Force-Closure Analysis of Multilink Cable-Driven Redundant Manipulators Considering Cable Coupling and Friction Effects

Multilink cable-driven redundant manipulators (MCDRMs) offer numerous advantages over conventional manipulators, making them well suited for operation in narrow and confined environments. However, MCDRMs face limitations in terms of cable quantity and cable routing scheme, which are crucial for achieving full constraint. Force closure, a crucial parameter for evaluating the performance of MCDRMs, ensures that the manipulator can exert sufficient force and torque to stably perform tasks within its workspace. In this article, we propose a novel force-closure analysis method for MCDRMs that considers both cable coupling and friction effects. First, we utilize the Euler-Eytelwein equation to analyze the effect of friction between cables and cable routing holes on the tension of different cable subsegments. Then, utilizing the reciprocal screw theory, we elucidate the cable coupling in MCDRMs and calculate the active joint torques provided by the cable tension, as well as passive joint torques generated by external wrenches. Furthermore, we analyze the force closure of the MCDRM by balancing the passive and active joint torques. Finally, simulations and experiments are conducted using a planar MCDRM. The results demonstrate that the proposed method enables systematic and accurate analysis of the force closure of MCDRDs with arbitrary cable routing schemes.