Singularities of parallel manipulators: A geometric treatment

IEEE Transactions on Robotics and Automation

Volumn 19, Issue 4, 2003, Pages 579-594

  Liu, Guanfeng ^a   Lou, Yunjiang ^a   Li, Zexiang ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Degenerate; Differential form; Morse function; Singularity; Topological order

Indexed keywords

ACTUATORS; DEGREES OF FREEDOM (MECHANICS); END EFFECTORS; GEOMETRY; KINEMATICS; MOTION PLANNING; NUMERICAL METHODS; TOPOLOGY; UNIVERSAL JOINTS;

DEGENERATE; DIFFERENTIAL FORM; MORSE FUNCTION; PARALLEL MANIPULATORS; SINGULARITIES; TOPOLOGICAL ORDER;

MANIPULATORS;

EID: 0042382766     PISSN: 1042296X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRA.2003.814507     Document Type: Article

References (43)

1. C. Gosselin and J. Angeles, "Singularity analysis of closed-loop kinematic chains," IEEE Trans. Robot. Automat., vol. 6, pp. 281-290, June 1990.
2. F. C. Park and J. W. Kim, "Singularity analysis of closed kinematic chains," Trans. ASME J. Mech. Des., vol. 121, no. 1, pp. 32-38, 1999.
3. S. J. Ryu, J. Kim, J. C. Hwang, C. B. Park, H. S. Cho, K. Lee, Y. H. Lee, U. Cornel, F. C. Park, and J. W. Kim, "Eclipse: an overactuated parallel mechanism for rapid machining," ASME Manuf. Sci. Eng., vol. 8, pp. 681-689, 1998.
4. J. W. Kim, J. C. Hwang, J. S. Kim, and F. C. Park, "Eclipse-II: a new parallel mechanism enabling continuous 360-degree spinning plus three-axis translational motions," in Proc. IEEE Int. Conf. Robotics and Automation, 2001, pp. 3274-3279.
5. S. Kock and W. Schumacher, "A mixed elastic and rigid-body dynamic model of an actuation redundant parallel robot with high-reduction gears," in Proc. IEEE Int. Conf. Robotics and Automation, 2000, pp. 1918-1923.
6. ____, "A parallel x-y manipulator with actuation redundancy for high-speed and active-stiffness applications," in Proc. IEEE Int. Conf. Robotics and Automation, 1998, pp. 2295-2300.
7. M. Nahon and J. Angeles, "Reducing the effects of shocks using redundant actuation," in Proc. IEEE Int. Conf. Robotics and Automation, 1991, pp. 238-243.
8. J. T. Wen and L. S. Wilfinger, "Kinematic manipulability of general constrained rigid multibody systems," IEEE Trans. Robot. Automat., vol. 15, pp. 558-567, June 1999.
9. A. K. Ramadorai, T. J. Tarn, A. K. Bejczy, and N. Xi, "Task-driven control of multi-arm system," IEEE Trans. Control Syst. Technol., vol. 2, pp. 198-206, Sept. 1994.
10. V. Kumar and K. J. Waldron, "Force distribution in walking vehicles," IEEE J. Robot. Automat., vol. 4, pp. 657-664, Dec. 1988.
11. J.-P. Merlet, "Singular configurations of parallel manipulators and Grassmann geometry," Int. J. Robot. Res., vol. 8, no. 5, pp. 45-56, Oct. 1989.
12. K. H. Hunt, "Special configurations of robot-arm via screw theory (part 1)," Robotica, vol. 4, no. 3, pp. 171-179, 1986.
13. O. Ma and J. Angeles, "Architecture singularities of platform manipulators," in Proc. IEEE Int. Conf. Robotics and Automation, 1991, pp. 1542-1547.
14. V. Kumar and J. F. Gardner, "Kinematics of redundantly actuated closed chains," IEEE Trans. Robot. Automat., vol. 6, pp. 269-274, Apr. 1990.
15. I. Ebert-Uphoff, J. Lee, and H. Lipkin, "Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs," IMECH J. Mech. Eng., vol. 216, no. C1, pp. 81-93, 2002.
16. B. Dasgupta and T. Mruthyunjaya, "Force redundancy in parallel manipulators: theoretical and practical issues," Mech. Mach. Theory, vol. 33, no. 6, pp. 727-742, 1998.
17. L. Notash, "Uncertainty configurations of parallel manipulators," Mech. Mach. Theory, vol. 33, no. 1/2, pp. 123-138, 1998.
18. J. P. Merlet, Parallel Robots. Norwell, MA: Kluwer, 2000.
19. C. Innocenti and V. Parenti-Castelli, "Singularity-free evolution from one configuration to another in serial fully-parallel manipulators," ASME J. Mech. Des., vol. 120, no. 1, pp. 73-79, Mar. 1998.
20. ____, "Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators," in Proc. 22nd Biennial Mechanisms Conf., 1992, pp. 553-560.
21. J. W. Burdick, "On the inverse kinematics of redundant manipulators: characterization of the self-motion manifolds," in Proc. IEEE Int. Conf. Robotics and Automation, 1989, pp. 264-270.
22. N. S. Bedrossian, "Classification of singular configurations for redundant manipulators," in Proc. IEEE Int. Conf. Robotics and Automation, 1990, pp. 818-823.
23. J. Kieffer, "Differential analysis of bifurcations and isolated singularities for robots and mechanisms," IEEE Trans. Robot. Automat., vol. 10, pp. 1-10, Feb. 1994.
24. L. W. Tsai, "Kinematics of a three-DOF platform with three extensible limbs," in Recent Advances in Robot Kinematics: Analysis and Control, J. Lenaric and M. L. Husty, Eds. Norwell, MA: Kluwer, 1996, pp. 49-58.
25. R. Di Gregorio and V. Parenti-Castelli, "A translational 3-DOF parallel manipulator," in Recent Advances in Robot Kinematics, J. Lenaric and V. Parenti-Castelli, Eds. Norwell, MA: Kluwer, 1998, pp. 401-410.
26. R. Di Gregorio, "Statics and singularity loci of the 3-UPU wrist," in Proc. IEEE/ASME Int. Conf. Advanced Intelligent Mechatronics, 2001, pp. 470-475.
27. R. Di Gregorio and V. Parenti-Castelli, "Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion," ASME J. Mech. Des., vol. 124, pp. 259-264, June 2002.
28. C. H. Han, J. W. Kim, J. W. Kim, and F. C. Park, "Kinematic sensitivity analysis of the 3-UPU parallel mechanism," Mech. Mach. Theory, 2002, to be published.
29. D. Zlatanov, I. A. Bonev, and C. M. Gosselin, "Constraint singularities of parallel mechanisms," in Proc. IEEE Int. Conf. Robotics and Automation, 2002, pp. 496-502.
30. S. A. Joshi and L. W. Tsai, "Jacobian analysis of limited-DOF parallel manipulators," ASME J. Mech. Des., vol. 124, no. 2, pp. 254-258, 2002.
31. N. Simaan and M. Shoham, "Singularity analysis of a class of composite serial in-parallel robots," IEEE Trans. Robot. Automat., vol. 17, pp. 301-311, June 2001.
32. A. Wolf, M. Shoham, and F. C. Park, "Investigation of singularities and self-motions of the 3-UPU robot," in Advances in Robot Kinematics, J. Lenaric and F. Thomas, Eds. Norwell, MA: Kluwer, 2002, pp. 165-174.
33. W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry. New York: Academic, 1975.
34. J. Milnor, Morse Theory. Princeton, NJ: Princeton Univ. Press, 1963.
35. K. H. Hunt, Kinematic Geometry of Mechanisms. Oxford, U. K.: Oxford Univ. Press, 1978.
36. R. Murray, Z. X. Li, and S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press, 1994.
37. H. Flanders, Differential Forms with Applications to Physical Science New York: Dover, 1989.
38. D. H. Sattinger and O. L. Weaver, Lie Groups and Lie Algebras with Applications to Physics, Geometry, and Mechanics New York: Springer-Verlag, 1986.
39. G. F. Liu and Z. X. Li, "General geometric algorithms for optical design of parallel manipulators," in Proc. 2-Day Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, 2002, pp. 106-111.
40. D. Zlatanov, B. Benhabib, and R. G. Fenton, "Singularity analysis of mechanism and robots via a velocity-equation model of the instantaneous kinematics," in Proc. IEEE Int. Conf. Robotics and Automation, 1994, pp. 986-991.
41. S. S. Chern, W. H. Chen, and K. S. Lam, Lectures on Differential Geometry, Singapore: World Scientific, 1999.
42. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps - Volumn I. Cambridge, MA: Birkhauser, 1985.
43. M. D. Do Carmo, Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976.