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Non-existence of Planar Projective Stewart Gough Platforms with Elliptic Self-Motions

  • Georg Nawratil
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)

Abstract

In this paper, we close the study on the self-motional behavior of non-architecturally singular parallel manipulators of Stewart Gough (SG) type, where the planar platform and the planar base are related by a projectivity \(\kappa \), by showing that planar projective SG platforms with elliptic self-motions do not exist. The proof of this result demonstrates the power of geometric and computational interaction, but it also points out the limits of symbolic computation.

Keywords

Self-motion Stewart Gough platform Borel Bricard problem 

Notes

Acknowledgments

This research is supported by Grant No. I 408-N13 of the Austrian Science Fund FWF within the project “Flexible polyhedra and frameworks in different spaces”, an international cooperation between FWF and RFBR, the Russian Foundation for Basic Research.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute of Discrete Mathematics and GeometryVienna University of TechnologyViennaAustria

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