Force-closure workspace analysis of cable-driven parallel mechanisms

A cable-driven parallel mechanism (CDPM) possesses a number of promising advantages over the conventional rigid-link mechanisms, such as simple and light-weight mechanical structure, high-loading capacity, and large reachable workspace. However, the formulations and results obtained for the rigid-link mechanisms cannot be directly applied to CDPMs due to the unilateral property of cables. This paper focuses on the workspace analysis of fully restrained positioning mechanisms. Because the cable tension is the most essential issue to constrain the moving platform, the force-closure workspace is mainly studied. A general approach is proposed to check the force-closure condition. This condition is expressed in terms of the convex hull which encloses the origin. However, such a condition is formulated and expressed in high dimensions. To simplify the analysis, a recursive dimension reduction algorithm is proposed to check convex hulls in one dimension spaces. This algorithm is verified through simulation results of various CDPMs.