二自由度柔性铰链连杆机构的设计方法与综合特性研究
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摘要
柔性机构作为现代机构学的一个重要分支，已成为很多学者研究的热点。柔性机构具有无摩擦、无间隙、噪声小等诸多优点，能够满足现代机械的要求，这也使得柔性机构在微机电系统（MEMS）、航空航天、生物医学等众多高科技领域得到广泛的应用。但柔性机构的设计理论和方法不够成熟，还有待完善。目前，很多学者对柔性铰链四杆机构的设计方法、动力学特性、优化设计等方面进行了较为深入的研究，但针对二自由度柔性铰链连杆机构的研究相对较少。而二自由度柔性铰链连杆机构是研究三自由度柔性连杆机构和其它空间柔性机构的基础。本文的研究成果将为进一步研究其它更为复杂的柔性机构提供理论支持。
本文选择以连杆作为结构单元的二自由度柔性铰链机构作为主要的研究对象，重点研究该机构的设计方法、动力学特性、可靠性和优化设计。
首先，柔性铰链作为柔性机构的四种基本组成元素之一，是柔性机构最重要的组成部分，决定了整个柔性机构的特殊性能。因此，本文分别对三种柔性铰链的柔度、精度特性、切口附近的最大应力进行了理论分析，得出了计算公式，并将对不同结构参数代入到计算公式进行求解。对精度特性和切口附近的最大应力进行了仿真实验，得出了精度特性和切口附近的最大应力随柔性铰链的结构参数之间的变化规律，并将切口附近的最大应力的理论分析值与仿真数据进行了对比分析，证明了理论推导的准确性。
其次，本文对三种柔性连杆机构的设计方法进行了研究，首次提出了二自由度柔性铰链六杆机构。三种连杆机构的研究方法基本相同：先根据虚功原理建立柔性机构的伪刚体模型，得出设计的普遍公式；然后在伪刚体模型的基础上建立拟柔性模型；最后对二自由度柔性铰链六杆机构进行仿真实验，并将实验结果和理论计算结果进行对比。
再次，对柔性连杆机构的综合特性进行了研究。进行动力学特性分析时，研究了三种机构的动力学特性，重点研究了二自由度柔性铰链五杆机构，得出了固有频率的计算方法。同时对该机构进行了仿真研究，得出了多阶振型的固有频率和幅频特性。研究可靠性时，先对基础理论进行了归纳和总结，接着对二自由度柔性铰链五杆机构进行了实例和仿真研究。仿真研究主要分析了仿真次数、载荷均值和宽度均值对可靠度的影响，并将仿真数据绘制成曲线，得出了四者之间的变化规律。
最后，开展了优化设计方面的研究工作。建立以追求柔性铰链的性能最优为目标和以追求整个机构的质量最小为目标的优化设计的数学模型，并对优化设计的数学模型进行了求解。
Compliant mechanisms as an important branch of modern mechanisms, have become theresearch focus for many scholars. Compliant mechanism have no friction, no clearance, littlenoise and many other advantages, it can meet the requirements of modern mechanical.Compliant mechanisms have been widely used in micro-electromechanical systems (MEMS),aerospace, biomedical and many other high-tech fields. Compliant mechanisms design theoryand methods are not mature enough yet to be perfected. At present, many scholars haveresearched on the design methods, dynamic, optimal design for the four-bar flexible hingemechanisms. But relatively few research on the two degrees of freedom of the flexiblehinge-bar mechanisms. Two degrees of freedom of the flexible hinge-bar mechanisms is thebasis of the three degrees of freedom of flexible hinge mechanisms and other flexible spacemechanisms. The result of this paper provides some theoretical support for the further studyon other more complex compliant mechanisms.
This paper have chosen the bar linkage as a structural unit of the two degrees of freedomcompliant mechanism as the main object of study, focus on the design method, dynamics,reliability and optimal design of the two degrees of freedom of the flexible hinge-barmechanisms.
Firstly, flexible hinge is one of the four basic elements of compliant mechanisms, and isthe most important part of compliant mechanisms, and determines the special behavior ofwhole compliant mechanisms. Therefore, this paper studies on flexibility, precisioncharacteristics and the maximum stress near the notch of three kinds of flexible hinge.Simulation experiment is also processed on precision characteristics and the maximum stressnear the notch, precision characteristics and the maximum stress near the notch with variation between the structural parameters of flexible hinge is gained, and theoretical analysis of valueand simulation data is compared, and it proves the accuracy of the theoretical derivation.
Secondly, this paper research on design method of three kinds of flexible hinge-barmechanisms, first proposed the two degrees of freedom of the flexible hinge six-barmechanisms. The research methods used by the three kinds of flexible hinge-bar mechanismsis basically the same: firstly, pseudo-rigid body model of the compliant mechanisms is created,according to the principle of virtual work. And draw the design of the universal formula; thenthe imitate-compliant-body model is created, which is on the basis of pseudo-rigid bodymodel. Finally, simulation experiment of the two degrees of freedom flexible hinge six-barmechanisms is also processed. And the simulation result and the theoretical computationresults are contrasted.
Again, this paper researches the synthetic characteristics of the flexible hinge-barmechanisms the integrated nature of the flexible bar linkage. It researches on the dynamicscharacteristics of three mechanisms. It focuses on the two degrees of freedom of the flexiblehinge five-bar mechanisms, the method of calculation of natural frequency is gained. Andsimulation research is also processed on the mechanisms, natural frequency andfrequency-amplitude characteristic under multiple vibration modeis is also gained. It firstlyresearches the conclusion and summary of basic theory when involves reliability.Then itresearches on the example and simulation of two degrees of freedom of the flexible hingefive-bar mechanisms. It researches the number of simulation, average load and average widthwhich impact on reliability, and simulation data is plotted as a curve, variation law is obtainedbetween the four.
Finally, optimal design research is also processed. The mathematical model of theoptimal design, which pursuit the performance optimization and pursuit the least value ofmass, is established. The solution of mathematical models of optimal design is obtained.
本文选择以连杆作为结构单元的二自由度柔性铰链机构作为主要的研究对象，重点研究该机构的设计方法、动力学特性、可靠性和优化设计。
首先，柔性铰链作为柔性机构的四种基本组成元素之一，是柔性机构最重要的组成部分，决定了整个柔性机构的特殊性能。因此，本文分别对三种柔性铰链的柔度、精度特性、切口附近的最大应力进行了理论分析，得出了计算公式，并将对不同结构参数代入到计算公式进行求解。对精度特性和切口附近的最大应力进行了仿真实验，得出了精度特性和切口附近的最大应力随柔性铰链的结构参数之间的变化规律，并将切口附近的最大应力的理论分析值与仿真数据进行了对比分析，证明了理论推导的准确性。
其次，本文对三种柔性连杆机构的设计方法进行了研究，首次提出了二自由度柔性铰链六杆机构。三种连杆机构的研究方法基本相同：先根据虚功原理建立柔性机构的伪刚体模型，得出设计的普遍公式；然后在伪刚体模型的基础上建立拟柔性模型；最后对二自由度柔性铰链六杆机构进行仿真实验，并将实验结果和理论计算结果进行对比。
再次，对柔性连杆机构的综合特性进行了研究。进行动力学特性分析时，研究了三种机构的动力学特性，重点研究了二自由度柔性铰链五杆机构，得出了固有频率的计算方法。同时对该机构进行了仿真研究，得出了多阶振型的固有频率和幅频特性。研究可靠性时，先对基础理论进行了归纳和总结，接着对二自由度柔性铰链五杆机构进行了实例和仿真研究。仿真研究主要分析了仿真次数、载荷均值和宽度均值对可靠度的影响，并将仿真数据绘制成曲线，得出了四者之间的变化规律。
最后，开展了优化设计方面的研究工作。建立以追求柔性铰链的性能最优为目标和以追求整个机构的质量最小为目标的优化设计的数学模型，并对优化设计的数学模型进行了求解。
Compliant mechanisms as an important branch of modern mechanisms, have become theresearch focus for many scholars. Compliant mechanism have no friction, no clearance, littlenoise and many other advantages, it can meet the requirements of modern mechanical.Compliant mechanisms have been widely used in micro-electromechanical systems (MEMS),aerospace, biomedical and many other high-tech fields. Compliant mechanisms design theoryand methods are not mature enough yet to be perfected. At present, many scholars haveresearched on the design methods, dynamic, optimal design for the four-bar flexible hingemechanisms. But relatively few research on the two degrees of freedom of the flexiblehinge-bar mechanisms. Two degrees of freedom of the flexible hinge-bar mechanisms is thebasis of the three degrees of freedom of flexible hinge mechanisms and other flexible spacemechanisms. The result of this paper provides some theoretical support for the further studyon other more complex compliant mechanisms.
This paper have chosen the bar linkage as a structural unit of the two degrees of freedomcompliant mechanism as the main object of study, focus on the design method, dynamics,reliability and optimal design of the two degrees of freedom of the flexible hinge-barmechanisms.
Firstly, flexible hinge is one of the four basic elements of compliant mechanisms, and isthe most important part of compliant mechanisms, and determines the special behavior ofwhole compliant mechanisms. Therefore, this paper studies on flexibility, precisioncharacteristics and the maximum stress near the notch of three kinds of flexible hinge.Simulation experiment is also processed on precision characteristics and the maximum stressnear the notch, precision characteristics and the maximum stress near the notch with variation between the structural parameters of flexible hinge is gained, and theoretical analysis of valueand simulation data is compared, and it proves the accuracy of the theoretical derivation.
Secondly, this paper research on design method of three kinds of flexible hinge-barmechanisms, first proposed the two degrees of freedom of the flexible hinge six-barmechanisms. The research methods used by the three kinds of flexible hinge-bar mechanismsis basically the same: firstly, pseudo-rigid body model of the compliant mechanisms is created,according to the principle of virtual work. And draw the design of the universal formula; thenthe imitate-compliant-body model is created, which is on the basis of pseudo-rigid bodymodel. Finally, simulation experiment of the two degrees of freedom flexible hinge six-barmechanisms is also processed. And the simulation result and the theoretical computationresults are contrasted.
Again, this paper researches the synthetic characteristics of the flexible hinge-barmechanisms the integrated nature of the flexible bar linkage. It researches on the dynamicscharacteristics of three mechanisms. It focuses on the two degrees of freedom of the flexiblehinge five-bar mechanisms, the method of calculation of natural frequency is gained. Andsimulation research is also processed on the mechanisms, natural frequency andfrequency-amplitude characteristic under multiple vibration modeis is also gained. It firstlyresearches the conclusion and summary of basic theory when involves reliability.Then itresearches on the example and simulation of two degrees of freedom of the flexible hingefive-bar mechanisms. It researches the number of simulation, average load and average widthwhich impact on reliability, and simulation data is plotted as a curve, variation law is obtainedbetween the four.
Finally, optimal design research is also processed. The mathematical model of theoptimal design, which pursuit the performance optimization and pursuit the least value ofmass, is established. The solution of mathematical models of optimal design is obtained.
引文
[1] Larry L Howell. Compliant Mechanisms[M]. John Wiley & Sons, 2001.
[2]于靖军,裴旭,毕树生等.柔性铰链机构设计方法的研究进展[J].机械工程学报,2010, 46(13): 2.13.
[3]张志丹.柔性机构动力学实验研究[D].北京工业大学, 2010.
[4] N. Lobontiu, J. S. N. Paine, E. O. Malley, etc. Parabolic and Hyperbolic Flexure Hinges:Flexibility, Motion Precision and Stress Characterization Based on ComplianceClosed-form Equations. Precision Engineering，2002, 26(2): 183-192.
[5] Paros J. M, Weisboro L. How to Design Flexure Hinges. Machine design, 1965, 37(27):151-157.
[6] Lobontiu, Nicolae, Paine, Jeffrey S N. Design of Symmetric Conic-Section FlexureHinges Based on Closed-form Compliance Equations[J]. Mechanism and MachineTheory, 2002, 37(5): 477-498.
[7] RUY J W, GWEON D G. Error Analysis of A Flexure Hinge Mechanism Induced byMachining Imperfection[J]. Precision Engineering, 2001, 21(4): 83-89.
[8] Yuen Kuan Yong, Tien-Fu Lu. Kinetostatic Modeling of 3-RRR Compliant Micro-Motion Stages with Flexure Hinges[J]. Mechanism and Machine Theory, 2009, 44(6): 1156-1175.
[9]张志杰,袁怡宝.单边导角形柔性铰链的计算与性能分析[J].光学精密工程, 2007,15(3): 384-389.
[10]王纪武,陈恳,李嘉等.典型柔性铰链精度性能的研究[J].清华大学学报(自然科学版), 2001, 41(11): 49-52.
[11]赵宏哲,毕树生,于靖军.三角形柔性铰链的建模与分析[J].机械工程学报, 2009,45(8): 1-5.
[12]陈贵敏,韩琪.深切口椭圆柔性铰链[J].光学精密工程, 2009, 17(3): 570-575.
[13]吴鹰飞,周兆英.柔性铰链的设计计算[J].工程力学, 2002, 19(6): 136-140.
[14]刘庆玲.变截面柔性铰链变形分析计算方法[J].机械设计, 2010, 27(4): 14-16.
[15]Howell L.L., Midha A. A Method for The Design of Compliant Mechanisms withSmall-length Flexure Pivots[J]. ASME Journal of Mechanical Design, 1994, 116(3):280-290.
[16]Midha A., Norton TW, Howell L. L. On the Nomenclature，Classification andAbstractions of Compliant Mechanism[J]. ASME Journal of Mechanical Design, 1994,116(1): 270-279.
[17]Midha. Limit Positions of Compliant Mechanisms Using the Pseudo-rigid-body ModelConcept[J]. 2001, 93(7): 99-115.
[18]Engin Tan k, Eres S ylemez. Analysis and Design of A Compliant Variable StrokeMechanism[J]. Mechanism and Machine Theory, 2010, 45(10): 1385-1394.
[19]Hafez Tari, Hai-Jun Su. A Complex Solution Framework for The Kinetostatic Synthesisof A Compliant Four-bar Mechanism[J]. Mechanism and Machine Theory, 2011, 46(8):1137-1152.
[20]于靖军,毕树生,宗光华等.基于伪刚体模型法的全柔性机构位置分析[J].机械工程学报, 2002, 38(2): 75-78.
[21]于靖军,宗光华,毕树生.全柔性机构与MEMS[J].光学精密工程, 2001, 9(1): 1-5.
[22]黄则兵,葛文杰,马利娥.柔性机构的研究现状及其在仿生领域的应用前景[J].机械设计与研究, 2004, 20(z1): 279-282.
[23]邱丽芳,刘庆玲,翁海珊等.微型双自由度全柔性五杆机构设计与分析[J].农业机械学报, 2010, 41(3): 195-199.
[24]邱丽芳,翁海珊,柳林等.全柔性四杆机构伪刚体模型分析计算方法的改进[J].农业机械学报,2008, 39(5): 142-145.
[25]邱丽芳,翁海珊,俞必强等.不完全分布柔度柔性机构拟柔性模型研究[J].农业机械学报, 2009, 40(4): 189-192.
[26]宗光华,裴旭,于靖军等.一种新型柔性直线导向机构及其运动精度分析[J].光学与精密工程, 2008, 16(4): 630-635.
[27]宗光华,于志伟,毕树生等.直角切口柔性铰链平行四杆机构的屈曲分析[J].航空学报, 2007, 2(3): 729-734.
[28]胡俊峰,张宪民.一种新型两自由度柔性并联机械手的优化设计[J].机器人, 2010,32(4): 459-463.
[29]冯忠磊,余跃庆,王雯静.柔性机构中大变形柔性梁的2自由度伪刚体模型[J].机械设计与研究, 2010, 26(3): 41-48.
[30]Y.Q.Yu, L. L. Howell, Y. Yue，et al. Dynamic Modeling of Compliant Mechanisms Basedon the Pseudo-Rigid-Body Model[J]. ASME Trans. on Mechanisms Design. 2005, 127(4):760-765.
[31]M. L. Scott, L. L. Howell. Dynamic Response of Compliant Mechanisms Using thePseudo-Rigid-Body Model[J]. Proceedings of DETC 97 ASME Design EngineeringTechnical Conference, 1997, Sacramento Canifornia: 78-91.
[32]P. R. Ouyang. A Spatial Hybrid Motion Compliant Mechanism: Design andOptimization[J]. Mechatronics, 2011, 21(3): 479-489.
[33]范叶森,王三民,袁茹等.集中式柔性机构动力学等效分析方法研究[J].机械科学与技术, 2007, 26(7): 880-884.
[34]王华伟,余跃庆,苏丽颖等.柔顺机构动力学建模新方法[J].机械工程学报, 2008,44(10): 96-103.
[35]杨东武,段宝岩,狄建杰.柔性机构的动力学综合法建模与分析[J].机械设计与研究, 2004, 20(6): 22-24.
[36]于靖军,周强,毕树生等.基于动力学性能的全柔性机构优化设计[J].机械工程学报, 2003, 39(8): 32-36.
[37]于靖军,毕树生,宗光华等.全柔性机器人机构结构动力学分析方法研究[J].机械工程学报, 2004, 40(8): 54-58.
[38]王雯静.柔性机构动力学分析与综合[D].北京工业大学, 2009.
[39]王雯静,余跃庆.基于有限元法的柔性机构动力学分析[J].机械工程学报, 2010,46(9): 80-86.
[40]Ananthasuresh. Topology Optimization for Synthesis of Contact-aided CompliantMechanisms Using Regularized Contact Modeling[J]. Computers and Structures, 1997,2(24): 1267-1290.
[41]Frecker. Topology Optimization of Compliant Mechanical Amplifiers for PiezoelectricActuators[J]. Structural and Multidisciplinary Optimization, 2000, 20(4): 269-279.
[42]G. K. Lau, H. Du，M. K. Lim. Use of Functional Specifications as Objective Functions inTopological Optimization of Compliant Mechanisms[J]. Comput. Methods Appl. Mech.Engrg. 2001, 190(2): 4421-4433.
[43]Wilfredo Montealegre Rubio, Shinji Nishiwaki, Emilio Carlos Nelli Silva. Design ofCompliant Mechanisms Considering Thermal Effect Compensation and TopologyOptimization[J]. Finite Elements in Analysis and Design, 2010, 46(12): 1049-1060.
[44]Gang-Won Jang, Kyung Joo Kim，Yoon Young Kim. Integrated Topology and ShapeOptimization Software for Compliant MEMS Mechanism Design[J]. Advances inEngineering Software, 2008, 39(1): 1-14.
[45]张宪民.柔性机构拓扑优化设计[J].机械工程学报, 2003, 39(11): 47-51.
[46]张宪民,陈永健.多输入多输出柔性机构拓扑优化及输出耦合的抑制[J].机械工程学报, 2006, 42(3): 162-165.
[47]Zhang Xian-min, Ouyang Gao-Fei. Level Set Method and Its Applications to TopologyOptimization of Compliant Mechanisms[J]. Journal of South China University ofTechnology（Natural Science Edition）, 2007, 35(10): 26-36.
[48]葛文杰,朱鹏刚,刘世丽等.基于柔性机构的机翼前缘变形多目标优化[J].西北工业大学学报, 2010, 28(2): 211-217.
[49]占金青,张宪民.基于基础结构法的柔性机构可靠性拓扑优化[J].机械工程学报,2010, 46(13): 42-47.
[50]李海燕,张宪民,彭惠青.柔性机构的疲劳可靠性优化设计[J].中国机械工程，2004,15(23): 2130-2133.
[51]郭为忠,裴灵，高峰.平面轨迹输出柔性机构的形状优化[J].机械工程学报, 2009,45(12): 1-6.
[52]罗维,李瑞琴,刘伟杰.二自由度柔性铰链六杆机构的设计与分析[J].机械传动,2011, 36(3): 35-39.
[53]王汝慧,李瑞琴.混合驱动六杆机构的轨迹特性及优化设计[J].机械设计与研究,2009, 25(2): 40-43.
[54]李瑞琴，邹慧君.可控机构的分类及应用[J].机械设计与研究, 2002, 18(4): 17-19.
[55]冯忠磊.柔性机构的2R伪刚体模型研究[D].北京工业大学, 2010.
[56]刘青.柔性铰链四杆机构变形分析与仿真[D].兰州理工大学, 2011.
[57]李世峻.柔性铰链静动力学、疲劳寿命及可靠性分析研究[D].西安电子科技大学,2006.
[58]丁霖冲,白广忱.柔性机构运动可靠性分析理论、方法与仿真[J].动力学与控制学报,2004, 2(2): 15-18.
[59]王春香,冯慧忠. MATLAB软件在机械优化设计中的应用[J].机械设计, 2004, 21(7):52-54.
[60]罗维,李瑞琴.机构优化设计综述与研究[J].现代机械, 2011, (3): 47-51.
[2]于靖军,裴旭,毕树生等.柔性铰链机构设计方法的研究进展[J].机械工程学报,2010, 46(13): 2.13.
[3]张志丹.柔性机构动力学实验研究[D].北京工业大学, 2010.
[4] N. Lobontiu, J. S. N. Paine, E. O. Malley, etc. Parabolic and Hyperbolic Flexure Hinges:Flexibility, Motion Precision and Stress Characterization Based on ComplianceClosed-form Equations. Precision Engineering，2002, 26(2): 183-192.
[5] Paros J. M, Weisboro L. How to Design Flexure Hinges. Machine design, 1965, 37(27):151-157.
[6] Lobontiu, Nicolae, Paine, Jeffrey S N. Design of Symmetric Conic-Section FlexureHinges Based on Closed-form Compliance Equations[J]. Mechanism and MachineTheory, 2002, 37(5): 477-498.
[7] RUY J W, GWEON D G. Error Analysis of A Flexure Hinge Mechanism Induced byMachining Imperfection[J]. Precision Engineering, 2001, 21(4): 83-89.
[8] Yuen Kuan Yong, Tien-Fu Lu. Kinetostatic Modeling of 3-RRR Compliant Micro-Motion Stages with Flexure Hinges[J]. Mechanism and Machine Theory, 2009, 44(6): 1156-1175.
[9]张志杰,袁怡宝.单边导角形柔性铰链的计算与性能分析[J].光学精密工程, 2007,15(3): 384-389.
[10]王纪武,陈恳,李嘉等.典型柔性铰链精度性能的研究[J].清华大学学报(自然科学版), 2001, 41(11): 49-52.
[11]赵宏哲,毕树生,于靖军.三角形柔性铰链的建模与分析[J].机械工程学报, 2009,45(8): 1-5.
[12]陈贵敏,韩琪.深切口椭圆柔性铰链[J].光学精密工程, 2009, 17(3): 570-575.
[13]吴鹰飞,周兆英.柔性铰链的设计计算[J].工程力学, 2002, 19(6): 136-140.
[14]刘庆玲.变截面柔性铰链变形分析计算方法[J].机械设计, 2010, 27(4): 14-16.
[15]Howell L.L., Midha A. A Method for The Design of Compliant Mechanisms withSmall-length Flexure Pivots[J]. ASME Journal of Mechanical Design, 1994, 116(3):280-290.
[16]Midha A., Norton TW, Howell L. L. On the Nomenclature，Classification andAbstractions of Compliant Mechanism[J]. ASME Journal of Mechanical Design, 1994,116(1): 270-279.
[17]Midha. Limit Positions of Compliant Mechanisms Using the Pseudo-rigid-body ModelConcept[J]. 2001, 93(7): 99-115.
[18]Engin Tan k, Eres S ylemez. Analysis and Design of A Compliant Variable StrokeMechanism[J]. Mechanism and Machine Theory, 2010, 45(10): 1385-1394.
[19]Hafez Tari, Hai-Jun Su. A Complex Solution Framework for The Kinetostatic Synthesisof A Compliant Four-bar Mechanism[J]. Mechanism and Machine Theory, 2011, 46(8):1137-1152.
[20]于靖军,毕树生,宗光华等.基于伪刚体模型法的全柔性机构位置分析[J].机械工程学报, 2002, 38(2): 75-78.
[21]于靖军,宗光华,毕树生.全柔性机构与MEMS[J].光学精密工程, 2001, 9(1): 1-5.
[22]黄则兵,葛文杰,马利娥.柔性机构的研究现状及其在仿生领域的应用前景[J].机械设计与研究, 2004, 20(z1): 279-282.
[23]邱丽芳,刘庆玲,翁海珊等.微型双自由度全柔性五杆机构设计与分析[J].农业机械学报, 2010, 41(3): 195-199.
[24]邱丽芳,翁海珊,柳林等.全柔性四杆机构伪刚体模型分析计算方法的改进[J].农业机械学报,2008, 39(5): 142-145.
[25]邱丽芳,翁海珊,俞必强等.不完全分布柔度柔性机构拟柔性模型研究[J].农业机械学报, 2009, 40(4): 189-192.
[26]宗光华,裴旭,于靖军等.一种新型柔性直线导向机构及其运动精度分析[J].光学与精密工程, 2008, 16(4): 630-635.
[27]宗光华,于志伟,毕树生等.直角切口柔性铰链平行四杆机构的屈曲分析[J].航空学报, 2007, 2(3): 729-734.
[28]胡俊峰,张宪民.一种新型两自由度柔性并联机械手的优化设计[J].机器人, 2010,32(4): 459-463.
[29]冯忠磊,余跃庆,王雯静.柔性机构中大变形柔性梁的2自由度伪刚体模型[J].机械设计与研究, 2010, 26(3): 41-48.
[30]Y.Q.Yu, L. L. Howell, Y. Yue，et al. Dynamic Modeling of Compliant Mechanisms Basedon the Pseudo-Rigid-Body Model[J]. ASME Trans. on Mechanisms Design. 2005, 127(4):760-765.
[31]M. L. Scott, L. L. Howell. Dynamic Response of Compliant Mechanisms Using thePseudo-Rigid-Body Model[J]. Proceedings of DETC 97 ASME Design EngineeringTechnical Conference, 1997, Sacramento Canifornia: 78-91.
[32]P. R. Ouyang. A Spatial Hybrid Motion Compliant Mechanism: Design andOptimization[J]. Mechatronics, 2011, 21(3): 479-489.
[33]范叶森,王三民,袁茹等.集中式柔性机构动力学等效分析方法研究[J].机械科学与技术, 2007, 26(7): 880-884.
[34]王华伟,余跃庆,苏丽颖等.柔顺机构动力学建模新方法[J].机械工程学报, 2008,44(10): 96-103.
[35]杨东武,段宝岩,狄建杰.柔性机构的动力学综合法建模与分析[J].机械设计与研究, 2004, 20(6): 22-24.
[36]于靖军,周强,毕树生等.基于动力学性能的全柔性机构优化设计[J].机械工程学报, 2003, 39(8): 32-36.
[37]于靖军,毕树生,宗光华等.全柔性机器人机构结构动力学分析方法研究[J].机械工程学报, 2004, 40(8): 54-58.
[38]王雯静.柔性机构动力学分析与综合[D].北京工业大学, 2009.
[39]王雯静,余跃庆.基于有限元法的柔性机构动力学分析[J].机械工程学报, 2010,46(9): 80-86.
[40]Ananthasuresh. Topology Optimization for Synthesis of Contact-aided CompliantMechanisms Using Regularized Contact Modeling[J]. Computers and Structures, 1997,2(24): 1267-1290.
[41]Frecker. Topology Optimization of Compliant Mechanical Amplifiers for PiezoelectricActuators[J]. Structural and Multidisciplinary Optimization, 2000, 20(4): 269-279.
[42]G. K. Lau, H. Du，M. K. Lim. Use of Functional Specifications as Objective Functions inTopological Optimization of Compliant Mechanisms[J]. Comput. Methods Appl. Mech.Engrg. 2001, 190(2): 4421-4433.
[43]Wilfredo Montealegre Rubio, Shinji Nishiwaki, Emilio Carlos Nelli Silva. Design ofCompliant Mechanisms Considering Thermal Effect Compensation and TopologyOptimization[J]. Finite Elements in Analysis and Design, 2010, 46(12): 1049-1060.
[44]Gang-Won Jang, Kyung Joo Kim，Yoon Young Kim. Integrated Topology and ShapeOptimization Software for Compliant MEMS Mechanism Design[J]. Advances inEngineering Software, 2008, 39(1): 1-14.
[45]张宪民.柔性机构拓扑优化设计[J].机械工程学报, 2003, 39(11): 47-51.
[46]张宪民,陈永健.多输入多输出柔性机构拓扑优化及输出耦合的抑制[J].机械工程学报, 2006, 42(3): 162-165.
[47]Zhang Xian-min, Ouyang Gao-Fei. Level Set Method and Its Applications to TopologyOptimization of Compliant Mechanisms[J]. Journal of South China University ofTechnology（Natural Science Edition）, 2007, 35(10): 26-36.
[48]葛文杰,朱鹏刚,刘世丽等.基于柔性机构的机翼前缘变形多目标优化[J].西北工业大学学报, 2010, 28(2): 211-217.
[49]占金青,张宪民.基于基础结构法的柔性机构可靠性拓扑优化[J].机械工程学报,2010, 46(13): 42-47.
[50]李海燕,张宪民,彭惠青.柔性机构的疲劳可靠性优化设计[J].中国机械工程，2004,15(23): 2130-2133.
[51]郭为忠,裴灵，高峰.平面轨迹输出柔性机构的形状优化[J].机械工程学报, 2009,45(12): 1-6.
[52]罗维,李瑞琴,刘伟杰.二自由度柔性铰链六杆机构的设计与分析[J].机械传动,2011, 36(3): 35-39.
[53]王汝慧,李瑞琴.混合驱动六杆机构的轨迹特性及优化设计[J].机械设计与研究,2009, 25(2): 40-43.
[54]李瑞琴，邹慧君.可控机构的分类及应用[J].机械设计与研究, 2002, 18(4): 17-19.
[55]冯忠磊.柔性机构的2R伪刚体模型研究[D].北京工业大学, 2010.
[56]刘青.柔性铰链四杆机构变形分析与仿真[D].兰州理工大学, 2011.
[57]李世峻.柔性铰链静动力学、疲劳寿命及可靠性分析研究[D].西安电子科技大学,2006.
[58]丁霖冲,白广忱.柔性机构运动可靠性分析理论、方法与仿真[J].动力学与控制学报,2004, 2(2): 15-18.
[59]王春香,冯慧忠. MATLAB软件在机械优化设计中的应用[J].机械设计, 2004, 21(7):52-54.
[60]罗维,李瑞琴.机构优化设计综述与研究[J].现代机械, 2011, (3): 47-51.
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