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Trajectory Singularities for a Class of Parallel Motions

  • Matthew W. Cocke
  • Peter Donelan
  • Christopher G. Gibson
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

A rigid body, three of whose points are constrained to move on the coordinate planes, has three degrees of freedom. Bottema and Roth [2] showed that there is a point whose trajectory is a solid tetrahedron, the vertices representing corank 3 singularities. A theorem of Gibson and Hobbs [9] implies that, for general 3-parameter motions, such singularities cannot occur generically. However motions subject to this kind of constraint arise as interesting examples of parallel motions in robotics and we show that, within this class, such singularities can occur stably.

Keywords

Screw system trajectory singularity parallel motion 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Matthew W. Cocke
    • 1
  • Peter Donelan
    • 2
  • Christopher G. Gibson
    • 1
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  2. 2.School of Mathematics, Statistics and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand

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