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Kinematics of Expansive Planar Periodic Mechanisms

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Advances in Robot Kinematics

Abstract

A flexible bar-and-joint framework is said to be moving expansively if the distance between any two of its joints either increases or stays the same. Expansive motions of finite 2D frameworks have been fully characterized. Here, we investigate their periodic counterparts. The key to their understanding is a family of one-degree-of-freedom mechanisms called periodic pointed pseudo-triangulations. Expansive infinitesimal motions for mechanisms with several degrees of freedom form a polyhedral cone whose extremal rays are obtained from different completions of the framework to pseudo-triangulations. We illustrate its structure on a framework associated to a stellated tiling of the plane.

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Acknowledgments

The authors are partially supported by National Science Foundation grant CCF-1319366. This research was conducted while visiting Technische Universität München, with funding for the second author from the DFG-Collaborative Research Center TRR109, Discretization in Geometry and Dynamics.

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Authors and Affiliations

  1. Department of Mathematics, Rider University, Lawrenceville, NJ, 08648, USA

    Ciprian S. Borcea

  2. Department of Computer Science, Smith College, Northampton, MA, 01083, USA

    Ileana Streinu

Authors
  1. Ciprian S. Borcea
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  2. Ileana Streinu
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Correspondence to Ileana Streinu .

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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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Borcea, C.S., Streinu, I. (2014). Kinematics of Expansive Planar Periodic Mechanisms. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_41

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  • DOI: https://doi.org/10.1007/978-3-319-06698-1_41

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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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