Multibody Dynamics of Closed, Open, and Switching Loop Mechanical Systems

  • Youm, Youn-Gil (Department of Mechanical Engineering, Pohang University of Science & Technology)
  • Published : 2005.01.01

Abstract

The vast mechanical systems could be classified as closed loop system, open loop system and open & closed (switching) system. In the closed loop system, the kinematics and dynamics of 3-D mechanisms will be reviewed and closed form solutions using the direction cosine matrix method and reflection transformation method will be introduced. In the open loop system, kinematic & dynamic analysis methods regarding the redundant system which has more degrees of freedom in joint space than those of task space are reviewed and discussed. Finally, switching system which changes its phase between closed and open loop motion is investigated with the principle of dynamical balance. Among switching systems, the human gait in biomechanics and humanoid in robotics are presented.

Keywords

References

  1. Baillieul, J., Hollerbach, J. M. and Brockett, R. W., 1984, Programming and Control of Kinematically Redundant Manipulators, 23rd IEEE Conf. Decision and Control (Las Vegas, Nevada), Dec., pp. 768-774 https://doi.org/10.1109/CDC.1984.272110
  2. Baillieul, J., 1985, Kinematic Programming Alternatives for Redundant Manipulators, Proc. IEEE Int. Conf. Robotics and Automation (St. Louis, MO), Mar, pp. 722-728
  3. Baker, D. R. and Wampler II, C. W., 1988, On the Inverse Kinematics of Redundant Manipulators, Int. J. Robotics Res., Vol.7, No.2, pp.3-21 https://doi.org/10.1177/027836498800700201
  4. Benhabib, B., Goldenberg, A. A. and Fenton, R. G., 1985, A Solution to the Inverse Kinematics of Redundant Manipulators, J. Robotic Systems, Vol. 2, No.4, pp. 373-385 https://doi.org/10.1002/rob.4620020404
  5. Ben-Israel, A. and Greville, T. N. E., 1980, Generalized Inverse: Theory and Applications, Robert E. Krieger Publishing Co., New York
  6. Borrel, P. and Liegeois, A., 1986, A Study of Multiple Manipulator Inverse Kinematic Solutions with Application to Trajectory Planning and Work Space Determination, Proc. IEEE Int. Conf. on Robotics and Automation, pp. 1180-1185
  7. Chace, M. A., 1965, Solution to the Vector Tetrahedron Equation, ASME Journal of Engineering for Industry, Vol. 87, pp. 228-234
  8. Chang, P. H., 1987, A Closed form Solution for Inverse Kinematics of Robot Manipulators with Redundancy, IEEE J. Robotics and Automation, Vol. RA-3, No.5, pp.393-403
  9. Chen, P. and Roth, B., 1969, Design Eqution for the Finitely and Infinitesimally Separated Position Synthesis of Binary Links and Combined Link Chains, Trans. ASME, Series B, Vol. 91, No. 1, pp.209-219
  10. Denavit, J., 1956, Description and Displacement Analysis of Mechanisms Based in $2{\times}2$ Dual Matrices, Ph.D. Thesis, Northwestern University, Evanster, I 11
  11. Denavit, J. and Hartenberg, RR. S., 1955, A Kinematic Notation for Lower Pair Mechanisms Based Matrices, ASME J. Applied Mechanics, 22: 215-21
  12. Dimentberg, F. M., 1950, The Determination of the Positions of Spatial Mechanism, Akad Nauk., Moscow, USSR, p. 142
  13. Dimentberg, F. M., 1965, The Screw Calculus and its Applications in Mechanics, USSR: Izd Nauka. Moscow, (English Trans. 1968, Foreign Tech. Div. WP-AFB, Ohio)
  14. Duffy, J., 1971, An Analysis of Five, Six and Seven-Link Spatial Mechanisms, Proceedings of the Third World Congress for the Theory of Machines and Mechanisms (Kupari, Yugoslavia), Vol. C, pp. 83-98
  15. Harrisberger, L., 1970, A Number Synthesis Survey of Three-Dimensional Mechanisms, ASME Journal of Applied Mechanics, Vol. 37, pp.713-718
  16. Hanafusa, H., Yoshikawa, T. and Nakamura, Y., 1981, Analysis and Control of Articulated Robot Robot Arms with Redundancy, Rprints IFAC 8th Triennial World Congress (Kyoto, Japan), Vol. 14, Aug., pp.79-83
  17. Hirose, S. and Ma, S., 1989, Redundancy Decomposition Control for Multi-Joint Manipulatiors, In Proc. 1989 IEEE Int. Conf. on Robotics Automation, pp. 119-124 https://doi.org/10.1109/ROBOT.1989.99977
  18. Hollerbach, J. M. and Suh, K. C., 1987, Redundancy Resolution fo Manipulator Through Torque Optimization, IEEE Trans. On Robotics and Automation, Vol. 2, No.4, pp. 308-316
  19. Hsu, P., Hauser, J. and Sastry, S., 1989, Dynamic Control of Redundant Manipulators, Journal of Robotic Systems, Vol.6, No.2, pp.133-148
  20. Huang, T. C. and Youm, Y., 1984, Exact Displacement Analysis of Four-Link Mechanisms by the Direction Cosine Matrix Method, J. of Applied Mechanics, Vol. 51, pp. 921-928
  21. Hunt, K. H., 1967, Screw Axes and Mobility in Spatial Mechanisms via the Linear Complex, Mechanisms, Vol. 3, pp.307-327 https://doi.org/10.1016/0022-2569(67)90005-5
  22. Kazerounian, K. and Nedungadi, A., 1987, Redundancy Resolution of Robotic Manipulators at the Acceleration Level, Proc. 7th IFToMM World Conf. Theory of Machines and Mechanism (Seveilla, Spain), Sept., pp. 1207-1211
  23. Khatib, O., 1983, Dynamic Control of Manipulators in Operationsl Space, Proc., 6th IFtoMM World Conf. Theory of Macnines and Mechanisms (New Delhi, India), Dec., pp. 15-20
  24. Khatib, O., 1986, 'Real Time Obstacle Avoidance for Manipulators and Mobile Robots,' International Journal of Robotics Research, Vol. 5, No. 1, pp. 90-96 https://doi.org/10.1177/027836498600500106
  25. Khatib, O., 1987, A Unified Approach for Motion and Force Control of Robot Manipulators: The Operationsal Space Formulation, IEEE Trans. Robotics and Automaition, Vol. RA-3, No.1, pp.43-53
  26. Klein, C. A. and Chirco, A. I., 1987, Dynamic Simulations of a Kinematically Redundant Manipulator System, Journal of Robotic Systems, Vol. 4, No. 1, pp.5-23 https://doi.org/10.1002/rob.4620040103
  27. Klein, C. A. and Huang, C. -H., 1983, Review of Pseudoinverse Control for use with Kinematically Redundant Manipulators, IEEE Trans. Systems, Man, and Cybernetics, Vol. SMC-13, No.2, pp.245-250
  28. Lee, D. Y., Youm, Y. and Chung, W. K., 1996, Mobility Analysis of Spatial 4- and 5-Link Mechanisms of the RS Class, Mechanism and Machine Theory, Vol. 31, No.5, pp.673-690 https://doi.org/10.1016/0094-114X(95)00099-K
  29. Liegeois, A., 1977, Automatic Supervisory Control of Configuration and Behavior of Multibody Mechanisms, IEEE Trans. Systems, Man, and Cybernetics, Vol. SMC-17, No.2, pp. 868-871
  30. Luca, A. D., 1989, Zero Dynamics in Robotic Systems, In C. I. Byrnes and A. Kurzhansky, eds., Nonlinear Synthesis: Proc. Of an IIASA Workshop, pp. 68-87, Birkhauser
  31. Maciejewski, A. A. and Klein, C. A., 1985, Obstacle A voidance for Kinematic Redundant Manipulators in Dynamically Varying Environments, International Journal of Robotics Research, Vol. 4, No.3, pp.109-117 https://doi.org/10.1177/027836498500400308
  32. Maciejewski, A. A., 1991, Kinetic Limitations on the Use of Redundancy in Robotic Manipulators, IEEE Trans. Robotics and Automation, Vol. 7, No.2, pp.205-210
  33. McAulay, A., 1898, Octonions-A Development of Cliffords Bi-Quaternions, Cambridge Univ. Press
  34. Nakamura, Y., Hanafusa, H. and Yoshikawa, T., 1987, Task Priority based Redundancy Control of Robot Manipulators, Int. J. Robotics Res., Vol. 6, No.2, pp.3-15, 1987 https://doi.org/10.1177/027836498700600201
  35. Nakamura, Y. and Hanafusa, H., 1987, Optimal Redundancy Control of Robot Manipulators, Int. J. Robotics Res., Vol. 6, No. 1, pp. 32-42 https://doi.org/10.1177/027836498700600103
  36. Nedungadi, A. and Kazerounian, K., 1989, A Local Solution with Global Characteristics for the Joint Torque Optimization of a Redundant Manipulaotors, Journal of Robotics Systems, Vol. 6, No.5, pp. 631-654
  37. Nenchev, D. N., 1989, Redundancy Resolution Through Local Optimization: A review, Journal of Robotic Systems, Vol. 6, No.6, pp.769-798
  38. Oh, S. -Y., Orin, D. and Bach, M., 1984, An Inverse Kinematic Solutions for Kinematically Redundant Robot Manipulators, J. Robotic Systems, Vol. 1, No.3, pp. 235-249
  39. Oriolo, G., 1994, Stabilization of Self-Motions in Redundant Robots, In Proc. 1994 IEEE Int. Conf. on Robotics and Automation, pp. 704-709 https://doi.org/10.1109/ROBOT.1994.351404
  40. Park, J., 2004, Principle of Dynamical Balance for Multibody Systems, Journal of Multibody System Dynamics, Submitted https://doi.org/10.1007/s11044-005-1356-y
  41. Park, J., Chung, W. and Youm, Y., 1996, Weighted Decomposition of Kinematics and Dynamics of Kinematically Redundant Manipulators, In Proc. 1996 IEEE Int. Conf. Robotics and Automation, pp.480-486 https://doi.org/10.1109/ROBOT.1996.503822
  42. Reauleaux, F., 1963, The Kinematics of Machinery, (English Translated Version by Alexander B. W. Kennedy), Dover Publication, INC. N.Y
  43. Seraji, H., 1989, Configuration Control of Redundant Manipulators: Theory and Implementation, IEEE Trans. Robotics and Automation, Vol. 5, No.4, pp.472-490 https://doi.org/10.1109/70.88062
  44. Shamir, T. and Yomdin, Y., 1988, Repeatability of Redundant Manipulators: Mathematical Solution of the Problem, IEEE Trans. Automatic Control, Vol. 33, No. 11, pp. 1004-1009 https://doi.org/10.1109/9.14412
  45. Sheth, P. N. and Dicker, J. J. Jr., 1971, A Generalized Symbolic Notation for Mechnisms, Trans. ASME, Series B, Vol. 93, No. 1, pp. 102-112
  46. Soni, A. H. and Pamidi, P. R., 1971, Closed Form Displacement Relationship of a Five-Link R-R-C-C-R Spatial Mechanisms, Trans. ASME, Series B, Vol. 93, No. 1, pp. 221-226
  47. Suh, C. H., 1968, Design of Space Mechanisms for Rigid Body Guidance, Trans, ASME, J. Engineering for Industry, Vol. 90, No.3, pp. 499-507
  48. Suh, K. C. and Hollerbach, J. M., 1987, Local versus Global Torque Optimization of Redundant Manipulators, Proc. IEEE Int. Conf. Robotics and Automation (Raleigh, NC), April, pp.619-624
  49. Uicker, J. J., Jr., Denavit. J. and Hartenberg, R. S., 1964, An Iterative Method for the Displacement Analysis of Spatial Mechanisms, J. of Applied Mechanics, Vol. 31, pp. 309-314
  50. Uicker, J. J. Jr., 1967, Dynamic Behavior of Spatial Linkages, Trans. ASME, Series, Vol. 89, No.2, pp. 418-428
  51. Usher, Avvott Payson, 1954, A History of Mechanical Inversions, Harvard University Press, Cambridge
  52. Vukobratovic, M. and Kircanski, M., 1984, A Dymanic Approach to Norminal Trajectory Systhesis for Redundant Manipulators, IEEE Trans. Systems, Man, and Cybernetics, Vol. SMC-14, No.4, pp. 580-586
  53. Waldron, K. J., 1966, Application of the Theory of Screw Axes to Linkages which Disobey the Kutzbach-Grubler Constraint Criterion, ASME paper, No. 66-MECH-36
  54. Wallace. D. M. and Freudenstein, F. F., 1970, The Displacement Analysis of the Generalized Tracta Coupling, ASME Journal of Applied Mechanics, Vol. 37, pp. 713-718
  55. Wampler II, C. W., 1987, Inverse Kinematic Functions for Redundant Manipulators, Proc. Int. Conf. Robotics and Automation (Raleigh, NC), April, pp. 610-617
  56. Whitney, D. E., 1972, The Mathematics of Coordinated Control fo Prosthetic Arms and Manipulators, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 94, No.4, pp.303-309
  57. Yang, A. T and Fredenstein F., 1964, Application of Dual Number Quarternion Algebra to the Analysis of Spatial Mechanisms, J. of Applied Mechanics, Vol. 31, pp. 300-308
  58. Yoshikawa, T., 1984, Analysis and Control of Robot Manipulators with Redundancy, Proc. The First Int. Symp. On Robotics Research, pp.745-748
  59. Youm, Y. and Huang, T. C., 1982, Displacement Analysis of Spatial Mechanisms by the Direction Cosine Matrix Method with Application to RRXX Group, ASME paper 82-DET-42
  60. Youm, Y. and Huang, T. C., 1987, Displacement Analysis of 4RIG Five-Link Spatial Mechanisms Using Exact Solutions of Four-Link Spatial Mechanisms, Mechanism and Machine Theory, Vol. 22, pp. 189-197 https://doi.org/10.1016/0094-114X(87)90001-2
  61. Yuan. M. S. S., 1970, Displacement Analysis of the RRCCR Five-Link Spatial Mechanism, ASME Journal of Applied Mechanics, Vol. 37, pp. 689-696