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

  • Ambuj Shahi
  • Sandipan BandyopadhyayEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 74)


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.


Cable-driven parallel robots wrench-closure workspace singularity-free sphere parallel robots cable robots 


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Authors and Affiliations

  1. 1.Department of Engineering DesignIndian Institute of Technology MadrasChennaiIndia

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