Identifying the largest sphere inscribed in the constant orientation wrench-closure workspace of a spatial parallel manipulator driven by seven cables

This paper presents a methodology to find the largest sphere inside the constant orientation wrench-closure workspace of spatial cable-driven parallel robots driven by seven cables. The sphere is centred at a prescribed point of interest and is obtained for a given orientation of the moving platform. The method builds upon the analytical description of the boundary of the constant orientation wrench-closure workspace to obtain the desired spheres. The problem has been reduced to solving seven systems, each consisting of three cubic polynomial equations in three unknowns. A computer algebra system (CAS) has been used to solve these systems of equations, using a formulation based on Sylvester’s dialytic elimination and generalised eigenproblem, which has been illustrated through an example.