平面整体式三自由度全柔顺并联机构拓扑优化构型设计及振动频率分析

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摘要通过建立并联原型机构的微分雅克比矩阵方程，实现平面整体式三自由度全柔顺并联机构与并联原型机构之间的矢量同构映射。在此基础上，建立平面整体式3-PRR型全柔顺并联机构SIMP拓扑优化模型，并采用优化准则算法，结合矢量同构映射方程，进行了平面整体式3-PRR型全柔顺并联机构同构构型设计，通过应力分布和前四阶振动固有频率仿真对比研究表明：所采取的拓扑优化设计方法使平面整体式全柔顺并联机构具有一定的均布刚度和较好的振动抑制性能，且对其振动频率的分析可为机构尺寸优化及振型优化提供了重要的依据。同时，微运动特性的仿真表明其与传统并联原型机构之间的运动学同构性一致。该结果对平面整体式全柔顺并联机构的构型拓扑优化设计有实际意义。

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	朱大昌宋马军

关键词 ：平面整体式三自由度全柔顺并联机构, 微分矢量同构映射, 拓扑优化, 振动固有频率

Abstract：By establishing the differential Jacobian matrix equation of parallel prototypical mechanism, the vector isomorphic mapping between planar integrated fully compliant parallel mechanism and parallel prototypical mechanism is realized. On this basis, the SIMP topology optimization model of 3-PRR type planar integrated fully compliant parallel mechanism is build, and optimization criteria algorithm is adopted, combined with the vector isomorphic mapping equation, the isomorphic structure of 3-PRR type planar integrated fully compliant parallel robot is design. By comparing its simulation of stress distribution and first four vibration natural frequencies, it shown that the topology optimization method introduced in this paper make planar integrated fully compliant parallel mechanism had enough uniform stiffness and better performance of vibration suppression, and the analysis of its vibration frequencies provide important basis for size and modal optimization of mechanism. Meanwhile, the simulation of differential kinematical characteristics shown kinematics of isomorphism between planar integrated fully compliant parallel mechanism and traditional parallel prototypical mechanism. The method and analysis above may be helpful for structural designing of planar integrated fully compliant parallel mechanism.

Key words： planar integrated 3-DOF fully compliant parallel manipulator, differential vector isomorphic mapping, topology optimization, vibration natural frequency

收稿日期: 2015-04-20 出版日期: 2016-01-25

引用本文:

朱大昌宋马军. 平面整体式三自由度全柔顺并联机构拓扑优化构型设计及振动频率分析[J]. 振动与冲击, 2016, 35(3): 27-33.
Zhu Dachang SongMajun. Configuration Design and Vibration Frequency Analysis with Topology Optimization for Planar Integrated 3-DOF Fully Compliant Parallel Mechanism. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(3): 27-33.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I3/27

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