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Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators

Abstract : This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gröbner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators.
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Contributor : Damien Chablat <>
Submitted on : Wednesday, April 25, 2012 - 8:19:02 AM
Last modification on : Thursday, February 7, 2019 - 3:45:29 PM
Document(s) archivé(s) le : Thursday, July 26, 2012 - 2:21:27 AM


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  • HAL Id : hal-00690975, version 1
  • ARXIV : 1204.5580


Montserrat Manubens, Guillaume Moroz, Damien Chablat, Philippe Wenger, Fabrice Rouillier. Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators. Journal of Mechanisms and Robotics, American Society of Mechanical Engineers, 2012, pp.1-10. ⟨hal-00690975⟩



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