PRRRRRP redundant planar parallel manipulator: Kinematics, workspace and singularity analysis

This paper presents a kinematically redundant four actuated-joint degrees of freedom planar parallel manipulator. The workspace of the proposed manipulator is larger than of the non-redundant counterpart and vast majority of its singularities can be avoided by using kinematic redundancy. First, the forward and inverse displacement problems of the manipulator are solved and its workspace is obtained numerically. Then, the Jacobian matrices are developed and the inverse and direct kinematic singularities are identified and their geometrical interpretations are illustrated. Finally, based on a geometrical measure of proximity to singular configurations, a cost function is defined which can be used to obtain an optimal solution for the inverse displacement problem of the manipulator.