Asymptotic singularities of planar parallel 3-RPR manipulators

We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace

Perturbation of symmetric 3-RPR manipulators and asymptotic singularities

International audienceSmall perturbations can affect the kinematic properties of manipulators with non-generic architecture. We study in this paper the perturbations of symmetric planar 3-RPR manipulators. We show in particular that one can obtain any of the three possible stable types of behaviour of 3-RPR manipulators for large values of the lengths of the legs

Nonsingular change of assembly mode without any cusp

International audienceThis paper shows for the first time a parallel manipulator that can execute nonsingular changes of assembly modes while its joint space is free of cusp points and cuspidal edges. The manipulator at hand has two degrees of freedom and is derived from a 3-RPR manipulator; the shape of its joint space is a thickening of a figure-eight curve. A few explanations concerning the relationship between cusps and alpha curves are given