基于共形几何代数的两种6自由度串并混联机构位置逆解分析

doi:10.3901/JME.2022.21.060

机械工程学报 ›› 2022, Vol. 58 ›› Issue (21): 60-68.doi: 10.3901/JME.2022.21.060

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基于共形几何代数的两种6自由度串并混联机构位置逆解分析

胡波^1,2, 高俊林³, 霍焱^1,2, 张达^1,2, 曾达幸⁴, 卢文娟⁴

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. 徐州重型机械有限公司徐州 221004;
4. 东莞理工学院机械工程学院东莞 523808

收稿日期:2022-05-09 修回日期:2022-08-27 出版日期:2022-11-05 发布日期:2022-12-23
通讯作者: 胡波(通信作者),男,1982年出生,教授,博士研究生导师。主要研究方向为机器人机构学理论。E-mail:hubo@ysu.edu.cn
作者简介:高俊林,男,1993年出生,硕士研究生。主要研究方向为并联机器人理论。E-mail:1394315379@qq.com;霍焱,女,1998年出生,硕士研究生。主要研究方向为并联机器人理论。E-mail:2224663054@qq.com;张达,男,1994年出生,硕士研究生。主要研究方向为并联机器人理论。E-mail:742220998@qq.com;曾达幸,男,1978年出生,教授,博士研究生导师。主要研究方向为机器人机构学。E-mail:zengdx@dgut.edu.cn;卢文娟,女,1983年出生,副教授,硕士研究生导师。主要研究方向为机器人机构学。E-mail:2019123@dgut.edu.cn
基金资助:
河北省自然科学基金面上（E2020203027）、河北省中央引导地方科技发展资金（206Z7602G）、广东省普通高校机器人与智能装备重点实验室（2017KSYS009）、东莞理工学院机器人与智能装备创新中心（KCYCXPT2017006）和2021年东莞市科技特派员（20211800500242）资助项目。

Inverse Position Analysis of Two Kinds of 6-DOF Serial-parallel Manipulators Based on Conformal Geometric Algebra

HU Bo^1,2, GAO Junlin³, HUO Yan^1,2, ZHANG Da^1,2, ZENG Daxing⁴, LU Wenjuan⁴

1. Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004;
2. Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao 066004;
3. Xuzhou Heavy Machinery Co., Ltd., Xuzhou 221004;
4. School of Mechanical Engineering, Dongguan University of Technology, Dongguan 533808

Received:2022-05-09 Revised:2022-08-27 Online:2022-11-05 Published:2022-12-23

摘要/Abstract

摘要： 基于共形几何代数（Conformal geometric algebra，CGA）基本理论，解决了（3-PRS）+（3-SPR）和（3-RPS）+（3-SPS+UP）两种典型串并混联机构的位置逆解问题。首先根据机构的几何结构特征选择合适的未知参数，基于共形几何代数的基本运算建立了与该参数相关的机构中间平台某一顶点的数学表达式；然后根据该顶点坐标表达式和机构中存在的几何和尺寸约束，构造若干相关的平面或球面几何体，并对其进行外积求交运算得出中间平台其他两个顶点坐标的共形几何表达式；最后结合得到的顶点坐标与共形几何代数中的矢量内积运算，推导出只含有一个未知参数的多项式方程，由此得到机构的全部位置反解。该方法具有计算简明、高效、几何直观性强的特点，避免了传统方法求解串并混联机构位置逆解时冗长复杂的计算过程，为此类机构位置逆解的研究提供了参考。

关键词: 共形几何代数, 串并混联机构, 位置逆解

Abstract: Based on the basic theory of conformal geometric algebra (CGA), the inverse displacement of (3-PRS)+(3-SPR) and (3-RPS)+(3-SPS+UP) typical serial-parallel manipulators are solved. First, a single unknown is selected according to the geometrical structure of the manipulators, and based on the basic operation of CGA, the mathematical expression of a vertex of the intermediate platform of the manipulators related to this parameter is established. Secondly, according to the coordinate expression of the this vertex and the geometric and dimensional constraints in the manipulators, some basic geometric elements including planes and spheres are constructed, and the conformal geometric expression of the coordinates of other two vertices of the intermediate platform are obtained using the outer product intersection operation. At last, combined with the expressions of the obtained vertices and the inner product operation in CGA, the input-output polynomial equation with a single unknown can be derived and all the inverse position solutions of the manipulators are obtained. The method has the characteristics of simple calculation, high efficiency and remarkable geometric intuition. It avoids the tedious and complicated calculation process compared with traditional methods, and provides a reference for the study of the inverse position analysis of serial-parallel manipulators.

Key words: conformal geometric algebra, serial-parallel manipulator, inverse displacement

中图分类号:

TG156

胡波, 高俊林, 霍焱, 张达, 曾达幸, 卢文娟. 基于共形几何代数的两种6自由度串并混联机构位置逆解分析[J]. 机械工程学报, 2022, 58(21): 60-68.

HU Bo, GAO Junlin, HUO Yan, ZHANG Da, ZENG Daxing, LU Wenjuan. Inverse Position Analysis of Two Kinds of 6-DOF Serial-parallel Manipulators Based on Conformal Geometric Algebra[J]. Journal of Mechanical Engineering, 2022, 58(21): 60-68.

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基于共形几何代数的两种6自由度串并混联机构位置逆解分析

Inverse Position Analysis of Two Kinds of 6-DOF Serial-parallel Manipulators Based on Conformal Geometric Algebra

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