A generic force-closure analysis algorithm for 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 driving property of cables, the cables in a CDPM must always maintain positive tension. In this paper, a methodology based on convex analysis is developed for the force-closure analysis of fully-constrained CDPMs. This method is systematic, easy to implement and satisfies both the necessary and sufficient conditions. The key point of this method is to define a critical vector that must be positively expressed by the tension vectors associated with the driving cables. The solution can be found by resolving a limited set of linear equations. Following the same approach, the method is also extended to generate the static workspace for under-constrained CDPMs. Therefore, this generic force-closure analysis can cater to the workspace analysis of both fully-constrained and under-constrained CDPMs. The computationally efficiency of the algorithm is verified through simulations.

Research Highlights
► Cables must always maintain positive tension to be controllable.
► In this paper, a method is proposed for the force-closure analysis.
► A critical vector must be positively expressed by the tension vectors.
► The method satisfies both the necessary and sufficient conditions.
► This method is generic, systematic and easy to implement.