Evaluation of velocity capabilities for redundant parallel robots

Polytopes are well-known tools to graphically represent force/motion capabilities for a manipulator. This paper focuses on the evaluation of velocity polytopes for redundant fully parallel robots for which a new intermediate space is introduced (in addition to classical joint space and task space) in order to take into account the specific kinematic relationships. In this space, additional constraint are imposed on the available velocities to be consistent with the kinematic constraints due to the redundant kinematic chains. An algorithm to correctly evaluate the task space velocity polytope is given, and numerical results are provided in the case of a planar redundant 3-DOF parallel arm