基于牛顿欧拉法的一种空间被动过约束并联机构动力学建模方法

doi:10.3901/JME.2020.11.048

机械工程学报 ›› 2020, Vol. 56 ›› Issue (11): 48-57.doi: 10.3901/JME.2020.11.048

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基于牛顿欧拉法的一种空间被动过约束并联机构动力学建模方法

李永泉^1,2, 郭雨^1,2, 张阳^1,2, 张立杰^2,3

1. 燕山大学河北省并联机器人与机电系统实验室秦皇岛 066004;
2. 燕山大学先进锻压成形技术与科学教育部重点实验室秦皇岛 066004;
3. 燕山大学河北省重型机械流体动力传输与控制实验室秦皇岛 066004

收稿日期:2019-04-24 修回日期:2019-07-17 出版日期:2020-06-05 发布日期:2020-06-12
通讯作者: 张立杰(通信作者),男,1969年出生,教授,博士研究生导师。主要研究方向为并联机构及机器人技术、液压系统集成及控制技术。发表论文50余篇。E-mail:ljzhang@ysu.edu.cn
作者简介:李永泉,男,1979年出生,副教授,硕士研究生导师。主要研究方向为并联机构及机器人技术。发表论文20余篇。E-mail:lijiang197879@sina.com;郭雨,男,1994年出生,硕士研究生。主要研究方向为并联机器人控制技术。E-mail:815035926@qq.com;张阳,男,1994年出生,硕士研究生。主要研究方向为并联机器人型综合。E-mail:1623641500@qq.com
基金资助:
国家自然科学基金（51405421）和河北省自然科学基金（E2015203101）资助项目。

Dynamic Modeling Method of Spatial Passive Over-constrained Parallel Mechanism Based on Newton Euler Method

LI Yongquan^1,2, GUO Yu^1,2, ZHANG Yang^1,2, ZHANG Lijie^2,3

1. Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004;
2. Key Laboratory of Advanced Forging & Stamping Technology and Science(Yanshan University), Ministry of Education of China, Qinhuangdao 066004;
3. Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control, Yanshan University, Qinhuangdao 066004

Received:2019-04-24 Revised:2019-07-17 Online:2020-06-05 Published:2020-06-12

摘要/Abstract

摘要： 以4-RPTR四自由度空间被动过约束（冗余约束）并联机构为研究对象，采用牛顿欧拉法结合补充变形协调方程对其进行动力学分析。基于牛顿欧拉法所建动力学方程为78个，但是由于该机构被动过约束的存在，所要求解的未知量为80个，当按照平面被动过约束机构的方法补充8个变形协调方程时，会与所建的78个方程线性相关，导致方程组无法求解。基于此，提出进行被动过约束并联机构动力学建模时，应首先分析机构产生被动过约束的原因，在此基础上，引入冗余约束力（力矩）引起的杆件变形与末端平台位姿误差的关系作为补充方程，能够保证方程组线性无关，可以求解。为此，引入直接引起冗余约束的转动关节约束力矩产生的杆件变形与末端平台位姿误差的关系，补充了8个变形协调方程，同时引入了6个未知量，从而得到86个方程，包含86个未知量，且方程组线性无关，得到了该机构的动力学全解模型。基于Matlab和ADAMS软件对该机构进行动力学仿真，在平台末端给定相同运动轨迹的情况下，对比两种方法仿真所得机构驱动力变化曲线，可以看出所建动力学模型的正确性。为该类空间被动过约束机构进行动力学建模提供了一个新的思路。

关键词: 并联机构, 过约束, 动力学, 变形协调性分析

Abstract: The 4-RPTR four-degree-of-freedom space passive over-constrained (redundant constrained) parallel mechanism is taken as the research object, and the Newton Euler method combined with the complementary deformation coordination equation is used to analyze the dynamics. The number of dynamic equations based on Newton’s Euler method is 78, but due to the existence of passive over-constraints of the mechanism, the unknown variables of the required solutions are 80. When the eight deformation coordination equations are added according to the method of planar over-constrained mechanism, it will be linearly related to the 78 equations built, resulting in the equations being unable to solve. Based on this, when proposing the dynamics modeling of passive over-constrained parallel mechanism, the reason for the passive over-constraint of the mechanism should be analyzed firstly. On this basis, adding the deformation of the member caused by the redundant constrained force (torque) and the position and posture error of the terminal platform as a complementary equation ensures that the equations are linearly independent and can be solved. To this end, the relationship between the deformation of the rod and the position and posture error of the terminal platform caused by the rotational joint restraining torque directly causing the redundant constraint is introduced, and eight deformation coordination equations are added, and six unknown variables are introduced, thereby obtaining 86 equations. Containing 86 unknowns, and the equations are linearly independent, the dynamic solution model of the mechanism is obtained. Based on matlab and adams software, the dynamics simulation of the mechanism is carried out. When the same motion trajectory is given at the terminal of the platform, the correctness of the dynamic model can be seen by comparing the driving force variation curves of the two methods. It provides a new idea for dynamic modeling of this type of space passive over-constrained mechanism.

Key words: parallel mechanism, over-constraint, dynamics, deformation coordination analysis

中图分类号:

TH113

李永泉, 郭雨, 张阳, 张立杰. 基于牛顿欧拉法的一种空间被动过约束并联机构动力学建模方法[J]. 机械工程学报, 2020, 56(11): 48-57.

LI Yongquan, GUO Yu, ZHANG Yang, ZHANG Lijie. Dynamic Modeling Method of Spatial Passive Over-constrained Parallel Mechanism Based on Newton Euler Method[J]. Journal of Mechanical Engineering, 2020, 56(11): 48-57.

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基于牛顿欧拉法的一种空间被动过约束并联机构动力学建模方法

Dynamic Modeling Method of Spatial Passive Over-constrained Parallel Mechanism Based on Newton Euler Method

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