并联柔索驱动操作臂静刚度的理论分析

文章对并联柔索驱动机器人(PWDRs)的静态刚度问题进行了理论分析。首先，基于微分变换原理，提出并证明了关于柔索矩阵微小变化变分形式的命题，在此基础上推导了操作臂完整刚度的解析公式，它包括与结构参数有关的刚度及与柔索张力有关的刚度两部分。然后，对这一理论结果进行了数值仿真。研究结果表明：操作臂刚度不仅依赖于机构几何尺寸、柔索与电机刚度及操作臂位置与姿态等结构参数，还与柔索的张力有关、因此，可以通过改变柔索张力来调节PWDRs操作臂的刚度．实现机构变刚度。

In this paper the static stiffness of a parallel wire driven robots (PWDRs) is theoretically studied. At first, based on the differential motion principle, a proposition about the small change of the Wire Matrix is presented and proved. And then the stiffness matrix of the manipulator consisting of structural-parameter-related stiffness and wire-tension-related stiffness is produced. Finally, the numerical simulation is done for verifying the conclusion. It is shown that the stiffness of this kind of manipulator depends not only on its structural parameters including the physical dimensions, the stiffness of wires and motors and the position and pose of the end effecter, but also on the tension of the wires. Those works lead to the conclusion that the stiffness of the PWDRs can be regulated by changing the internal tension of wires, and a variable stiffness mechanism can be realized.

国家自然科学基金 (50 2 751 4 3)资助