On the Redundancy of Cable-Driven Parallel Robots

This paper addresses the concept of redundancy for cable-driven parallel robot (CDPR). We show that although CDPR may be considered as kinematically redundant, they constitute a special class for which the self-motion manifold is 0-dimensional and that they are not not statically redundant (i.e. the tension distribution cannot be changed continuously while keeping the platform at a given pose). A direct consequence is that a CDPR with more than 6 cables is always in a configuration where at most 6 cables are simultaneously under tension. However for a given pose there may be several set of 6 cables that are valid, which allow us to define the concept of weak statical redundancy. We show how the possible valid configuration(s) may be determined on a trajectory. All these concepts are illustrated on a real robot.