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arXiv: 1107.4498

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IEEE/RSJ International Conference on Intelligent Robots and Systems, San Franisco : United States (2011)

Singular surfaces and cusps in symmetric planar 3-RPR manipulators

Michel Coste 1, Philippe Wenger 2, Damien Chablat (  Corresponding author ) 2

(2011-09-25)

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the cusp edges. These latter second order singularities are important for nonsingular assembly mode changing. We show how to sort assembly modes and use this sorting for motion planning in the joint space.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
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

Research team: Géométrie algébrique réelle

Subject

:

Computer Science/Robotics

Keyword(s): Parallel robot – singularity – nonsingular assembly mode changing

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From: Damien Chablat <>

Submitted on: Thursday, 21 July 2011 15:31:43

Updated on: Tuesday, 5 March 2013 17:40:24