Conditions on the Cable-Routing Matrix for Wrench Closure of Multilink Cable-Driven Manipulators

Wrench-closure is an important property of cable-driven parallel manipulators (CDPMs), representing the ability to generate wrench in any direction by positive cable forces. For single link CDPMs, it is well known that m >= n + 1 cables are necessary for an n degrees-of-freedom CDPM to achieve wrench-closure. However, for multilink cable-driven manipulators (MCDMs), this condition is too relaxed and the cable routing should also be considered. In this paper, necessary conditions to achieve wrench-closure for MCDMs are mathematically derived based on the cable routing arrangements. Since the approach is independent on the exact attachment locations, the proposed necessary conditions can be efficiently validated during the design and synthesis of MCDMs. Analysis is performed on a range of different MCDM structures to identify cable arrangements that do not satisfy wrench-closure for an MCDM.