Skip to main content

A Redundant Spatial Stewart-Gough Platform with a Maximal Forward Kinematics Solution Set

  • Chapter

Abstract

This paper discusses the possibility of designing a redundant spatial parallel manipulator with a maximal forward kinematics solution set. We show that when the anchor points for the joints of the platform and base are planar, in almost every case an infinite number of legs may be added without changing the kinematics of the mechanism. The possible anchor points lie on a cubic which may be split into a line and a conic.

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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

  • Borel, E. (1908). Mémoire sur les déplacements à trajectoires sphériques. In Mém. Acad. Sci,pages 1–128, Paris.

    Google Scholar 

  • Bricard, M. R. (1906). Mémoire sur les déplacements à trajectoires sphériques. In Journ. École Polyt, pages 1–96, Paris.

    Google Scholar 

  • Cox, D., Little, J., and O’Shea, D., editors (1992). Ideals, Varieties, and Algorithms. Springer Verlag, Berlin, Heidelberg, New York.

    Google Scholar 

  • Husty, M. L. and Karger, A. (2000). Self-Motions of Griffis-Duffy Type Platforms. In Proc. of IEEE conference on Robotics and Automation (ICRA 2000), pages 7–12, San Francisco, USA.

    Google Scholar 

  • Husty, M. L., Mielczarek, S., and Hiller, M. (2001). Constructing an Overconstrained Planar 4RPR Manipulator with Maximal Forward Kinematics Solution Set. In Proc. of the RAAD’01 Robotics in the Alpe-Adria-Danube Region,Vienna, Austria.

    Google Scholar 

  • Husty, M. L. (1996). An algorithm for solving the direct kinematic of Stewart-Goughtype platforms. Mechanism and Machine Theory, 31 (4): 365–380.

    Article  Google Scholar 

  • Karger, A. and Husty, M. L. (1997). Singularities and Self-motions of a Stewart-Gough Platforms. In Angeles, J. and Zakhariev, E., editors, Proc. NATO-A SI Computational methods in Kinematics, pages 279–288, Varna, Bulgaria. NATO.

    Google Scholar 

  • Ming, A. and Higuchi, T. (1994). Study on multiple degree-of-freedom positioning mechanism using wires (part 1) — concept, design and control. Int. Journal of the Jap. Soc. for Precision Engineering, 28 (2): 131–138.

    Google Scholar 

  • Study, E. (1903). Geometrie der Dynamen

    Google Scholar 

  • Wampler, C. W. (1996). Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using soma coordinates Mechanism and Machine Theory, 31 (3): 331–337.

    Article  Google Scholar 

  • Weiss, E. A. (1935). Einführung in die Liniengeometrie und Kinematik. Teubner Verlag, Leipzig, Berlin, Germany.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Husty, M., Mielczarek, S., Hiller, M. (2002). A Redundant Spatial Stewart-Gough Platform with a Maximal Forward Kinematics Solution Set. In: Lenarčič, J., Thomas, F. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0657-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0657-5_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6054-9

  • Online ISBN: 978-94-017-0657-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics