Modelling of cable wrapping phenomenon towards improved cable-driven mechanisms

Traditional parallel driven cable robots relied on the fact that the cables connecting the fixed frame and the moving platform remain straight and taut under tension during operation. Most studies implicitly or explicitly modelled the cables as straight lines. As consequence, the contacts between the cables and the platform have been excluded from the admissible workspace. This practice also excludes some beneficial properties, such as higher fidelity in modelling, the ability to generate larger workspace and higher moments by allowing cable to wrap around rigid bodies. In this paper, cable wrapping phenomenon is modelled and studied. The study is limited to the modelling of a single cable wrapping around a rigid body, illustrated on a specific case of a cylindrical bar connected to the base through a ball joint. The objective of this paper is to build up a mathematical foundation to investigate the kinematics and dynamics relationship between the cable and the resulting displacement of the cylindrical bar with the assumption of a taut wrapping. The path taken by the cable is shown to be a combined curve consisting of a helix and a straight line while it is in tension under the wrapping phenomenon.