Singularity Analysis of the H4 Robot using Grassmann-Cayley Algebra

Semaan Amine (1) , Stéphane Caro (1) , Philippe Wenger (1) , Daniel Kanaan (2)

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

This paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann-Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

Mots clés: screw theory; articulated nacelle; projective space; superbracket.; parallel singularity; Grassmann-Cayley algebra; superbracket

Domaines: Electronique

Semaan Amine, Stéphane Caro, Philippe Wenger, Daniel Kanaan. Singularity Analysis of the H4 Robot using Grassmann-Cayley Algebra. Robotica, 2011, pp.1-10. ⟨10.1017/S0263574711001330⟩. ⟨hal-00642230⟩