On the determination of cusp points of 3-R\underline{P}R parallel manipulators

Guillaume Moroz; Fabrice Rouillier; Damien Chablat; Philippe Wenger

hal-00545502, version 1

On the determination of cusp points of 3-R\underline{P}R parallel manipulators

Guillaume Moroz () ^1, 2, Fabrice Rouillier () ^3, 4, Damien Chablat () ², Philippe Wenger () ²

Mechanism and Machine Theory 45, 11 (2010) 1555-1567

Résumé : This paper investigates the cuspidal configurations of 3-RPR parallel manipulators that may appear on their singular surfaces in the joint space. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a non-singular change of assembly mode. In previous works, the cusp points were calculated in sections of the joint space by solving a 24th-degree polynomial without any proof that this polynomial was the only one that gives all solutions. The purpose of this study is to propose a rigorous methodology to determine the cusp points of 3-R\underline{P}R manipulators and to certify that all cusp points are found. This methodology uses the notion of discriminant varieties and resorts to Gröbner bases for the solutions of systems of equations.

1 : VEGAS (INRIA Lorraine - LORIA)
INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2 : Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN)
CNRS : UMR6597 – PRES Université Nantes Angers Le Mans [UNAM] – École Centrale de Nantes – École Nationale Supérieure des Mines - Nantes – Ecole Polytechnique de l'Université de Nantes
3 : SALSA (INRIA Rocquencourt)
INRIA – CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI
4 : Laboratoire d'Informatique de Paris 6 (LIP6)
CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI

hal-00545502, version 1
http://hal.archives-ouvertes.fr/hal-00545502
oai:hal.archives-ouvertes.fr:hal-00545502
Contributeur : Damien Chablat <>
Soumis le : Vendredi 10 Décembre 2010, 14:03:38
Dernière modification le : Mercredi 13 Avril 2011, 16:29:28

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arXiv : 1012.2668

DOI : 10.1016/j.mechmachtheory.2010.06.016

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