非结式消元7R双环球面机构运动学位移分析

doi:10.3901/JME.2024.07.045

机械工程学报 ›› 2024, Vol. 60 ›› Issue (7): 45-53.doi: 10.3901/JME.2024.07.045

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非结式消元7R双环球面机构运动学位移分析

刘伟¹, 刘宏昭²

1. 西安工程大学机电工程学院西安 710048;
2. 西安理工大学机械与精密仪器工程学院西安 710048

收稿日期:2023-04-10 修回日期:2023-09-19 出版日期:2024-04-05 发布日期:2024-06-07
通讯作者: 刘宏昭，男，1954年出生，博士，教授，博士研究生导师。主要研究方向为机构学、机械动力学。E-mail：liu-hongzhao@163.com
作者简介:刘伟，男，1985年出生，博士，讲师。主要研究方向为机构设计。E-mail：liuweilw@xpu.edu.cn
基金资助:
国家自然科学基金(51275404)、西安工程大学博士科研启动基金(BS202106)和中国纺织工业联合会科技计划指导(2021073)资助项目。

Kinematic Position Analysis of a 7R Double Loops Spherical Mechanism without Resultant Elimination

LIU Wei¹, LIU Hongzhao²

1. College of Mechanical and Electrical Engineering, Xi'an Polytechnic University, Xi'an 710048;
2. Faculty of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi'an 710048

Received:2023-04-10 Revised:2023-09-19 Online:2024-04-05 Published:2024-06-07

摘要/Abstract

摘要： 提出一种7R双环球面机构运动学位移分析的方法。将球面4R机构连杆的方向矢量作为中间变量，建立关于其线性方程组，不进行结式消元，直接得到输入与输出一对一的运动学位移方程，位移分析结果与现有文献中数据一致。该方法的优点是不需将中间关节变量引入运动学位移方程，使得机构位移分析过程简化。使用该方法对一种多模式7R双环球面机构运动学位移进行分析，通过对运动学方程进行因式分解，确定了机构具有的两种运动模式和其共同位型，分析机构的转动工作空间。结果表明该7R双环球面机构具有一维转动位移子群与一维转动位移流形两种运动模式。提出的运动学位移分析方法，在分析结构参数对7R双环球面机构运动模式的影响方面具有一定的理论应用价值。

关键词: 7R, 双环球面机构, 运动模式

Abstract: A method for kinematic analysis of a 7R double loops spherical mechanism is proposed. Taking the direction vector of the spherical 4R linkage as an intermediate variable, a set of linear equations about it is established. Without resultant elimination, the motion equations of input and output are directly obtained. The displacement analysis results are consistent with the data in the existing literature. The advantage of this method is that it does not need to introduce intermediate joint variables into the kinematic equation, which simplifies the process of mechanism displacement analysis. This method is used to analyze the motion of a multi-mode 7R double loops spherical mechanism. By factoring the kinematic equation, the two motion modes and their common positions of the mechanism are determined, and the rotating workspace of the mechanism is analyzed. The results show that the 7R double loops spherical mechanism has two motion modes that are belong to one dimensional rotational displacement subgroup and one dimensional rotational displacement manifold. This method has certain theoretical application value in analyzing the influence of structural parameters on the motion mode of 7R double loops spherical mechanism.

Key words: 7R, double loops spherical mechanism, motion mode

中图分类号:

TH112

刘伟, 刘宏昭. 非结式消元7R双环球面机构运动学位移分析[J]. 机械工程学报, 2024, 60(7): 45-53.

LIU Wei, LIU Hongzhao. Kinematic Position Analysis of a 7R Double Loops Spherical Mechanism without Resultant Elimination[J]. Journal of Mechanical Engineering, 2024, 60(7): 45-53.

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非结式消元7R双环球面机构运动学位移分析

Kinematic Position Analysis of a 7R Double Loops Spherical Mechanism without Resultant Elimination

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