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TECHNICAL PAPERS

A Differential-Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators

[+] Author and Article Information
Ashitava Ghosal

Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012e-mail: asitava@mecheng.iisc.ernet.in

Bahram Ravani

Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616e-mail: bravani@ucdavis.edu

J. Mech. Des 123(1), 80-89 (Jul 01, 1998) (10 pages) doi:10.1115/1.1325008 History: Received July 01, 1998
Copyright © 2001 by ASME
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References

Wang,  S. L., and Waldron,  K. J., 1987, “A Study of the Singular Configurations of Serial Manipulators,” ASME J. Mech., Transm., Autom. Des., 109, pp. 14–20.
Litvin,  F. L., Zhang,  Y., Castelli,  V. P., and Innocenti,  C., 1990, “Singularities, Configurations and Displacement Functions for Manipulators,” Int. J. Robot. Res., 5, pp. 52–65.
Hunt,  K. H., 1986, “Special Configurations of Robot Arms via Screw Theory, Part 1. The Jacobian and its Matrix Cofactors,” Robotica, 4, pp. 171–179.
Martinez, J. M. R., Alvarado, J. G., and Duffy, J. A., 1994, “A Determination of Singular Configurations of Serial Non-Redundant Manipulators and Their Escapement From Singularities Using Lie Products,” in Proc. of the Conference on Computational Kinematics.
Lipkin,  H., and Pohl,  E., 1991, “Enumeration of Singular Configurations for Robotic Manipulators,” ASME J. Mech. Des., 113, pp. 272–279.
Karger,  A., 1995, “Classification of Robot-Manipulators With Only Singularity Configurations,” Mech. Mach. Theory, 30, pp. 727–736.
Karger,  A., 1996, “Classification of Robot-Manipulators With Nonremovable Singularities,” ASME J. Mech. Des., 118, pp. 202–208.
Sugimoto,  K., Duffy,  J., and Hunt,  K. H., 1982, “Special Configurations of Spatial Mechanisms and Robot Arms,” Mech. Mach. Theory, 1982, pp. 119–132.
Gosselin,  C., and Angeles,  J., 1990, “Singularity Analysis of Closed Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6, pp. 281–290.
Litvin,  F. L., Fanghella,  P., Tan,  J., and Zhang,  Y., 1986, “Singularities in Motion and Displacement Functions of Spatial Linkages,” ASME J. Mech. Trans. Auto. Des., 108, pp. 516–523.
Merlet,  J. P., 1991, “Singularity Configurations of Parallel Manipulators and Grassman Geometry,” Int. J. Robot. Res., 10, pp. 123–134.
Stanisic,  M. M., and Duta,  O., 1990, “Symmetrically Actuated Double Pointing Systems–the Basis of Singularity Free Wrists,” IEEE Trans. Rob. Autom., 6, pp. 562–569.
Tchnon,  K., and Matuszok,  A., 1995, “On Avoiding Singularity in Redundant Robot Kinematics,” Robotica, 13, pp. 599–606.
Shamir,  T., 1990, “The Singularities of Redundant Robot Arms,” Int. J. Robot. Res., 9, pp. 113–121.
Karger,  A., 1996, “Singularity Analysis of Serial-Robot Manipulators,” ASME J. Mech. Des., 118, pp. 520–525.
Chevallereau,  C., 1998, “Feasible Trajectories in Task Space From a Singularity for a Non-Redundant or Redundant Robot Manipulator,” Int. J. Robot. Res., 17, pp. 56–69.
Lloyd, J. E., 1996, “Using Puiseux Series to Control Non-Redundant Robots at Singularities,” in Proc. of IEEE Conf. on Robotics and Automation, pp. 1877–1882.
Nenchev, D. N., Tsumaki, Y., Uchiyama, M., Senft, V., and Hirzinger, G., 1996, Two Approaches to Singularity Consistent Motion of Non-Redundant Robotic Mechanisms, in Proc. of IEEE Conf. on Robotics and Automation, pp. 1883–1890.
Nenchev, D. N., and Uchiyama, M., 1996, “Singularity Consistent Path Planning and Control of Parallel Robot Motion Through Instantaneous-Self-Motion Type Singularities,” in Proc. of IEEE Conf. on Robotics and Automation, pp. 1864–1870.
Sardis, R., Ravani, B., and Bodduluri, R. M. C., 1992, “A Kinematic Design Criterion for Singularity Avoidance in Redundant Manipulators,” in Proc. of 3rd ARK Conference, pp. 257–261.
Golubitsky, M., and Guillemin, V., 1973, Stable Mappings and Their Singularities, Springer-Verlag.
Kieffer,  J., 1992, “Manipulator Inverse Kinematics for Untimed End-Effector Trajectories With Singularities,” Int. J. Robot. Res., 11, pp. 225–237.
Kieffer,  J., 1994, “Differential Analysis of Bifurcations and Isolated Singularities for Robots and Mechanisms,” IEEE Trans. Rob. Autom., 10, pp. 1–10.
Tchnon,  K., and Muszynski,  R., 1997, “Singularities of Non-Redundant Robot Kinematics,” Int. J. Robot. Res., 16, pp. 60–76.
Ghosal,  A., and Roth,  B., 1987, “Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Point Trajectories,” ASME J. Mech., Transm., Autom. Des., 109, pp. 107–115.
Millman, R. S., and Parker, G. D., 1977, Elements of Differential Geometry, Prentice-Hall, NJ.
Strubecker, K., 1969, Differentialgeometrie, Vol II, Theorie der Flächenmetrik, Walter de Gruyter, Berlin.
Yoshikawa, T., 1985, “Manipulability of Robotic Mechanisms,” in Robotics Research: The Second International Symposium, pp. 206–214.
Nakamura, Y., 1991, Advanced Robotics: Redundancy and Optimization. Addison-Wesley, Reading, MA.
Golub, G. H., and Loan, C. F. V., 1989, Matrix Computations, Johns Hopkins.
Karger,  A., 1989, “Curvature Properties of 6-Parametric Robot Manipulators,” Manuscr. Math., 65, pp. 311–328.
Bedrossain, N. S., 1990, “Classification of Singular Configuration for Redundant Manipulators,” in Proc. of IEEE Conf. on Robotics and Automation, pp. 818–823.
Lee,  K. M., and Shah,  D., 1988, “Kinematic Analysis of a Three-Degrees-of-Freedom in-Parallel Actuated Manipulator,” IEEE Trans. Rob. Autom., 4, pp. 354–360.

Figures

Grahic Jump Location
A schematic of a general 2R manipulator
Grahic Jump Location
Velocity ellipse at a non-singular point (θ12)=(0,0)°
Grahic Jump Location
Degenerate velocity “ellipse” at a singular point
Grahic Jump Location
The RPSSPR-SPR parallel manipulator
Grahic Jump Location
Velocity ellipsoid at a non-singular point
Grahic Jump Location
Velocity ellipse at a singular point
Grahic Jump Location
Velocity at a singular point
Grahic Jump Location
Velocity ellipse at a singular point

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