多输入多输出柔顺机构的特征驱动拓扑优化设计

doi:10.3901/JME.260698

摘要/Abstract

摘要： 针对多输入多输出柔顺机构拓扑优化设计中存在的三个典型问题——输入输出耦合、类铰链现象和拓扑图提取困难，提出了一种基于特征驱动技术的新型有效解决方法。首先，在初始布局中使用多个特征(基本设计要素)将柔顺机构的输入端、输出端和固定端两两相连，每个特征均由两个B样条曲线函数分别控制其弯曲变形和宽度变化，因而在优化过程中具备足够的变形能力。然后，构建兼顾耦合效应和类铰链现象的优化设计模型，通过添加抑制耦合位移的约束以期实现完全解耦的高精度操纵；通过在目标函数中对结构柔顺度和输出位移进行自适应加权以期获得“刚柔并济”、不含类铰链的分布式柔顺机构。进而推导出优化目标函数和约束函数对特征变量的灵敏度。最后，通过典型多输入多输出柔顺机构优化算例验证了所提方法在解决输入输出耦合及类铰链问题上的有效性和优越性，并且得益于可灵活变形特征的参数化几何描述，本方法的优化结果可直接、精确地在CAD系统中生成，无需繁琐的拓扑图提取操作。

关键词: 柔顺机构, 拓扑优化, 特征驱动, 输入输出耦合, 类铰链

Abstract: A new topology optimization design framework based on the feature-driven method is proposed to solve the three typical problems in the multi-input-multi-output (MIMO) compliant mechanism synthesis — movement coupling, de facto hinge and topology extraction. In the initial layout of topology optimization, the fixed boundary as well as input and output ports of the MIMO compliant mechanism are connected in pairs by using several features (i.e., basic design primitives) with sufficient deformation capacity, whose bending deformation and width variation are expressed by B-spline curve functions. The optimization design model considering the coupling issue and de facto hinges is then established, in which input and output coupling constraints are introduced to achieve the fully decoupled design, and a weighted objective function is adopted to realize the synthesis of the rigid-flexible combined compliant mechanism (i.e., the distributed compliant mechanism) without de facto hinges. The sensitivity analysis related to the objective function and constraint functions is further carried out. A numerical example concerning the topology optimization of the classical MIMO displacement inverter is tested to demonstrate the effectiveness of the proposed method in tackling the movement coupling and de facto hinge problems, and it can also be seen that, owing to the parametric geometric description of the flexibly deformable features, the design result composed of multiple features can be directly and precisely generated in CAD systems without tedious topology extraction.

Key words: compliant mechanism, topology optimization, feature driven, input and output coupling terms, de facto hinge

中图分类号:

TH122

蔡守宇, 张倩倩, 徐文涛, 周文尚. 多输入多输出柔顺机构的特征驱动拓扑优化设计[J]. 机械工程学报, 2026, 62(13): 283-293.

CAI Shouyu, ZHANG Qianqian, XU Wentao, ZHOU Wenshang. Feature-driven Topology Optimization Design of Multi-input-multi-output Compliant Mechanism[J]. Journal of Mechanical Engineering, 2026, 62(13): 283-293.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I13/283

参考文献

[1] HOWELL L L. Compliant mechanisms[M]. London：Springer-Verlag，2013.
[2] 牛斌，于浩俣. 基于归一化傅里叶描述子的柔性翼肋结构指定变形设计[J]. 机械工程学报，2025，61(9)：123-131. NIU Bin，YU Haoyu. Design optimization of flexible airfoil rib structures for the specified deformation based on normalized fourier descriptors[J]. Journal of Mechanical Engineering，2025，61(9)：123-131.
[3] 潘杰，于靖军，裴旭. 柔性手爪机构设计与变刚度技术研究发展综述[J]. 机械工程学报，2024，60(13)：281-296. PAN Jie，YU Jingjun，PEI Xu. Development of flexible gripper mechanism design and variable stiffness technology research[J]. Journal of Mechanical Engineering，2024，60(13)：281-296.
[4] 卢清华，亢诗迪，陈为林，等. 基于柔顺铰链拓扑优化的桥式位移放大机构设计、分析与实验测试[J]. 机械工程学报，2022，58(11)：57-71. LU Qinghua，KANG Shidi，CHEN Weilin，et al. Design，analysis and experimental test of the bridge-type displacement amplification mechanism based on the topology optimization of flexure hinge[J]. Journal of Mechanical Engineering，2022，58(11)：57-71.
[5] 王振海，张卫红. 柔性结构拓扑优化设计发展概况[J]. 机械设计，2004，21(3)：1-4. WANG Zhenhai，ZHANG Weihong. Topological optimization design for flexible structure[J]. Journal of Machine Design，2004，21(3)：1-4.
[6] ZHANG X M，ZHU B L. Topology optimization of compliant mechanisms[M]. Singapore：Springer-Verlag，2018.
[7] XIA S H，GONG T，CHEN B C，et al. Topology optimization for rigid and compliant hybrid mechanisms[J]. Computer Methods in Applied Mechanics and Engineering，2024，424：116909.
[8] 许洁，高杰，肖蜜，等. 基于等几何拓扑优化的柔性机构设计[J]. 机械工程学报，2024，60(1)：137-148. XU Jie，GAO Jie，XIAO Mi，et al. Design of compliant mechanisms by topology optimization based on isogeometric analysis[J]. Journal of Mechanical Engineering，2024，60(1)：137-148.
[9] XIA S H，WANG N F，CHEN B C，et al. Topology optimization of compliant mechanisms including links，supports and material distribution[J]. Computers and Structures，2024，291：107210.
[10] ANANTHASURESH G K，KOTA S，KIKUCHI N. Strategies for systematic synthesis of compliant MEMS[C]. Proceedings of the ASME winter annual meeting，1994：677-686.
[11] SIGMUND O. On the design of compliant mechanisms using topology optimization[J]. Mechanics of Structures and Machines，1997，25(4)：493-524.
[12] FRECKER M，KIKUCHI N，KOTA S. Topology optimization of compliant mechanisms with multiple outputs[J]. Structural Optimization，1999，17(4)：269-278.
[13] WANG M Y，CHEN S K，WANG X M，et al. Design of multimaterial compliant mechanisms using level-set methods[J]. Journal of Mechanical Design，2005，127(5)：941-956.
[14] ANSOLA R，VEGUERIA E，CANALES J，et al. A simple evolutionary topology optimization procedure for compliant mechanism design[J]. Finite Elements in Analysis and Design，2007，44(1-2)：53-62.
[15] 魏鹏，何磊，许伟鹏，等. 基于水平集带方法的柔顺机构拓扑优化研究[J]. 华南理工大学学报，2024，52(3)：93-101. WEI Peng，HE Lei，XU Weipeng，et al. Research on topological optimization of compliant mechanisms based on the level set band method[J]. Journal of South China University of Technology，2024，52(3)：93-101.
[16] 何健，何猛，夏凉，等. 基于双向渐进结构优化法的柔性机构设计[J]. 机械工程学报，2021，57(19)：39-47. HE Jian，HE Meng，XIA Liang，et al. Design of compliant actuation mechanisms by evolutionary structural optimization method[J]. Journal of Mechanical Engineering，2021，57(19)：39-47.
[17] ZHU B L，ZHANG X M，ZHANG H C，et al. Design of compliant mechanisms using continuum topology optimization：A review[J]. Mechanism and Machine Theory，2020，143：103622.
[18] EMMENDOERFER J H，MAUTE K，FANCELLO E A，et al. A level set-based optimized design of multi-material compliant mechanisms considering stress constraints[J]. Computer Methods in Applied Mechanics and Engineering，2022，391：114556.
[19] SELTMANN S，HASSE A. Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints[J]. Mechanism and Machine Theory，2023，180：105133.
[20] 荣见华，彭罗，易继军，等. 一种新的多输入多输出柔顺机构拓扑优化方法[J]. 长沙理工大学学报，2021，18(1)：66-78. RONG Jianhua，PENG Luo，YI Jijun，et al. A new topology optimization method for multi-input-multi-output compliant mechanisms[J]. Journal of Changsha University of Science & Technology，2021，18(1)：66-78.
[21] 乔赫廷，武双双，闫明，等. 基于转动约束策略的柔顺机构拓扑优化[J]. 机械工程学报，2023，59(1)：82-90. QIAO Heting，WU Shuangshuang，YAN Ming，et al. Topology optimization of compliant mechanisms based on rotation constraint strategy[J]. Journal of Mechanical Engineering，2023，59(1)：82-90.
[22] 张宪民，陈永健. 多输入多输出柔顺机构拓扑优化及输出耦合的抑制[J]. 机械工程学报，2006，41(3)：162-165. ZHANG Xianmin，CHEN Yongjian. Topology optimization of multiple inputs and outputs compliant mechanisms with coupling terms control[J]. Journal of Mechanical Engineering，2006，41(3)：162-165.
[23] LU Y F，TONG L Y. Topology and orientation optimization of multi-material hinge-free composite compliant mechanisms under multiple design-dependent loadings[J]. Structural and Multidisciplinary Optimization，2024，67(2)：17.
[24] ZHU B L，CHEN Q，JIN M H，et al. Design of fully decoupled compliant mechanisms with multiple degrees of freedom using topology optimization[J]. Mechanism and Machine Theory，2018，126：413-428.
[25] RONG J H，RONG X P，PENG L，et al. A new method for optimizing the topology of hinge-free and fully decoupled compliant mechanisms with multiple inputs and multiple outputs[J]. International Journal for Numerical Methods in Engineering，2021，122(12)：2863-2890.
[26] 付永清，张宪民. 结构及柔顺机构拓扑优化设计中的拓扑图提取[J]. 力学进展，2006，36(1)：75-84. FU Yongqing，ZHANG Xianmin. Topology extraction in the topology optimization design for structures and compliant mechanisms[J]. Advances in Mechanics，2006，36(1)：75-84.
[27] 付永清，朱健璎，金周晟. 柔顺机构拓扑优化设计中的拓扑图提取综述[J]. 组合机床与自动化加工技术，2017(5)：1-4. FU Yongqing，ZHU Jianying，JIN Zhousheng. Topology extraction synthesis in the topology optimization design of compliant mechanisms[J]. Modular Machine Tool & Automatic Manufacturing，2017(5)：1-4.
[28] CAI S Y，ZHOU W S，WEI H T，et al. Topology optimization design of multi-input-multi-output compliant mechanisms with hinge-free characteristic and totally decoupled kinematics[J]. Applied Sciences，2023，13(7)：4627.
[29] ZHANG W H，ZHOU Y. Feature-driven approach for structural optimization design[M]. Shanghai：Shanghai Jiao Tong University Press，2022.
[30] ZHOU Y，ZHANG W H，ZHU J H，et al. Feature-driven topology optimization method with signed distance function[J]. Computer Methods in Applied Mechanics and Engineering，2016，310：1-32.
[31] ZHANG W H，ZHOU Y，ZHU J H. A comprehensive study of feature definitions with solids and voids for topology optimization[J]. Computer Methods in Applied Mechanics and Engineering，2017，325：289-313.
[32] GUO X，ZHANG W S，ZHONG W L. Doing topology optimization explicitly and geometrically—A new moving morphable components based framework[J]. Journal of Applied Mechanics，2014，81(8)：081009.
[33] DU Z L，CUI T C，LIU C，et al. An efficient and easy-to-extend Matlab code of the moving morphable component (MMC) method for three-dimensional topology optimization[J]. Structural and Multidisciplinary Optimization，2022，65(5)：158.
[34] ZHANG W S，YANG W Y，ZHOU J H，et al. Structural topology optimization through explicit boundary evolution[J]. Journal of Applied Mechanics，2017，84(1)：011011.
[35] CAI S Y，ZHANG W H. An adaptive bubble method for structural shape and topology optimization[J]. Computer Methods in Applied Mechanics and Engineering，2020，360：112778.
[36] CAI S Y，ZHANG H L，ZHANG W H. An integrated design approach for simultaneous shape and topology optimization of shell structures[J]. Computer Methods in Applied Mechanics and Engineering，2023，415：116218.
[37] ZHU B L，WANG R X，WANG N F，et al. Explicit structural topology optimization using moving wide Bezier components with constrained ends[J]. Structural and Multidisciplinary Optimization，2021，64：53-70.
[38] ZHU B L，WANG R X，LIANG J W，et al. Design of compliant mechanisms：An explicit topology optimization method using end-constrained spline curves with variable width[J]. Mechanism and Machine Theory，2022，171：104713.
[39] CAI S Y，ZHANG W H，ZHU J H，et al. Stress constrained shape and topology optimization with fixed mesh：A B-spline finite cell method combined with level set function[J]. Computer Methods in Applied Mechanics and Engineering，2014，278：361-387.
[40] SVANBERG K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering，1987，24(2)：359-373.