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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (8): 1505-1515    DOI: 10.3785/j.issn.1008-973X.2020.08.008
机械工程     
七自由度冗余混联机械臂的动力学分析
王泽胜(),李研彪*(),罗怡沁,孙鹏,陈波,郑航
浙江工业大学 机械工程学院，浙江 杭州 310032
Dynamic analysis of a 7-DOF redundant and hybrid mechanical arm
Ze-sheng WANG(),Yan-biao LI*(),Yi-qin LUO,Peng SUN,Bo CHEN,Hang ZHENG
College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
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摘要：

结合人体手臂关节的运动特点，提出新型七自由度冗余串并混联拟人机械臂机构，并以该机构为例提出混联机构动力学建模方法. 根据运动的传递特性，采用矢量法推导出各个构件在各关节坐标系中的速度和加速度. 基于牛顿-欧拉法在各关节坐标系建立冗余混联机械臂机构的力平衡方程，由于肩关节为过约束机构，所要求解的未知量为27个，基于牛顿欧拉法所建动力学方程为24个. 引入冗余约束力（力矩）引起的杆件变形与动平台位置误差的关系作为补充条件，利用小变形叠加原理补充3个肩关节机构的变形协调方程，联立方程组得到机械臂动力学全解模型. 通过直线、抛物线和圆形轨迹的算例仿真结果验证动力学模型的正确性，为该机构的进一步研究及应用奠定理论基础.
关键词： 拟人机械臂;  冗余自由度;  混联;  动力学建模;  变形协调方程    
Abstract:

A novel 7-DOF redundant and serial-parallel hybrid humanoid arm mechanism was proposed, inspired by the motion characteristics of human arm joints, and the dynamic modeling method of the hybrid mechanism was proposed taking the mechanism as an example. The velocity and acceleration of each component are derived by the vector method in respective joint coordinate system, according to the motion transmissibility characteristics. The equilibrium equations of the redundant hybrid mechanical arm are established by the Newton-Euler method in respective joint coordinate system. The number of the unknown variables of the required solutions are 27, since the shoulder joint is an over-constrain mechanism. The number of dynamic equations based on Newton's Euler method is 24. Three deformation coordination equations are derived by utilizing the micro-deformation and superposition principle, by adding the relation between the deformation of the member caused by the redundant constrained force (torque) and the position error of the moving platform as a complementary condition. The complete dynamics model of the manipulator is obtained by simultaneous equations. The correctness of dynamics model is verified by simulation results of the linear, parabolic and circular trajectories. The correctness of the modeling lays the foundation for further research and application of the mechanism.
Key words: humanoid robotic arm    redundant DOFs    hybrid    dynamic model    deformation coordination equation
收稿日期: 2019-07-15 出版日期: 2020-08-28
CLC:  TP 113  
基金资助: 国家自然科学基金资助项目（51975523，51905481，51475424）；浙江省自然科学基金杰出青年资助项目（LR18E050003）
通讯作者: 李研彪     E-mail: wzs163yx@163.com;lybrory@zjut.edu.cn
作者简介: 王泽胜（1994—），男，硕士生，从事机器人技术研究. orcid.org/0000-0002-2144-5207. E-mail： wzs163yx@163.com
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王泽胜
李研彪
罗怡沁
孙鹏
陈波
郑航

引用本文:

王泽胜,李研彪,罗怡沁,孙鹏,陈波,郑航. 七自由度冗余混联机械臂的动力学分析[J]. 浙江大学学报(工学版), 2020, 54(8): 1505-1515.

Ze-sheng WANG,Yan-biao LI,Yi-qin LUO,Peng SUN,Bo CHEN,Hang ZHENG. Dynamic analysis of a 7-DOF redundant and hybrid mechanical arm. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1505-1515.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.08.008    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I8/1505

图 1  拟人机械臂机构模型图
图 2  拟人机械臂机构简图
图 3  腕关节受力图
图 4  肩关节动平台受力图
图 5  杆A1B1变形分析模型a
图 6  杆A1B1变形分析模型b
图 7  杆B1C1受力变形模型
机构惯性参数 数值/（kg·m2）
Is diag [5.80,5.40,2.61]×10?3
Im diag [8.34,7.80,0.572]×10?4
Ie diag [4.40,4.38,1.23]×10?3
Iw diag [4.81,2.43,2.43]×10?4
Ia diag [2.58,2.57,0.0556]×10?4
Ib diag [9.03,9.03,0.0348]×10?5
表 1  拟人机械臂的惯量参数
kg
机构质量参数 数值 机构质量参数 数值
ms 1.420 ms3 0.366
mmc 0.409 ml 0.0217
mec 0.856 mu 0.0764
ms1 0.399 mwm 0.212
ms2 0.326 mws 0.385
表 2  拟人机械臂的质量参数
m
机构长度参数 数值 机构长度参数 数值
r1 0.119 rs1 0.102
r2 0.268 rs2 0.102
r3 0.343 rs3 0.102
r4 0.100 rw3 0.134
ds 0.00775 la 0.0504
dm 0.121 lb 0.0366
de 0.119 ? ?
表 3  拟人机械臂的长度参数
轨迹 最大误差/%
肩关节 上臂 前臂 腕关节
直线 2.87 2.73 2.35 2.31
抛物线 2.91 2.85 2.32 2.23
圆形 2.98 2.67 2.30 2.27
表 4  各关节驱动力矩/力的最大误差
图 8  各驱动力矩/力理论值与仿真值
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