Skip to main content

Special Cases of Schönflies-Singular Planar Stewart Gough Platforms

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

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

Abstract

Parallel manipulators which are singular with respect to the Sch¨onflies motion group X(a) are called Schönflies-singular, or more precisely X(a)-singular, where a denotes the rotary axis. A special class of such manipulators are architecturally singular ones because they are singular with respect to any Schönflies group. Another remarkable set of Schönflies-singular planar Stewart Gough platforms was already presented by the author in [5]. Moreover the main theorem on these manipulators was given in [6]. In this paper we give a complete discussion of the remaining special cases which also include so-called Cartesian-singular planar manipulators as byproduct.

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. Karger, A., Singularities and self-motions of equiform platforms, Mechanism and Machine Theory, 36(7):801–815, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  2. Karger, A., Architecture singular planar parallel manipulators, Mechanism and Machine Theory, 38(11):1149–1164, 2003.

    Article  MATH  Google Scholar 

  3. Karger, A., Parallel manipulators with simple geometrical structure. In Proc. 2nd European Conference on Mechanism Science, M. Ceccarelli (Ed.), pp. 463–470, Springer, 2008.

    Google Scholar 

  4. Mick, S. and Röschel, O., Geometry & architecturally shaky platforms. In Advances in Robot Kinematics: Analysis and Control, J. Lenarcic and M.L. Husty (Eds.), pp. 455–464, Kluwer, 1998.

    Google Scholar 

  5. Nawratil, G., A remarkable set of Schönflies-singular planar Stewart Gough platforms, Technical Report No. 198, Geometry Preprint Series, Vienna University of Technology, 2009.

    Google Scholar 

  6. Nawratil, G., Main theorem on Schönflies-singular planar Stewart Gough platforms. In Advances in Robot Kinematics, J. Lenarcic and M.M. Stanisic (Eds.), Springer, 2010.

    Google Scholar 

  7. Nawratil, G., Special cases of Schönflies-singular planar Stewart Gough platforms, Technical Report No. 202, Geometry Preprint Series, Vienna University of Technology, 2009.

    Google Scholar 

  8. Röschel, O. and Mick, S., Characterisation of architecturally shaky platforms. In Advances in Robot Kinematics: Analysis and Control, J. Lenarcic, M. Husty (Eds.), pp. 465–474, Kluwer, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Nawratil .

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

Nawratil, G. (2010). Special Cases of Schönflies-Singular Planar Stewart Gough Platforms. 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_6

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9689-0_6

  • 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