Design optimization of a cable-driven two-DOF flexible joint module

Abstract

This paper focuses on the kinematics, kinetostatics and design optimization of a 2-DOF cable-driven flexible joint module. Based on the motion characteristics of the 2-DOF joint module, the concept of instantaneous screw axis in conjunction with the Product-Of-Exponentials (POE) formula is proposed to formulate its kinematic model. However, as the instantaneous screw axis is unfixed, the Lie group method is employed to derive the instantaneous kinematic model of the joint module. In order to generate the feasible workspace subject to positive tension constraint, the kinetostatics of the joint module is addressed, where the stiffness resulting from both the driving cables and the flexible backbone are considered. A numerical orientation workspace evaluation method is proposed based on an equi-volumetric partition in its parametric space and the volume-element associated integral factor. A global singular value (GSV) index, which considers the minimum singular value of the stiffness matrix of joint module over the achievable workspace, is employed to optimize the geometric size of joint module. The simulation results demonstrate the effectiveness of the proposed GSV optimization algorithm.