Skip to main content

Methods for Resolving Velocity Degeneracies of Joint-Redundant Manipulators

  • Chapter

Abstract

Two methods for finding velocity-degenerate (singular) configurations of joint-redundant manipulators are presented. The first method is based on reciprocity of screws. The second method is based on concurrency of zero 6×6 sub-matrix determinants of the Jacobian J. For spatial manipulators with more than seven joints, it is concluded that the reciprocity-based method is more appropriate. An example is presented to demonstrate both methods.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Burdick, J. W. (1995). A Recursive Method for Finding Revolute-Jointed Manipulator Singularities. Trans. ASME, J. Mech. Des., Vol. 117, March, pp. 55–63

    Article  Google Scholar 

  • Denavit, J., Hartenberh, R.S. (1995). A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices. Trans. ASME, J. App. Mech., June, pp. 215–221.

    Google Scholar 

  • Gorla, B. (1981). Influence of the Control on the Structure of a Manipulator From a Kinematic Point of View. Proc. 4th Sym. Theory and Practise of Robots and Manipulators, Zaborow, Poland, pp. 30–46.

    Google Scholar 

  • Hollerbach, J. M. (1985). Optimum Kinematic Design of a Seven Degree of Freedom Manipulator. Proc. 2nd Int. Sym.. on Rob. Res., pp. 215–222.

    Google Scholar 

  • Hunt, K. H. (1978). Kinematic Geometry of Mechanisms, Oxford University Press: Toronto.

    MATH  Google Scholar 

  • Hunt, K. H. (1987). Special Configurations of Robot-Arms Via Screw Theory, Part 2: Available End-Effector Displacements. Robotica, Vol. 5, pp. 17–22.

    Article  Google Scholar 

  • Litvin, F.L., et al. (1985). Configurations of Robot’s Manipulators and Their Identification, and the Execution of Prescribed Trajectories. Part 2: Investigations of Manipulators Having Five, Seven, and Eight Degrees of Freedom. Trans. ASME, J. Mech., Trans., and Auto. In Des., Vol. 107, June, pp. 179–188.

    Article  Google Scholar 

  • Nokleby, S. B., Podhorodeski, R. P. (1999). Reciprocity-Based Resolution of Velocity Degeneracies for the Canadian Space Agency/International Submarine Engineering STEAR Testbed Manipulator (STM). Submitted to Int. J. Rob. Res.

    Google Scholar 

  • Podhorodeski, R. P., Goldenberg, A. A., Fenton, R. G. (1991). Resolving Redundant Manipulator joint Rates and Identifying Special Arm Configurations Using Jacobian Null-Space Bases. IEEE Trans. Rob. and Auto., Vol. 7, No. 5, pp. 607–618.

    Article  Google Scholar 

  • Podhorodeski, R. P., Nokleby, S. B., Wittchen, J. D. (1999). Resolving Velocity-Degenerate Configurations (Singularities) of Redundant Manipulators. Submitted to Trans. ASME, J. Mech. Des.

    Google Scholar 

  • Sugimoto, K., Duffy, J., Hunt, K. H. (1982). Special Configurations of Spatial Mechanisms and Robot Arms. Mech. and Mach. Theory, Vol. 17, No. 2, pp. 119–132.

    Article  Google Scholar 

  • Waldron, K. H., Wang, S.-L., Bolin, S.J. (1985). A Study of the Jacobian Maxtrix of Serial Manipulators. Trans. ASME, J. Mech., Trans., and Anto. In Des., Vol. 107, June, pp. 230–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Nokleby, S.B., Podhorodeski, R.P. (2000). Methods for Resolving Velocity Degeneracies of Joint-Redundant Manipulators. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4120-8_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5803-2

  • Online ISBN: 978-94-011-4120-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics