A generic tension-closure analysis method for fully-constrained cable-driven parallel manipulators

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Due to the unilateral property of the cables, all the driving cables in a fully-constrained CDPM must always maintain positive tension. As a result, tension analysis is the most essential issue for these CDPMs. By drawing upon the mathematical theory from convex analysis, a sufficient and necessary tension-closure condition is proposed in this paper. The key point of this tension-closure condition is to construct a critical vector that must be positively expressed by the tension vectors associated with the driving cables. It has been verified that such a tension-closure condition is general enough to cater for CDPMs with different numbers of cables and DOFs. Using the tension-closure condition, a computationally efficient algorithm is developed for the tension-closure pose analysis of CDPMs, in which only a limited set of deterministic linear equation systems need to be resolved. This algorithm has been employed for the tension-closure workspace analysis of CDPMs and verified by a number of computational examples. The computational time required by the proposed algorithm is always shorter as compared to other existing algorithms.