Skip to main content

Implementation of a New and Efficient Algorithm for the Inverse Kinematics of Serial 6R Chains

  • Conference paper
  • First Online:
New Trends in Mechanism Science

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 5))

Abstract

The aim of the reported project was to implement a new and efficient algorithm that yields simultaneously all solutions of the inverse kinematics of general 6R chains in a fast software prototype based on a C# code. The algorithm itself was developed in the working group of the authors and was previously only running in a computer algebra system. It is well known that the inverse kinematics problem of general 6R chains is highly nonlinear and yields in general 16 solutions. Using geometric preprocessing the new algorithm reduces the initial mathematical description to several linear and only two nonlinear equations. This paper recalls the algorithm, discusses the software and shows how this tool can be used in path planning and singularity detection along a path.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Denavit, J. and Hartenberg, R.S., A kinematic notation for lower-pair mechanisms based on matrices, Journal of Applied Mechanics, 77:215–221, 1955.

    MathSciNet  Google Scholar 

  2. Husty, M.L., Pfurner, M. and Schröcker, H.P., A new and efficient algorithm for the inverse kinematics of a general 6R, Mechanism and Machine Theory, 42(1):66–81, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  3. Husty, M.L., Pfurner, M., Schröcker, H.P. and Brunnthaler, K., Algebraic methods in mechanism analysis and synthesis, Robotica, 25:661–675, 2007.

    Article  Google Scholar 

  4. Lee, H.Y. and Liang, C.G., Displacement analysis of the general 7-link 7R mechanism. Mechanism and Machine Theory, 23(3), 209–217, 1988.

    Article  Google Scholar 

  5. Manocha, D. and Zhu, Y., A fast algorithm and system for the inverse kinematics of general serial manipulators. In Proceedings of IEEE Conference on Robotics and Automation, pp. 3348–3354, 1994.

    Google Scholar 

  6. Pfurner, M., Analysis of spatial serial manipulators using kinematic mapping. PhD Thesis, Innsbruck, 2006. Available at http://repository.uibk.ac.at/alo?ohjid=1015078

    Google Scholar 

  7. Rhagavan, M. and Roth, B., Kinematic analysis of the 6R manipulator of general geometry, In: Proceedings of the 5th Internat. Symposium on Robotics Research, Tokyo, pp. 263–269, 1990.

    Google Scholar 

  8. Study, E., Geometrie der Dynamen. B.G. Teubner, Leipzig, 1903.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Pfurner .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Pfurner, M., Husty, M.L. (2010). Implementation of a New and Efficient Algorithm for the Inverse Kinematics of Serial 6R Chains. In: Pisla, D., Ceccarelli, M., Husty, M., Corves, B. (eds) New Trends in Mechanism Science. Mechanisms and Machine Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9689-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9689-0_11

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9688-3

  • Online ISBN: 978-90-481-9689-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics