An Algorithm for Computing Cusp Points in the Joint Space of 3-RPR Parallel Manipulators

Mazen Zein (1) , Philippe Wenger (1) , Damien Chablat (1)

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

This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel manipulators was shown to be associated with the existence of cusp points. At each of these points, three direct kinematic solutions coincide. In the literature, a condition for the existence of three coincident direct kinematic solutions was established, but has never been exploited, because the algebra involved was too complicated to be solved. The algorithm presented in this paper solves this equation and detects all the cusp points in the joint space of these manipulators.

Mots clés: Cusp points; 3-RPR parallel manipulator; singularity; joint space; assembly mode

Domaines: Robotique [cs.RO]

Mazen Zein, Philippe Wenger, Damien Chablat. An Algorithm for Computing Cusp Points in the Joint Space of 3-RPR Parallel Manipulators. European Conference on Mechanism Science, Feb 2006, Obergurgl, Austria. pp.1-12. ⟨hal-00145468⟩