一种支链含 Pa 副的新型 2T1R 并联机器人的运动学分析与多目标性能优化研究

段纯

doi:10.13433/j.cnki.1003-8728.20200558

一种支链含 Pa 副的新型 2T1R 并联机器人的运动学分析与多目标性能优化研究

doi: 10.13433/j.cnki.1003-8728.20200558

段纯

安徽新闻出版职业技术学院机电信息系，合肥　230601

基金项目: 2020 年度高校学科（专业）拔尖人才学术项目（gxbjZD-2020129）

详细信息

作者简介:
段纯（1979−），副教授，硕士，研究方向为机电控制系统、机器人技术，invincible2012@163.com

中图分类号: TH122
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- 被引次数: 0
出版历程
- 收稿日期: 2020-03-15
- 刊出日期: 2023-03-25

Kinematics Analysis and Performance Optimization of a New 2T1R Parallel Robot with Pa Pairs in Branch Chain

DUAN Chun

Department of Mechanical and Electrical Information, Anhui Vocational College of Press and Publishing, Hefei 230601, China

摘要

摘要: 以并联机构2T1R作为研究对象，基于并联机构拓扑结构设计理论综合出一类支链含Pa平行四边形机构的2T1R并联机构，并优选出两种新型2PRPaR-PPaR与2RRPaR-PPaR并联机构，以2PRPaR-PPaR并联机构为例，利用方位特征集拓扑结构理论计算机构的方位特征集、自由度、耦合度等拓扑特性，根据建立的特征方程并得到机构的运动学逆解解析式。基于此，分别对机构的工作空间、灵巧度、转动能力等性能指标可视化分析，并通过图形化对比分析机构参数对这些性能指标的影响，最后建立工作空间和全局灵巧度多目标优化模型，选择快速非支配多目标优化算法（NSGA-Ⅱ）实现机构尺度综合，结果表明：2PRPaR-PPaR机构具有工作空间较大、灵巧度较好、转动能力高等优良特性，优化出一组不同姿态角下的对工作空间和全局灵巧度的多目标pareto优化解。
- 并联机构 /
- 工作空间 /
- 灵巧度 /
- 转动能力 /
- 多目标pareto优化
Abstract: The parallel mechanism 2T1R was taken as the research object, based on the topological structure design theory of parallel mechanism, a kind of 2T1R parallel mechanism with Pa parallelogram and branch chain is synthesized, and two new types of 2PRPaR-PPaR and 2RRPaR-PPaR parallel mechanisms are selected. Taking 2PRPaR-PPaR parallel mechanism as an example, the topological characteristics of mechanism such as azimuth feature set, degree of freedom and coupling degree are calculated by using the topological structure theory of azimuth feature set. The inverse kinematics solution of the mechanism is obtained based on the established characteristic equation. Based on this, the performance indexes of the mechanism, such as workspace, dexterity and rotation ability, are visualized and analyzed respectively, and the influence of the mechanism parameters on these performance indexes is analyzed through the graphical comparison. Finally, the multi-objective optimization model of workspace and global dexterity is established, and the fast non dominated multi-objective optimization algorithm (NSGA -Ⅱ) is selected to realize the scale synthesis of mechanism. The results show that 2 PRPaR-PPaR mechanism has the advantages of large workspace, good dexterity and high rotation ability, and a set of multi-objective Pareto optimization solutions for workspace and global dexterity under different attitude angles are optimized out.
- parallel manipulator /
- workspace /
- dexterity /
- rotation ability /
- multi objective Pareto optimization

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图 1 3自由度2PRPaR-PPaR并联机构结构简图

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图 2 3自由度2PRPaR-PPaR并联机构三维图

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图 3 2PRPaR-PPaR并联机构的可达工作空间

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图 4 不同姿态角下并联机构的定姿态工作空间

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图 5 2PRPaR-PPaR并联机构在工作空间内的转动能力分布

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图 6 3种姿态角下2PRPaR-PPaR并联机构的灵巧度分布

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图 7 不同参数下的定姿态工作空间面积随姿态角的分布

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图 8 不同参数下的全局灵巧度随姿态角的分布

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图 9 定姿态工作空间随参数空间的分布

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图 10 定姿态工作空间内全局灵巧度在参数空间的分布

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图 11 全局转动能力指标在参数空间的分布

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图 12 不同姿态角下的多目标优化的Pareto优化解前沿

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表 1 机构输出特征与支链描述

方位特征集	编号	支链描述及简图
$ \left[ {\begin{array}{*{20}{c}} {{t^2}} \\ {{r^1}} \end{array}} \right] $	A₁	HSOC{−P(⊥P^(4R)//R−)}
	A₂	HSOC{−◇(P^(4R)−P^(4R)//R−)}
	A₃	HSOC{−◇(P^(4−4R), P^(4−4R)//R−)}
$ \left[ {\begin{array}{*{20}{c}} {{t^3}} \\ {{r^1}} \end{array}} \right] $	B₁	HSOC{−P//R(⊥P^(4R)//R−)}
	B₂	HSOC{−P//R(⊥P^(4R)//R−)}

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表 2 2T1R并联机构组合方案

编号	特点	支链描述
1	支链结构完全相同	$ 3 - HSOC\{ { { - P( { \bot {P^{( {4R} )}}} )//R - } \}} $
2	支链结构完全相同	$ 3 - HSOC\{ { { - \diamondsuit ( {{P^{( {4R} )}} - } ){P^{( {4R} )}}//R - } \}} $
3	支链结构完全相同	$ 3 - HSOC\{ { { - \diamondsuit ( {{P^{4 - ( {4R} )}} - } ){P^{( {4 - 4R} )}}//R - } \}} $
4	支链结构部分相同	$ 1 - HSOC\{ { { - P( { \bot {P^{( {4R} )}}} )//R - } \}} $ $ 2 - HSOC\{ { { - P//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
5	支链结构部分相同	$ 1 - HSOC\{ { { - \diamondsuit ( {{P^{( {4R} )}} - } ){P^{( {4R} )}}//R - } \}} $ $ 2 - HSOC\{ { { - P//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
6	支链结构部分相同	$ 1 - HSOC\{ { { - \diamondsuit ( {{P^{4 - ( {4R} )}} - } ){P^{( {4 - 4R} )}}//R - } \}} $ $ 2 - HSOC\{ { { - P//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
7	支链结构部分相同	$ 1 - HSOC\{ { { - P( { \bot {P^{( {4R} )}}} )//R - } \}} $ $ 2 - HSOC\{ { { - R//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
8	支链结构部分相同	$ 1 - HSOC\{ { { - \diamondsuit ( {{P^{( {4R} )}} - } ){P^{( {4R} )}}//R - } \}} $ $ 2 - HSOC\{ { { - R//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
9	支链结构部分相同	$ 1 - HSOC\{ { { - \diamondsuit ( {{P^{4 - ( {4R} )}} - } ){P^{( {4 - 4R} )}}//R - } \}} $ $ 2 - HSOC\{ { { - R//R( { \bot {P^{( {4R} )}}} )//R - } \}} $
10	支链结构完全不同	$ 1 - HSOC\{ { { - P( { \bot {P^{( {4R} )}}} )//R - } \}} $ $ 1 - HSOC\{ { { - \diamondsuit ( {{P^{( {4R} )}} - } ){P^{( {4R} )}}//R - } \}} $ $ 1 - HSOC\{ { { - \diamondsuit ( {{P^{4 - ( {4R} )}} - } ){P^{( {4 - 4R} )}}//R - } \}} $

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表 3 在工作空间面积约为15 m²的典型的Pareto最优解

参数	0°	60°	120°	180°
L/m	1.785	2	2	2
r/cm	0.502	1	0.607	0.563
R/m	1.999	1.45	1.036	1.167
S/m²	15.28	14.74	15.98	15.95
$ {G_{CI}} $	0.108	0.224	0.1621	0.119

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