Kinematic analysis and design optimization of a cable-driven universal joint module

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. So CDPMs have a light-weight structure with large reachable workspace. The aim of this paper is to provide the kinematic analysis and the design optimization of a cable-driven 2-DOF module, comprised of a passive universal joint, for a reconfigurable system. This universal joint module can be part of a modular reconfigurable system where various cable-driven modules can be attached serially into many different configurations. Based on a symmetric design approach, six topological configurations are enumerated with three or four cables arrangements. With a variable constrained axis, the structure matrix of the universal joint has to be formulated with respect to the intermediate frame. The orientation workspace of the universal joint is a submanifold of SO(3). Therefore, the workspace representation is a plane in R². With the integral measure for the submanifold expressed as a cosine function of one of the angles of rotation, an equivolumetric method is employed to numerically calculate the workspace volume. The orientation workspace volume of the universal joint module is found to be 2 pi. Optimization results show that the 4-1 cable arrangement produces the largest workspace with better Global Conditioning Index.