Abstract
This paper addresses the determination of the force distribution in the cables of a redundantly actuated cable-driven parallel mechanism. First, the static model of cable-driven parallel mechanisms is derived based on the wrench matrix. Then, four performance indices are considered in order to solve the underdetermined problem associated with the distribution of the forces. A simple numerical example is then developed in order to provide insight into the problem, which leads to a geometric interpretation of the results. Based on the presented results, it is proposed to use a p-norm (e.g. a 4-norm) to optimize the distribution of the forces in a cable-driven parallel mechanism in order to minimize the largest deviations from the median forces (or other target values) while maintaining continuity in the solution. A non-iterative polynomial formulation is then proposed for the 4-norm. It is also pointed out that this formulation leads to a unique real solution.
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Gosselin, C., Grenier, M. On the determination of the force distribution in overconstrained cable-driven parallel mechanisms. Meccanica 46, 3–15 (2011). https://doi.org/10.1007/s11012-010-9369-x
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DOI: https://doi.org/10.1007/s11012-010-9369-x