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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (4): 654-663    DOI: 10.3785/j.issn.1008-973X.2019.04.006
    
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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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)     
Received: 20 March 2018      Published: 28 March 2019
CLC:  TP 24  
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Yan-biao LI
Hang ZHENG
Meng-ru XU
Yi-qin LUO
Peng SUN
Cite this article:

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.

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


5-PSS/UPU并联机构的多目标性能参数优化

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) 
Fig.1 Structure of 5-PSS/UPU parallel mechanism
Fig.2 Euler transformation of branch coordinate system
Fig.3 Screw analysis of PSS-driven branch
Fig.5 Global performance atlases of 5-PSS/UPU
Fig.4 Geometric space and planar mapping of 5-PSS/UPU parallel mechanism
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
Tab.1 Raw data of 5-PSS/UPU parallel mechanism’s each performance index
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
Tab.2 5-PSS/UPU parallel mechanism each performance index after standardization processing
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
Tab.3 Correlation matrix R of each performance index
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
Tab.4 Analysis and calculation results of principle component analysis
Fig.6 Map of comprehensive performance index
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
Tab.5 Comprehensive performance index of structural parameters
Fig.7 Comparision of comprehensive performance between different sizes (z=0)
Fig.8 5-PSS/UPU parallel mechanism
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