新型2-2PRUR并联机构运动学分析及工作空间优化

李典; 郭盛; 黄冠宇; 赵福群

doi:10.13700/j.bh.1001-5965.2016.0816

新型2-2PRUR并联机构运动学分析及工作空间优化

doi: 10.13700/j.bh.1001-5965.2016.0816

北京交通大学机械与电子控制工程学院机器人研究所, 北京 100044

基金项目:

国家自然科学基金 51475035

详细信息

作者简介:
李典, 男, 博士研究生。主要研究方向:并联机器人机构学; 郭盛, 男, 博士, 教授, 博士生导师。主要研究方向:并联机器人机构学、工厂过程自动化控制及装备、环保节能装备设计、运动控制学、机电一体化

郭盛, 男，博士，教授，博士生导师。主要研究方向：并联机器人机构学、工厂过程自动化控制及装备、环保节能装备设计、运动控制学、机电一体化

通讯作者:
郭盛, E-mail: shguo@bjtu.edu.cn

中图分类号: TH112
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- 被引次数: 0
出版历程
- 收稿日期: 2016-10-19
- 录用日期: 2016-12-16
- 网络出版日期: 2017-10-20

Kinematic analysis and workspace optimization of a novel 2-2PRUR parallel mechanism

Robotics Institute, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China

Funds:

National Natural Science Foundation of China 51475035

More Information

Corresponding author: GUO Sheng, E-mail: shguo@bjtu.edu.cn

摘要

摘要:
基于工业生产线实际需求，设计了新型2-2PRUR并联机构，进行运动学分析的同时基于散点图对工作空间进行了优化。提出了通过拆分动平台为两部分并加装行星轮系以解决四自由度并联机构过约束及增大转动自由度转角的方法；运用坐标法写出机构约束方程并求解位置正反解；利用位置反解方程解的散点画出机构工作空间，同时以散点数最大为原则运用遗传算法对工作空间进行优化，获得了合理的结构参数。为此类并联机构的研究和应用奠定了基础。
- 并联机构 /
- 非过约束 /
- 自由度 /
- 运动学分析 /
- 工作空间优化
Abstract:
A novel 2-2PRUR parallel mechanism is proposed to fit the actual demand of industrial production line. Kinematics analysis and workspace optimization are performed based on scatter plot. A method is presented by splitting the moving platform into two parts and adding planetary gear train, which could solve the over-constraints of four degrees of freedom parallel mechanism and increase the turning angle. The constraint equations are obtained using the coordinate method. The inverse-forward solutions of the mechanism are worked out. And the workspace is obtained by using the scatter plot of inverse kinematic solutions. Meanwhile, reasonable structural parameters are obtained by optimizing workspace with the principle of maximizing scattered points based on genetic algorithm. This work would lay the foundation for the future research and application of this type of parallel mechanism.
- parallel mechanism /
- non-overconstrained /
- degree of freedom /
- kinematic analysis /
- workspace optimization

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图 1 动平台拆分过程

Figure 1. Moving platform split process

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图 2 行星轮系结构示意图

Figure 2. Schematic diagram of planetary gear train structure

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图 3 动平台结构示意图

Figure 3. Schematic diagram of moving platform structure

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图 4 2-2PRUR机构及其简图

Figure 4. 2-2PRUR mechanism and its diagrams

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图 5 4PRUR与2-2PRUR机构构型简图

Figure 5. 4PRUR and 2-2PRUR mechanism configurations' diagrams

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图 6 姿态角为0°时的工作空间

Figure 6. Workspace with posture angle values 0°

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图 7 姿态角为±45°时的工作空间

Figure 7. Workspace with posture angle values ±45°

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图 8 各代适应度函数m值

Figure 8. m values of each generation of fitness function

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图 9 优化后的工作空间视图

Figure 9. Optimized workspace view

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图 10 优化前后的工作空间截面边界图

Figure 10. Cross section boundary of workspace before and after optimization

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表 1 2-2PRUR并联机构位置反解结果

Table 1. Inverse kinematic solutions of 2-2PRUR parallel mechanism

mm
x	y₁	y₂	z	l₁	l₂	l₃	l₄
160	100	200	-150	106.0144	66.5415	21.0464	95.1702
140	100	200	-150	105.2031	21.0464	66.5415	108.8730
150	90	190	-150	105.9616	66.5415	21.0464	103.9075
150	110	210	-150	105.9616	21.0464	66.5415	99.04466
160	110	210	-120	136.0012	79.3318	79.3318	120.7044
140	100	200	-120	135.2031	51.0464	96.5415	138.8730

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表 2 2-2PRUR并联机构位置正解结果

Table 2. Forward kinematic solutions of 2-2PRUR parallel mechanism

mm
l₁	l₂	l₃	l₄	x	y₁	y₂	z
106	66	21	95	160.0099	100.0035	200.3694	-150.0141
105	21	66	108	146.8173	107.2413	206.5883	-148.6636
105	66	21	103	149.9972	90.1848	189.6942	-150.9609
105	21	66	99	149.3046	109.5547	209.1319	-150.9323
136	79	79	120	160.5072	110.3637	210.6410	-119.9843
135	51	96	138	146.8173	107.2413	206.5883	-178.6636

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表 3 2-2PRUR并联机构初始参数值

Table 3. Initial parameter values of 2-2PRUR parallel mechanism

参数	初始值
k_ij/mm	150
a/mm	300
l/mm	100
r/mm	50
l_i/mm	0≤l_i≤100
P(x，y，z)运动范围/mm	50≤x≤250
	50≤y≤250
	-400≤z≤-100

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表 4 2-2PRUR并联机构参数及散点数目值

Table 4. Parameters of 2-2PRUR parallel mechanism and scatter number

参数	初始值	优化值
k₁₁/mm	150	58.21356151
k₁₂/mm	150	128.4783055
k₂₁/mm	150	57.12848677
k₂₂/mm	150	116.0951255
a/mm	300	226.6077689
l/mm	100	148.1780424
r/mm	50	149.8667562
m	37852×3	161928×3

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