada, pp. 851-856.
37. Stewart, D., 1965, “A Platform With Six Degrees of Freedom,” Proc. Institution of Mech. Engrs., Vol. 180, Part 1, No. 15, pp. 371-378.
38. Wohlhart, K, 1992, “Direct Kinematic Solution of the General Planar Stewart Platform,” Proc. of the Int. Conf. on Comp. Int. Manu., Zakopane, pp. 403-411.
39. Yun, X., Kumar, V., Sarkar, N., Paljug, E., 1992, “Control of Multiple Arms with Rolling Constraints,” Proc. of IEEE Int. Conf. Rob. Aut., Nice, France, pp. 2193-2198.
40. Agrawal, S. K., and Pandravada, R., 1992, “Inverse Kinematic Solutions of a Rolling Disk Between Two Planar Manipulators,” Robotics, Spatial Mechanisms, and Mechanical Systems, ASME, DE-Vol. 45, pp. 473-478.
41. Agrawal, S. K., and Pandravada, R., 1993, “Kinematics and Workspace of a Rolling Disk Between Planar Manipulators,” Proc. Am. Control Conf., San Francisco, CA, pp. 741-745.
42. Angeles, J., 1997, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer-Verlag, New York, N.Y., p. 318.
43. Blaschke, W., 1911, “Euklidische Kinematik und nichteuklidischc Geometric,” Zeitschr. Math. Phys., Vol. 60, pp. 203-204.
44. Bottema, O., and Roth, B., 1990, Theoretical Kinematics, (originally published in 1979 by North-Holland Publishing Co., Amsterdam, as Vol. 24 of North-Holland Series in Applied Mathematics and Mechanics) Dover Publications, Inc, New York, N.Y.
45. Chen, W., and Kumar, V., 1995, “Workspace of Planar Cooperating Robots with Rolling Contacts,” Advanced Robotics, The Int’l J. of the Robotics Soc. of Japan, Vol. 9, No. 5, pp. 483-504.
46. Cole, A., Hauser, J., and Sastry, S., 1988, “Kinematics and Control of Multifingered Hands with Rolling Contact,” Proc. of IEEE Int. Conf. on Rob. and Aut., pp. 228-233.
47. Coxeter, H. S. M., 1969, Introduction to Geometry, second edition, John Wiiey & Sons, inc., Toronto, Ont., Canada.
48. De Sa, S., 1979, “Classification and Properties of Planar Motion Using Kinematic Mappings,” Dissertation, Stanford University, Stanford, CA.
49. De Sa, S., Roth, B., 1981, “Kinematic Mappings. Part 1: Classification of Algebraic Motions in the Plane,” ASME, J. of Mech. Design, Vol. 103, pp. 585-591.
50. Gosselin, C., 1988, “Kinematic Analysis, Optimization and Programming of Parallel Robotic Manipulators,” Ph.D. thesis, Dept, of Mech. Eng., McGill University, Montréal, Que, Canada.
51. Gosselin, C., and Sefrioui, J., 1991, “Polynomial Solutions for the Direct Kinematics Problem of Planar Parallel Three-Degree-of-Freedom Parallel Manipulators,” Proc. 5th int. Conf. on Adv. Rob. (ICAR), Pisa, Italy, pp. 1124-1129.
52. Gough, V. E., 1956, “Discussion in London: Automobile Stability, Control, and Tyre Performance,” Proc. Automobile Division, Institution of Mech. Engrs., pp. 392-394.
53. Grünwald, J., 1911, “Ein Abbildungsprinzip, welches die ebene Geometrie und Kinematik mit der räumlichen Geometrie verknüpft,” Sitzber. Ak. Wiss. Wien, Vol. 120, pp. 677-741.
54. Hayes, M. J. D., Zsombor-Murray, P. J., 1996a, “A Planar Parallel Manipulator with Holonomie Higher Pairs: Inverse Kinematics,” Proc, CSME Forum 1996, Symposium on the Theory of Machines and Mechanisms, Hamilton, Ont., Canada, pp. 109-116.
55. Hayes, M. J. D., Zsombor-Murray, P., 1996b, “Kinematic Mapping of 3legged Planar Platforms With Holonomie Higher Pairs,” Recent Advances in Robotic Kinematics, eds. Lenarčič, J., Parenti-Castelli, V., Kluwer Academic Publishers, Dordrecht, pp. 421-430.
56. Hayes, M. J. D., and Zsombor-Murray, P., 1998, “Inverse Kinematics of a Planar Manipulator with Holonomie Higher Pairs,” Recent Advances in Robotic Kinematics, eds. Lenarčič, Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 59-68.
57. Hui, R., and Goldenberg, A. A., 1989, “Formulation of the Hybrid Control Architecture Using the Constrained Manipulator Model-Application to Rolling Manipulation of a Rigid Object Using a Dextrous Robotic Hand,” Second Workshop on Military Robotic Applications, Kingston, Ont., Canada, pp. 316-323.
58. Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford, England.
59. Hunt, K. H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot Arms,” ASME J. of Mech., Trans, and Automation in Design, Vol. 105, No. 4, pp. 705-712.
60. Husty, M. L., 1995, “Kinematic Mapping of Planar Three-Legged Platforms,” Proc. 15th Canadian Congress of Applied Mechanics, CANCAM 1995, Vol. 2, pp. 876-877.
61. Husty, M. L., 1996a, “On The Workspace of Planar Three-legged Platforms,” Proc. World Automation Conf, 6th Int. Symposium on Rob. and Manuf. (ISRAM 1996), Montpellier, France, Vol. 3, pp. 339-344.
62. Husty, M. L., 1996b, “An Algorithm for Solving the Direct Kinematics of General Stewart-Gough Platforms,” Mechanism and Machine Theory, Vol. 31, No. 4, pp. 365-379.
63. Merlet, J-P., 1996, “Direct Kinematics of Planar Parallel Manipulators,” IEEE Int. Conf. on Robotics and Automation, Minneapolis, MN, pp. 3744-3749.
64. Merlet, J-P., 1998, “Determination of the Presence of Singularities in 6-D Workspace of a Gough Parallel Manipulator,” Advances in Robot Kinematics: Analysis and Control, eds. Lenarčič, J., Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 39-48.
65. Mimura, N., and Funahashi, Y, 1992, “Kinematics of Planar Multiiin-gered Robot Hand with Displacement of Contact Points,” JSME International Journal, Series 3, Vol. 35, No. 3, pp. 462-469.
66. Murray, A. P., Pierrot, F., 1998, “N-Position Synthesis of Parallel Planar RPR Platforms,” Advances in Robot Kinematics: Analysis and Control, eds. Lenarčič, J., Husty, M. L., Kluwer Academic Publishers, Dordrecht, pp. 69-78.
67. Nielsen, J., and Roth, B., 1996, “The Direct Kinematics of the General 6-5 Stewart-Gough Mechanism,” Recent Advances in Robotic Kinematics, eds. Lenarčič, J., Parenti-Castelli, V., Kluwer Academic Publishers, Dordrecht, pp. 716.
68. Pennock, G. R., and Kassner, D. J., 1992, “Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 114, No. 1, pp. 87-95.
69. Pennock, G. R., and Kassner, D. J., 1993, “The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 115, pp. 269-276.
70. Ravani, B., 1982, “Kinematic Mappings as Applied to Motion Approximation and Mechanism Synthesis,” Dissertation, Stanford University, Stanford, CA
71. Ravani, B., and Roth, B., 1983, “Motion Synthesis Using Kinematic Mappings,” ASME Journal of Mechanisms, Transmissions, & Automation in Design, Vol. 105, pp. 460-467.
72. Rooney, J., and Earle, C. F., 1983, “Manipulator Postures and Kinematics Assembly Configurations,” 6th World Congress on Theory of Machines and Mechanisms, New Delhi, pp. 1014-1020.
73. Salisbury, J. K., and Roth, B., 1983, “Kinematic and Force Analysis of Articulated Mechanical Hands,” ASME Journal of Mechanical Transmissions and Automation in Design, Vol. 105, pp. 35-41.
74. Salmon, G., 1885, Lessons Introductory to the Modern Higher Algebra, fourth edition, Hodges, Foster, and Figgis, Dublin, Ireland.
75. Shirkhodaie, A. H., and Soni, A. H., 1987, “Forward and inverse Synthesis for a Robot with Three Degrees of Freedom,” 19th Summer Computation Simulation Conference, Montreal, Quebec, Canada, pp. 851-856.
76. Stewart, D., 1965, “A Platform With Six Degrees of Freedom,” Proc. Institution of Mech. Engrs., Vol. 180, Part 1, No. 15, pp. 371-378.
77. Wohlhart, K, 1992, “Direct Kinematic Solution of the General Planar Stewart Platform,” Proc. of the Int. Conf. on Comp. Int. Manu., Zakopane, pp. 403-411.
78. Yun, X., Kumar, V., Sarkar, N., Paljug, E., 1992, “Control of Multiple Arms with Rolling Constraints,” Proc. of IEEE Int. Conf. Rob. Aut., Nice, France, pp. 2193-2198.