Dynamic analysis of a 7-DOF redundant and hybrid mechanical arm

doi:10.3785/j.issn.1008-973X.2020.08.008

Journal of ZheJiang University (Engineering Science)

2020, Vol. 54

Issue (8): 1505-1515 DOI: 10.3785/j.issn.1008-973X.2020.08.008

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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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

Received: 15 July 2019 Published: 28 August 2020

CLC:

TP 113

Corresponding Authors: Yan-biao LI E-mail: wzs163yx@163.com;lybrory@zjut.edu.cn

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	Hang ZHENG

Cite this article:

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.

URL:

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

七自由度冗余混联机械臂的动力学分析

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

Fig.1 Model of humanoid arm mechanism

Fig.2 Structure of humanoid arm mechanism

Fig.3 Force diagram of wrist joint

Fig.4 Force diagram of shoulder joint platform

Fig.5 Deformation analysis model a of member A₁B₁

Fig.6 Deformation analysis model b of member A₁B₁

Fig.7 Deformation analysis model of member B₁C₁

Tab.1 Inertia parameters of humanoid arm

Tab.2 Quality parameters of humanoid arm

Tab.3 Length parameters of humanoid arm

Tab.4 Maximum error of each joint drive torque/force

Fig.8 Theoretical and simulated values of each drive torque/force


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