Singularity Analysis of a Six-dof Parallel Manipulator using Grassmann-Cayley Algebra and Gröbner Bases

Stéphane Caro (1, 2, 3) , Guillaume Moroz (4) , Thibault Gayral (4) , Damien Chablat (4) , Chao Chen (5)

1 LS2N - équipe RoMas - Robots and Machines for Manufacturing, Society and Services
2 CNRS - Centre National de la Recherche Scientifique
3 LS2N - Laboratoire des Sciences du Numérique de Nantes
4 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
5 Monash University [Malaysia]

The subject of this paper deals with the singularity analysis of a six-dof three-legged parallel manipulator for force-feedback interface. To this end, a geometric condition for the manipulator singularities is obtained by means of Grassmann-Cayley algebra; the parallel singularities of the manipulator are computed using Jacobian and Gröbner basis. As a result, the algebraic relations of the singularities satisfied by the orientation variables are reported. Finally, the parallel singularities of the manipulator are plotted in its orientation workspace.

Mots clés: Parallel Manipulators; Grassmann-Cayley Algebra; Gröbner Bases; Singularity Analysis

Domaines: Electronique

Stéphane Caro, Guillaume Moroz, Thibault Gayral, Damien Chablat, Chao Chen. Singularity Analysis of a Six-dof Parallel Manipulator using Grassmann-Cayley Algebra and Gröbner Bases. Angeles J., Boulet B., Clark J.J., Kövecses J., Siddiqi K. Brain, Body and Machine. Advances in Intelligent and Soft Computing, 83, pp.341-352, 2010, 978-3-642-16258-9. ⟨10.1007/978-3-642-16259-6_26⟩. ⟨hal-00545747⟩