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Self-Motions of Planar Projective Stewart Gough Platforms

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Latest Advances in Robot Kinematics

Abstract

In this paper, we study self-motions of non-architecturally singular parallel manipulators of Stewart Gough type, where the planar platform and the planar base are related by a projectivity. By using mainly geometric arguments, we show that these manipulators have either so-called elliptic self-motions or pure translational self-motions. In the latter case, the projectivity has to be an affinity a+Ax, where the singular values s 1 and s 2 of the 2×2 transformation matrix A with 0<s 1≤s 2 fulfill the condition s 1≤1≤s 2.

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Notes

  1. 1.

    If κ is singular, one set of anchor points would collapse into a line or a point, which yields trivial cases of architecturally singular manipulators.

  2. 2.

    Neither all platform anchor points nor all base anchor points collapse into one point.

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Acknowledgements

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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Authors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria

    G. Nawratil

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  1. G. Nawratil
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Correspondence to G. Nawratil .

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Editors and Affiliations

  1. J. Stefan Institute, Jamova 39, Ljubljana-Vic-Rudnik, 1000, Slovenia

    Jadran Lenarcic

  2. Inst. Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstr. 13, Innsbruck, 6020, Austria

    Manfred Husty

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Nawratil, G. (2012). Self-Motions of Planar Projective Stewart Gough Platforms. In: Lenarcic, J., Husty, M. (eds) Latest Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4620-6_4

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  • DOI: https://doi.org/10.1007/978-94-007-4620-6_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4619-0

  • Online ISBN: 978-94-007-4620-6

  • eBook Packages: EngineeringEngineering (R0)

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