On the Design of Singularity-Free Cable-Driven Parallel Mechanism Based on Grassmann Geometry

This paper deals with the design of singularity-free cable-driven parallel mechanism. Due to the negative effect on the performance, singularities should be avoided in the design. The singular configurations of mechanisms can be numerically determined by calculating the rank of its Jacobian matrix. However, this method is inefficient and non-intuitive. In this paper, we investigate the singularities of planar and spatial cable-driven parallel mechanisms using Grassmann line geometry. Considering cables as line vectors in projective space, the singularity conditions are identified with clear geometric meaning which results in useful method for singularity analysis of the cable-driven parallel mechanisms. The method is applied to 3-DOF planar and 6-DOF spatial cable-driven mechanisms to determine their singular configurations. The results show that the singularities of both mechanisms can be eliminated by changing the dimensions of the mechanisms or adding extra cables.