Singularities of a planar 3-RPR parallel manipulator with joint clearance

Abstract

SUMMARYIf the joint clearances of the joints of a manipulator are considered, an unconstrained motion of the end-effector can be computed. This is true for all poses of the manipulator, even with all actuators locked.This paper presents how this unconstrained motion can be determined for a planar 3-RPR manipulator. The singularities are then studied. It is shown that when clearances are considered, the singularity curves normally found in the workspace of such a manipulator become singular zones. These zones can be significant and greatly reduce the usable workspace of a manipulator. Since a prescribed configuration that would not, in theory, corresponds to a singular pose can become singular due to the unconstrained motion, the results of this paper are relevant to manipulator design and trajectory planning.