冗余驱动支链对3RPS并联机构刚度的改善

摘要/Abstract

摘要：

在考虑雅可比矩阵变化与动平台姿态偏移之间映射关系的基础上，基于螺旋理论和矢量微分法建立了3RPS并联机构末端位姿偏移与支链构件变形之间的映射模型。首先采用螺旋理论和矢量微分法分析了支链各构件刚度与整个支链刚度之间的关系，然后建立了3RPS并联机构的瞬时刚度模型，并分析了雅可比矩阵的变化对机构刚度的影响。对冗余驱动支链改善并联机构刚度的原理进行了分析，建立了冗余驱动并联机构的整机刚度模型。仿真分析和实验验证，冗余驱动支链确实能够改善并联机构的刚度。

关键词: 冗余驱动, 瞬时刚度模型, 矢量微分法, 并联运动机构, 位姿偏移

Abstract:

Considering the relationship between the changes of the Jacobian matrix and the orientation deviation of the moving platform, the mapping model between the 3RPS PKM end-effector offset and the deformation of the branches was established by using the vector differential method, based on the screw theory. The functional expression of the rigidity of the chain and its components was derived, and then the instant stiffness model of the 3RPS PKM was built up. The influences of the changes of the Jacobian matrix on the stiffness of the PKM were analyzed. The theories that the redundant actuating leg could increase the stiffness of the PKM were discussed, and were also verified by the simulation and the tests.

Key words: redundant actuation, instant stiffness model, vector differential method, parallel kinematic machanism(PKM);position and orientation offset

中图分类号:

TH112

崔学良, 陈五一, 韩先国, 祝锡晶, 王建青, 成, 全. 冗余驱动支链对3RPS并联机构刚度的改善[J]. 中国机械工程, 2015, 26(23): 3162-3167.

Cui Xueliang, Chen Wuyi, Han Xianguo, Zhu Xijing, Wang Jianqing, Cheng Quan. Stiffness Improvement of 3RPS PKM by Redundant Actuating Leg[J]. China Mechanical Engineering, 2015, 26(23): 3162-3167.

参考文献

[1]Wu Jun, Wang Jinsong, Wang Liping. Dynamics and Control of a Planar 3-DOF Parallel Manipulator with Actuation Redundancy[J]. Mechanism and Machine Theory, 2009, 44: 835-849.
[2]Wang Songtao, Cheng Gang, Pang Yusong, et al. Integrated Stiffness Analysis of Redundant Parallel Manipulator Based on Finite Element Method[J]. Journal of Information & Computational Science, 2015, 12(1): 351-365.
[3]白志富，陈五一. 球铰刚度计算模型及靠冗余支链实现并联机床刚度的改善[J]. 机械工程学报, 2006, 42(10): 142-145.
Bai Zhifu, Chen Wuyi. Stiffness Computation Model of Spherical Joints and PKM’s Stiffness Improvement by Redundant Leg[J]. Chinese Journal of Mechanical Engineering, 2006, 42(10): 142-145.
[4]宋轶民，翟学东，孙涛,等. 一种三自由度冗余驱动并联模块的刚度分析[J]. 天津大学学报(自然科学与工程技术版), 2015, 48(1): 25-32.
Song Yimin, Zhai Xuedong, Sun Tao, et al. Stiffness Analysis of a 3-DOF Redundantly Actuated Parallel Module[J]. Journal of Tianjin University(Science and Technology), 2015, 48(1): 25-32.
[5]周鑫，许允斗，姚建涛,等. 5-UPS/PRPU冗余驱动并联机床完整刚度模型及其刚度特性[J]. 光学精密工程，2015，23（4）:1070-1080.
Zhou Xin, Xu Yundou, Yao Jiantao, et al. Complete Stiffness Model and Stiffness Performance of
5-UPS/PRPU Redundantly Actuated Parallel Machine Tool[J]. Optics and Precision Engineering, 2015，23（4）:1070-1080.
[6]Xu Yundou, Yao Jiantao, Zhao Yongsheng. Inverse Dynamics and Internal Forces of the Redundantly Actuated Parallel Manipulators[J]. Mechanism and Machine Theory, 2012, 51: 172-184.
[7]Zhang Dan, Shi Qi, Li Jian.A Comparison Study of Three Degree-of-freedom Micro-motion Parallel Kinematic Machines with/without Actuation Redundancy[C]//2010 International Conference on Manufacturing Automation. Hongkong,2010: 239-245.
[8]Jin Sangrok, Kim Jongwon,Seo TaeWon. Optimization of a Redundantly Actuated 5R Symmetrical Parallel Mechanism Based on Structural Stiffness[J].Robotica, 2015, 7: 1-11.
[9]窦玉超，姚建涛，高思慧,等. 冗余驱动并联机器人动力学建模与驱动力协调分配[J]. 农业机械学报,2014， 45（1）：293-299.
Dou Yuchao, Yao Jiantao, Gao Sihui, et al. Dynaimic Modeling and Driving Force Coordinate Distribution of the Parallel Robot with Redundant Actuation[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014，45（1）：293-299.

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[13]	敖银辉. 平面并联机构的自适应控制方法研究 [J]. 中国机械工程, 2010, 21(7): 835-838.
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