This paper studies the direct geometrico-static problem (DGP) of underconstrained cable-driven parallel robots (CDPRs) with three cables. The task consists in determining the end-effector pose and the cable tensile forces when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled, and they must be tackled simultaneously. An effective elimination procedure is proposed and a least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem. This is proven to admit 156 solutions in the complex field. Several approaches for the efficient computation of the complete solution set are presented, including an eigenproblem formulation and homotopy continuation.
Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables1
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received March 24, 2012; final manuscript received April 17, 2013; published online June 20, 2013. Assoc. Editor: Vijay Kumar.
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Carricato, M. (June 24, 2013). "Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables." ASME. J. Mechanisms Robotics. August 2013; 5(3): 031008. https://doi.org/10.1115/1.4024293
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