绳牵引机器人加入弹簧后刚度分析

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摘要刚度是机器人重要的设计评价指标之一，不仅影响机构的动态特性，还决定机器人在负载情况下末端执行器的定位精度。对于n自由度的绳索牵引并联机器人，由于绳索只能承受拉力而不能承受压力，故至少要由n+1根绳索来驱动，冗余驱动的绳索拉力求解非常复杂。当在绳索牵引并联机器人中适当位置引入弹簧，构成绳索-弹簧机构，则可以实现n自由度的绳索-弹簧机构由n根绳索驱动。本文从刚度的基本定义出发，在绳索-弹簧机构静力学平衡方程的基础上推导出机构在可行工作空间内不同位姿点处的刚度矩阵解析表达式，即被动刚度矩阵和主动刚度中海瑟矩阵的解析式。加入弹簧后，绳索驱动机器人在力封闭可行工作空间内的主、被动刚度增加，并以3根绳索1根弹簧和4根绳索的平面3自由度机构模型的数值算例进行了验证。

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关键词 ：绳索-弹簧机构, 静刚度, 刚度矩阵, 海瑟矩阵

Abstract：Stiffness is one of the important design index of robot. It affects the dynamic characteristics of the robot mechanism, and determines the load positioning accuracy of the end effector. Since cables can only pull but not push, the Cable-Driven Parallel Mechanism (CDPM) with n degrees of freedom requires at least n+1 cables to fully constrain the end-effector. However it has been shown that the redundant cable leads to increased costs of actuator and results in the complexity of solving the cable force. When springs are added properly into the CDPM between the end-effecter and the base frame, it constitutes a Cable-Spring Mechanism, which can achieve the same number of actuators with cables to fully constrain the end-effector of the Cable-Spring Mechanism. In this paper, the static model of a planar Cable-Spring Mechanism is established, and the static analysis of the Cable-Spring Mechanism is performed. According to the definition of rigidity, the analytical expressions of stiffness matrix are derived on the basis of the static equilibrium equation of the Cable-Spring Mechanism at the position of a feasible workspace point. The Hessian matrix of active stiffness and passive stiffness matrix are derived. The stiffness effect of the cable-driven mechanism by adding the spring is analyzed. A numerical example, a planar Cable-Spring Mechanism with 3 cables and 1 spring compared with a 4-cable driven mechanism, was verified.

Key words： Cable-spring mechanism Static stiffness Stiffness matrix Hessian matrix

收稿日期: 2015-04-29 出版日期: 2017-05-15

引用本文:

李清桓1，段清娟2，李帆，段学超. 绳牵引机器人加入弹簧后刚度分析[J]. 振动与冲击, 2017, 36(10): 197-202.
LI Qinghuan DUAN Qingjuan LI Fan DUAN Xuechao. Stiffness analysis of a cable-driven parallel robot by adding springs. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(10): 197-202.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2017/V36/I10/197

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