Study on Stiffness-Oriented Cable Tension Distribution for a Symmetrical Cable-Driven Mechanism

Abstract

In this paper, we focus on the issues pertaining to stiffness-oriented cable tension distributionfor a symmetrical 6-cable-driven spherical joint module (6-CSJM), which can be employed to constructmodular cable-driven manipulators. Due to the redundant actuation of the 6-CSJM, three cables areemployed for position regulation by adjusting the cable lengths, and the remaining three cables areutilized for stiffness regulation by adjusting the cable tensions, i.e., the position and stiffness can beregulated simultaneously. To increase the range of stiffness regulation, a variable stiffness device(VSD) is designed, which is serially connected to the driving cable. Since the stiffness model of the6-CSJM with VSDs is very complicated, it is difficult to directly solve the cable tensions from thedesired stiffness. The stiffness-oriented cable tension distribution issue is formulated as a nonlinearconstrained optimization problem, and the Complex method is employed to obtain optimal tensiondistributions. Furthermore, to significantly improve the computation efficiency, a decision variableelimination technique is proposed to deal with the equality constraints, which reduces decision variablesfrom 6 to 3. A comprehensive simulation study is conducted to verify the effectiveness of the proposedmethod, showing that the 6-CSJM can accurately achieve the desired stiffness through cable tensionoptimization.