Singularity Analysis of 3T2R Parallel Mechanisms using Grassmann-Cayley Algebra and Grassmann Line Geometry

Semaan Amine (1) , M Tale Masouleh (2) , Stéphane Caro (1) , Philippe Wenger (1) , Clément Gosselin (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Laboratoire de robotique

This paper deals with the singular configurations of symmetric 5-DOF parallel mechanisms performing three translational and two independent rotational DOFs. The screw theory approach is adopted in order to obtain the Jacobian matrices. The regularity of these matrices is examined using Grassmann-Cayley algebra and~Grassmann geometry. More emphasis is placed on the geometric investigation of singular configurations by means of Grassmann-Cayley Algebra for a class of simplified designs whereas Grassmann geometry is used for a matter of comparison. The results provide algebraic expressions for the singularity conditions, in terms of some bracket monomials obtained from the superbracket decomposition. Accordingly, all the singularity conditions can be enumerated.

Mots clés: Parallel singularity; screw theory; 5-DOF parallel mechanisms; Grassmann geometry; Grassmann-Cayley algebra; Jacobian matrix; superbracket decomposition

Domaines: Automatique / Robotique

Semaan Amine, M Tale Masouleh, Stéphane Caro, Philippe Wenger, Clément Gosselin. Singularity Analysis of 3T2R Parallel Mechanisms using Grassmann-Cayley Algebra and Grassmann Line Geometry. Mechanism and Machine Theory, 2012, 52, pp.326-340. ⟨10.1016/j.mechmachtheory.2011.11.015⟩. ⟨hal-00833520⟩