Research on Controllable Stiffness of Redundant Cable-Driven Parallel Robots

In this paper, to solve the problem of variable stiffness of cable-driven parallel robots (CDPR), a new static stiffness analysis and cable tension distribution method are proposed for studying the CDPRs' controllable stiffness. First, a three-dimensional Hessian matrix of the structure matrix to position differential is deduced by introducing a line vector and differential transform, and a static stiffness model is established for analyzing the relationship between cable tension and the stiffness of the robots. Furthermore, a calculation algorithm for cable tension polygons based on Graham's Scan is introduced that effectively obtains the cable tension feasible region (CTFR) of CDPRs. Next, a method involving “the relationship between the external force and the pose change value of the moving-platform” is proposed to measure the variation of system stiffness. The CDPR's controllable stiffness is also analyzed based on the CTFR by considering the variation of each driving-cable's tension and each component of the moving-platform's pose. The results of experimental and theoretical analyses verify the correctness and efficacy of the proposed method. In addition, they show that the proposed method is computationally efficient and easily establishes the relationship between cable tension and the CDPR's controllable stiffness.