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Some Remarks on the RRR Linkage

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Advances in Robot Kinematics

Abstract

The variety of rigid-body displacements of the final link of a 3\(R\) kinematic chain are investigated. In most cases the variety generated is a Segre manifold; the Cartesian product of three projective lines. The homology of this variety as a subvariety of the Study quadric is found and simple applications to some enumerative problems in kinematics are given. The conditions for the variety to fail to be a Segre variety are investigated in full and the case where the linkage forms the first three joints of a Bennett mechanism is examined.

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Notes

  1. 1.

    This results is due to Josef Schicho.

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Authors and Affiliations

  1. London South Bank University, London, SE1 0AA, UK

    J. M. Selig

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  1. J. M. Selig
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Correspondence to J. M. Selig .

Editor information

Editors and Affiliations

  1. J. Stefan Institute, Ljubljana-Vic-Rudnik, Slovenia

    Jadran Lenarčič

  2. Department of Computer Science Artificial Intelligence Laboratory, Stanford University, Stanford, California, USA

    Oussama Khatib

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Selig, J. (2014). Some Remarks on the RRR Linkage. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-06698-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06697-4

  • Online ISBN: 978-3-319-06698-1

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