Cable Wrapping Phenomenon in Cable-Driven Parallel Manipulators

In the study of cable-driven parallel manipulators (CDPMs), the interference between the cable and the rigid link(s) of the mechanisms have generally been excluded when the workspace is considered. This leads to the loss of perfectly feasible and useful areas in the workspace. In this paper, we model such a phenomenon by letting the cable wrap around the rigid link and including the results under workspace considerations. We construct a kinematic model of the cable path in a CDPM to include that segment of the cable wrapped over the surface of the rigid link, in addition to modeling the straight (unwrapped) segments of actuation cables in a conventional manner. The path that the cable wrapping around the rigid link describes is a function of the displacement of one or more rigid links. When wrapping occurs, contact between the cable and the rigid link is no longer restricted to a stationary point on the body attached frame, as in the case of a conventional CDPM, but becomes instead a function of the rigid link's pose. The cable is assumed to be taut at all times, so finding the cable configuration is equivalent to finding the geodesic solution for the convex hull of a rigid body. Analysis is firstly presented for a basic case of finding the path of a single cable wrapped over an arbitrary (convex) rigid body, with specific illustration performed for a cylindrical rigid body. Modeling and analysis are then applied to the case of a certain CDPM that enables wrapped cable segments in its operation.