Dynamics analysis of a redundant parallel manipulator driven by elastic cables

In this paper the dynamic analysis of a cable-driven parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of large adaptive reflector (LAR), the Canadian design of next generation giant radio telescopes. This structure consists of a parallel redundant manipulator actuated by long cables. The dynamic equations of this structure are nonlinear and implicit. Long cables, large amounts of impelling forces and high accelerations raise more concern about the elasticity of cables during dynamic analysis, which has been neglected in the preceding works. In this paper, the kinematic analysis of such manipulator is illustrated first. Then the nonlinear dynamic of such mechanism is derived using Newton-Euler formulation. Next a simple model for cable dynamics containing elastic and damping behavior is proposed. The proposed model neither ignores longitude elasticity properties of cable nor makes dynamic formulations heavily complicated like previous researches. Finally, manipulator dynamic with cable dynamic is derived, and the cable elasticity effects are compared in a simulation study. The results show significant role of elasticity in a cable-driven parallel manipulator such as the one used in LAR mechanism.