On the determination of the force distribution in overconstrained cable-driven parallel mechanisms
On the determination of the force distribution in overconstrained cable-driven parallel mechanisms
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DOI：
10.1007/s11012-010-9369-x
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发表时间：
2011-02-01
期刊：
影响因子：
2.7
通讯作者：
Grenier, Martin
中科院分区：
文献类型：
--
作者：
Gosselin, Clement;Grenier, Martin
研究了冗余驱动索驱动并联机构中索力分布的确定问题。首先，基于扳手矩阵推导了索驱动并联机构的静力学模型。然后，四个性能指标被认为是为了解决欠定问题与力的分布。一个简单的数值例子，然后开发，以提供深入了解的问题，这导致的结果的几何解释。基于所给出的结果，建议使用p范数（例如，4范数）来优化索驱动并联机构中的力的分布，以使与中值力（或其他目标值）的最大偏差最小化，同时保持解的连续性。一个非迭代多项式制定，然后提出了4-范数。它还指出，这种配方导致一个独特的真实的解决方案。
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.