Tensionability Conditions of a Multi-Body System Driven by Cables

Abstract

Cable-driven mechanisms have been reported in the literature for the manipulation of a single rigid body. A cable-driven mechanism configured as a Completely Restrained Positioning Mechanism (CRPM) [6], requires a minimum of n+1 cables to maintain the tensionability of the manipulator (i.e. all cables can be made taut), where n is the dimension of the motion space (typically 3 in the planar and 6 in spatial manipulators). In this paper, the idea of cable-driven manipulators is extended to the manipulation of a multi-body system by cables. The first and most fundamental issue to be addressed is the required number of cables and the cable distribution over the links. This problem is thoroughly investigated in this paper. The major issue that differentiates between single rigid body and multi-body cable-driven systems is that in the multi-body systems, each link is subjected to not only the unilateral force of the cables, but also to the bilateral constraint forces and moments of the joints. This requires a new approach for the analysis of the tensionability. The proposed approach in this paper is based on the fundamental equilibrium equations. This will be shown to result that every subsystems of the cable-driven multi-body should satisfy the tensionability condition which also provides all the necessary conditions on the number of the cables attached to that sub-system. These necessary conditions will be then complied to provide the total sufficient number of the cables and their required distribution on the links.