Kinematic Modelling of Cable Wrapping on Rigid-link Phenomenon in Cable-driven Parallel Manipulators

In cable-driven parallel manipulators, the interference between the cable and the rigid link(s) of the mechanisms were generally excluded from the workspace consideration. This leads to the loss of perfectly feasible workspace of the mechanism. In this paper, the kinematic modelling of the cable path in a cable-driven parallel manipulator which involves a segment of the cable wrapped over the surface of the rigid link, is presented. The wrapping of the cable is dependent on the displacement of the rigid link and the contact between the cable and the rigid link will no longer be restricted to the cable attachment point (as in the case of a conventional cable-driven parallel manipulator), but could be extended to a line on the surface of the rigid link (ie. cable wrapping over the rigid link). It is assumed that the cable remains taut at all time, therefore finding the cable configuration is equivalent to finding a geodesic solution of a convex hull of a rigid body. The analysis is extended from finding the solution to the path of a single cable wrapped over an arbitrary rigid body to address a cable-driven parallel manipulator that allows wrapped cable segments in its operation.