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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (4): 654-663    DOI: 10.3785/j.issn.1008-973X.2019.04.006
机械与能源工程     
5-PSS/UPU并联机构的多目标性能参数优化
李研彪(),郑航,徐梦茹,罗怡沁,孙鹏
浙江工业大学 机械工程学院，浙江 杭州 310032
Multi-target parameters of performance optimization for 5-PSS/UPU parallel mechanism
Yan-biao LI(),Hang ZHENG,Meng-ru XU,Yi-qin LUO,Peng SUN
College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
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摘要：

在并联机构多目标参数优化方面，针对5-PSS/UPU并联机构，提出基于空间模型技术与主成分分析法相结合的多目标性能参数优化方法. 推导出机构的位置反解、运动传递平衡方程，对单个驱动分支进行螺旋分析，给出多个全域性能指标；应用空间模型技术，研究各全域性能评价指标与机构结构参数之间的分布规律，绘制了各项全域性能图谱；应用主成分分析（PCA）法，研究各全域性能指标之间的相关性，得到综合性能评价指标函数并绘制综合性能图谱；基于综合性能图谱，选取多组结构参数并计算综合性能指标在机构工作空间下的分布规律.研究结果表明，空间模型技术结合PCA法能够综合考虑机构的各项性能，对结构参数进行优化设计，该优化方法同样适用于其他并联机构.
关键词： 并联机构;  运动学分析;  性能指标;  主成分分析(PCA)    
Abstract:

The multi-target parameters of performance optimization for the 5-PSS/UPU parallel mechanism were optimized by using the principal component analysis (PCA) method and space models in aspect of comprehensively considering the multi-objective parallel mechanism performance. Several performance evaluation indices were proposed and discussed according to the inverse position equations, kinematics transmission equations and screw theory analysis of this five-DOF parallel mechanism. Then the spatial model technology was used to reveal the relationship of each performance evaluation indexes and structure parameters of this 5-PSS/UPU parallel mechanism. The multi-dimensional performance indicators were effectively integrated by reducing redundant data based on PCA, and the comprehensive performance optimization and design space were obtained. Multiple sets of structural parameters were selected based on comprehensive design space, and the distribution of performance indicators in the working space of the 5-PSS/UPU parallel mechanism was calculated. Results show that the method of PCA and space models can optimize the sizes of the mechanism considering all of mechanism performances. The optimization method is also suitable for other parallel mechanisms.
Key words: parallel manipulator    kinematics analysis    performance indicator    principal component analysis (PCA)
收稿日期: 2018-03-20 出版日期: 2019-03-28
CLC:  TP 24  
作者简介: 李研彪(1978—)，男，教授，从事精密加工与机器人技术研究. orcid. org/0000-0001-9768-0687. E-mail： lybrory@zjut.edu.cn
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李研彪
郑航
徐梦茹
罗怡沁
孙鹏

引用本文:

李研彪,郑航,徐梦茹,罗怡沁,孙鹏. 5-PSS/UPU并联机构的多目标性能参数优化[J]. 浙江大学学报(工学版), 2019, 53(4): 654-663.

Yan-biao LI,Hang ZHENG,Meng-ru XU,Yi-qin LUO,Peng SUN. Multi-target parameters of performance optimization for 5-PSS/UPU parallel mechanism. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 654-663.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.04.006    或    http://www.zjujournals.com/eng/CN/Y2019/V53/I4/654

图 1  5-PSS/UPU并联机构简图
图 2  分支坐标系的欧拉变换图
图 3  PSS驱动分支螺旋分析
图 5  5-PSS/UPU并联机构的各全域性能图谱
图 4  5-PSS/UPU并联机构的空间模型及平面映射
样本序号 ${\bar K_v}$ ${\bar K_w}$ ${\bar K_\lambda }$ ${\bar K_\eta }$
1 0.310 9 0.140 4 0.451 2 0.034 1
2 0.339 7 0.164 5 0.501 8 0.041 2
3 0.331 8 0.184 3 0.441 8 0.033 2
$ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $
158 0.401 2 0.061 8 0.132 2 0.172 6
159 0.380 2 0.052 8 0.103 6 0.161 6
160 0.361 3 0.040 8 0.080 9 0.151 2
表 1  5-PSS/UPU并联机构各性能指标原始数据
样本序号 ${Z_v}$ ${Z_w}$ ${Z_\lambda }$ ${Z_\eta }$
1 ?1.038 2 ?1.252 7 ?0.153 2 ?1.997 7
2 ?0.813 4 ?1.150 2 0.043 8 ?1.944 8
3 ?1.038 2 ?1.047 7 ?0.192 6 ?1.997 7
$ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $
158 ?0.504 3 ?1.662 8 ?1.413 7 ?1.257 4
159 ?0.616 7 ?1.714 0 ?1.531 8 ?1.310 3
160 ?0.729 1 ?1.765 3 ?1.606 7 ?1.363 2
表 2  5-PSS/UPU并联机构各性能指标标准化数据
性能指标 ${\bar K_v}$ ${\bar K_w }$ ${\bar K_\lambda }$ ${\bar K_\eta }$
${\bar K_v}$ 1 0.036 0.870 0.190
${\bar K_\omega }$ 0.036 1 0.330 0.310
${\bar K_\lambda }$ 0.870 0.330 1 0.064
${\bar K_\eta }$ 0.190 0.310 0.064 1
表 3  性能指标的相关系数矩阵 ${{R}}$
特征值 特征向量 ${\delta _i}\Big/\text{%}$ ${\delta {^{\rm t}_i}}\Big/\text{%}$
2.00 [0.63, 0.32, 0.66, 0.25] 50.31 50.31
1.17 [?0.34, 0.63, ?0.23, 0.66] 29.44 79.75
0.75 [0.25, ?0.65, ?0.19, 0.69] 18.87 98.62
0.055 [0.65, 0.27, ?0.69, ?0.17] 1.38 100.00
表 4  主成分分析法分析计算结果
图 6  综合评价性能指标分布图
组 $X$ $Y$ $r$/mm $R$/mm $\theta $/rad $L$/mm ${\overline K _v}$ ${\overline K _w }$ ${\overline K _\lambda }$ ${\overline K _\eta }$ F
1 2.13 1.1 303 646 30 551 0.58 0.76 0.58 0.60 2.88
2 2.10 1.3 300 661 32 734 0.42 0.82 0.52 0.54 2.81
3 2.40 1.0 161 600 28 380 0.40 0.46 0.37 0.71 2.44
表 5  各结构参数下的全域综合性能指标
图 7  不同尺寸下的综合性能对比情况（z=0）
图 8  5-PSS/UPU并联机构
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