Design Optimization of a Cable-Driven Two-DOF Joint Module with a Flexible Backbone

A cable-driven snake-like robot arm (CDSLRA) with a flexible backbone possesses a number of promising advantages over the conventional rigid-link manipulators, such as lightweight mechanical structure, large reachable workspace, and high maneuverability. In general, a CDSLRA is a hyper-redundant manipulator that consists of a large number of active segments. As the basic building block of a CDSLRA, a 2-DOF cable-driven joint module with a flexible backbone is proposed. This paper focuses on the kinematics, kinetostatics and design optimization of the 2-DOF flexible joint module. Based on the 2-DOF joint module design as well as its resultant motion characteristics, the concept of instantaneous screw axis is proposed to formulate the kinematic model of the 2-DOF joint module, in which the Product-Of-Exponentials (POE) formula is employed. In order to generate the feasible workspace subject to the positive tension constraint, the kinetostatics of the 2-DOF cable-driven 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 multi-performance index, which takes both the stiffness condition index and the workspace volume into account, is employed to optimize the geometric size of the joint module. The simulation results demonstrate the effectiveness of the proposed multi-performance optimization algorithm.