柔顺机构动力学分析与综合
摘要
柔顺机构主要靠机构中柔性构件的变形来实现机构的运动和功能。与传统刚性机构相比,它具有减少机构重量、安装时间、间隙和摩擦磨损,提高机构精度、增加可靠性、减少维护等方面的优点,适应现代科技发展对机械设备的要求,引起了学者们的广泛关注。目前,柔顺机构的绝大部分研究都是围绕着结构和运动分析以及拓扑优化设计开展的,而在动力学方面却很少涉及。随着柔顺机构的应用范围和工作要求的不断提高,如何改善柔顺机构的动力学特性,提高柔顺机构设计水平,将成为柔顺机构领域的关键问题,此项研究具有重要的理论意义和应用价值。
本文以平面柔顺机构为研究对象,重点研究柔顺机构动力学问题,主要包括建模与特性分析、优化设计和实验研究等方面的内容。
首先,建立了以柔性铰链为主要特征的柔顺机构动力学模型。推导出四种常见柔性铰链的刚度计算公式,并分析柔性铰链各参数对其刚度的影响。在此基础上,针对平行导向柔顺机构和曲柄滑块柔顺机构,应用拉格朗日方程,建立了该柔顺机构动力学模型。
其次,建立了以柔顺杆为主要特征的柔顺机构动力学模型。首先充分考虑杆件的大变形特性,分别采用数值拟合方法和有限元方法建立了以柔顺杆为主要特征的柔顺机构动力学模型,分析了两种模型的差别和适用范围。
再次,深入分析了柔顺机构的动力学特性。计算了柔顺机构的固有频率;研究了机构参数对动力学性能的影响及其灵敏度问题;分析了柔顺杆的动态应力及应变,给出了杆件最大动应力以及发生的位置;基于动应力造成的累积疲劳损伤,预测了杆件的疲劳寿命;推导出以柔性铰链为主要特征的柔顺机构驱动力矩的计算公式,分析了柔性铰链刚度及未变形位置与驱动特性之间的内在关系。
然后,进行了柔顺机构的优化设计。根据柔顺机构的特点,探讨了柔顺机构材料的选择准则;以固有频率、驱动力矩等为约束条件,以柔性铰链的刚度最小为优化目标,对以柔性铰链为主要特征的柔顺机构进行了优化设计;还分别以柔顺机构总质量最小、变形能最大为优化目标,以固有频率、动应力等为约束条件,优化设计出了以柔顺杆为主要特征的柔顺机构。
最后,进行了柔顺机构的实验研究。设计、加工了一个平行导向柔顺机构。对该平行导向柔顺机构的固有频率及应变等问题进行了实验研究,通过实验结果与理论计算结果的对比和分析,相互验证了实验系统和理论模型的有效性和正确性。
Compliant mechanisms gain their motion from the relative flexibility of their members. Compared with conventional rigid-body mechanisms, compliant mechanisms have many advantages such as part-count reduction, reduced assembly time, simplified manufacturing processes, increased precision, reduced wear, and reduced weight. At present, compliant mechanisms have attracted much attention and become the focus of mechanisms research. They have been developed rapidly in recent years due to their advantages as required in modern machinery. Most of these works are focused on the structural and kinematic analysis and design of compliant mechanisms. However, the study of the dynamics of compliant mechanisms is lacking. With the increasing requirements of task and application, the dynamic analysis to improving the dynamic characteristics and design of compliant mechanism is a new hot topic in mechanism research. The study of the dynamic analysis of compliant mechanisms has great theoretical significance and practical value.
By taking the planar compliant mechanisms as subject investigated, the dynamics and synthesis of the compliant mechanisms are studied in aspects of dynamic modeling, dynamic analysis, optimal design and experiment verification in this dissertation.
Firstly, the dynamic models of compliant mechanisms with flexure hinges are created. The stiffness of four flexure hinges are deduced respectively, and the effect of design parameters on stiffness of flexure hinge is studied. By taking the compliant parallel-guiding mechanism and compliant slider-crank mechanism as subject investigated, the dynamic model of compliant mechanisms with flexure hinges is created based on the Lagrange equation.
Secondly, the dynamic models of compliant mechanisms with compliant links are developed. Considering the large deflection of compliant links, the numerical method and the finite element method are utilized respectively to generate the dynamic models of compliant mechanisms with compliant links. The difference and application of these models are discussed.
Thirdly, the dynamic characteristics of compliant mechanisms are investigated. Based on the proposed dynamic models of the compliant mechanisms, the natural frequency is calculated. By using direct differential method for sensitivity analysis, the effect of design parameters on dynamic characteristics is discussed. The compliant link’s dynamic stress and strain are calculated,the value and position of maximal stress were derived. Based on the cumulative damage resulted from the alternate dynamic stress, the fatigue lives of the compliant links are predicted. A new method is obtained for calculating the driving torque, it shows that the flexure hinges have impact on the driving characteristics of compliant mechanisms.
Fourthly, optimal design of compliant mechanisms is investigated. Based on the characteristics analysis, the material selection is studied. The stiffness of flexure hinge is taken as optimal design objective. The natural frequency and driving torque are taken as constraints. The optimal design of compliant mechanism with flexure hinges is performed. Then, the total compliant links mass and the total strain energy are taken as optimal design objective, respectively. The natural frequency and dynamic stresses are taken as constraints. The optimal design of compliant mechanism with compliant links is performed.
Finally, the experimental study of compliant mechanism is performed. The compliant parallel-guiding mechanism is developed. The experimental studies of natural frequency and strain are performed. The comparison between the experiment results and the theoretical results verifies the validity of the experiment system and theoretical models.
本文以平面柔顺机构为研究对象,重点研究柔顺机构动力学问题,主要包括建模与特性分析、优化设计和实验研究等方面的内容。
首先,建立了以柔性铰链为主要特征的柔顺机构动力学模型。推导出四种常见柔性铰链的刚度计算公式,并分析柔性铰链各参数对其刚度的影响。在此基础上,针对平行导向柔顺机构和曲柄滑块柔顺机构,应用拉格朗日方程,建立了该柔顺机构动力学模型。
其次,建立了以柔顺杆为主要特征的柔顺机构动力学模型。首先充分考虑杆件的大变形特性,分别采用数值拟合方法和有限元方法建立了以柔顺杆为主要特征的柔顺机构动力学模型,分析了两种模型的差别和适用范围。
再次,深入分析了柔顺机构的动力学特性。计算了柔顺机构的固有频率;研究了机构参数对动力学性能的影响及其灵敏度问题;分析了柔顺杆的动态应力及应变,给出了杆件最大动应力以及发生的位置;基于动应力造成的累积疲劳损伤,预测了杆件的疲劳寿命;推导出以柔性铰链为主要特征的柔顺机构驱动力矩的计算公式,分析了柔性铰链刚度及未变形位置与驱动特性之间的内在关系。
然后,进行了柔顺机构的优化设计。根据柔顺机构的特点,探讨了柔顺机构材料的选择准则;以固有频率、驱动力矩等为约束条件,以柔性铰链的刚度最小为优化目标,对以柔性铰链为主要特征的柔顺机构进行了优化设计;还分别以柔顺机构总质量最小、变形能最大为优化目标,以固有频率、动应力等为约束条件,优化设计出了以柔顺杆为主要特征的柔顺机构。
最后,进行了柔顺机构的实验研究。设计、加工了一个平行导向柔顺机构。对该平行导向柔顺机构的固有频率及应变等问题进行了实验研究,通过实验结果与理论计算结果的对比和分析,相互验证了实验系统和理论模型的有效性和正确性。
Compliant mechanisms gain their motion from the relative flexibility of their members. Compared with conventional rigid-body mechanisms, compliant mechanisms have many advantages such as part-count reduction, reduced assembly time, simplified manufacturing processes, increased precision, reduced wear, and reduced weight. At present, compliant mechanisms have attracted much attention and become the focus of mechanisms research. They have been developed rapidly in recent years due to their advantages as required in modern machinery. Most of these works are focused on the structural and kinematic analysis and design of compliant mechanisms. However, the study of the dynamics of compliant mechanisms is lacking. With the increasing requirements of task and application, the dynamic analysis to improving the dynamic characteristics and design of compliant mechanism is a new hot topic in mechanism research. The study of the dynamic analysis of compliant mechanisms has great theoretical significance and practical value.
By taking the planar compliant mechanisms as subject investigated, the dynamics and synthesis of the compliant mechanisms are studied in aspects of dynamic modeling, dynamic analysis, optimal design and experiment verification in this dissertation.
Firstly, the dynamic models of compliant mechanisms with flexure hinges are created. The stiffness of four flexure hinges are deduced respectively, and the effect of design parameters on stiffness of flexure hinge is studied. By taking the compliant parallel-guiding mechanism and compliant slider-crank mechanism as subject investigated, the dynamic model of compliant mechanisms with flexure hinges is created based on the Lagrange equation.
Secondly, the dynamic models of compliant mechanisms with compliant links are developed. Considering the large deflection of compliant links, the numerical method and the finite element method are utilized respectively to generate the dynamic models of compliant mechanisms with compliant links. The difference and application of these models are discussed.
Thirdly, the dynamic characteristics of compliant mechanisms are investigated. Based on the proposed dynamic models of the compliant mechanisms, the natural frequency is calculated. By using direct differential method for sensitivity analysis, the effect of design parameters on dynamic characteristics is discussed. The compliant link’s dynamic stress and strain are calculated,the value and position of maximal stress were derived. Based on the cumulative damage resulted from the alternate dynamic stress, the fatigue lives of the compliant links are predicted. A new method is obtained for calculating the driving torque, it shows that the flexure hinges have impact on the driving characteristics of compliant mechanisms.
Fourthly, optimal design of compliant mechanisms is investigated. Based on the characteristics analysis, the material selection is studied. The stiffness of flexure hinge is taken as optimal design objective. The natural frequency and driving torque are taken as constraints. The optimal design of compliant mechanism with flexure hinges is performed. Then, the total compliant links mass and the total strain energy are taken as optimal design objective, respectively. The natural frequency and dynamic stresses are taken as constraints. The optimal design of compliant mechanism with compliant links is performed.
Finally, the experimental study of compliant mechanism is performed. The compliant parallel-guiding mechanism is developed. The experimental studies of natural frequency and strain are performed. The comparison between the experiment results and the theoretical results verifies the validity of the experiment system and theoretical models.
引文
1国家自然科学基金委员会工程与材料科部.学科发展战略研究报告(2006-2010)-机械与制造学科.科学出版社, 2006
2 L. L. Howell. Compliant Mechanisms. John Wiley & Sons, 2001:1～100
3 I. Her. Methodology for Compliant Mechanisms Design. Ph.D. dissertation. Purdue University. West Lafayette. IN. 1986:19～26
4 G. M. Roach, S. M. Lyon, L. L. Howell. A Compliant Overrunning Ratchet and Pawl Clutch With Centrifugal Throw-out. Proceedings of the ASME Design Engineering Technical Conferences, 1998,Istenbul:214～226
5 G. M. Roach, L. L. Howell. Compliant Overrunning Clutch With Centrifugal Throw-out. U.S. Patent 6, 148, 979, 2000
6 R. N. Motsinger. Flexural Devices in Measurement Systems. Measurement Engineering. Phoenix, AZ, 1964
7 S. B. Tuttle. Semifixed Flexural Mechanisms, Mechanisms for Engineering Design. Wiley, 1967:40～75
8 J. M. Derderian. The Pseudo-Rigid-Body Model Concept and Its Application to Micro Compliant Mechanisms. M.S. Thesis of Brigham Young University. 1996:20～42
9 B D Jensen, L L Howell, D B Gunyan, et al. The Design and Analysis of Compliant MEMS Using the Pseudo-Rigid-Body Model. ASME international Mechanical Engineering Congress and Exposition, 1997:119～126
10 G. K. Ananthasuresh, S. Kota, Y. Gianchandani. A Methodical Approach to the Design of Compliant Micromechanisms, Solid-State Sensor and Actuator Workshop. Hilton Head Island. 1994:189～192
11 V. D. Larsen, O. Sigmund, S. Bouwstra. Design and Fabrication of Compliant Micromechanisms and Structures with Negative Poisson’s Ratio. Proceeding of the 9th Annual International Workshop on Micro Electro Mechanical Systems, 1996,San Diego: 365～371
12 D. Clements. Implementing Compliant Mechanisms in Micro-Electro-Mechanical Systems (MEMS). M. S. Thesis of Brigham Young University. 2000:61～89
13 M. B. Parkinson, B. D. Jensen, G. M. Roach, Optimization-Based Design of a Fully-Compliant Bistable Micromechanism. Proceedings of the 26th Biennial Mechanisms and Robotics Conference, 2000:146～159
14 L. G. Salmon, D. B. Gunyan, J. M. Derderian, et al. Use of the Pseudo-Rigid-Body Model toSimplify the Description of Compliant Micromechanisms. Solid-State Sensor and Actuator Workshop, 1994:136～139
15 A. Midha, M. D. Murphy, L. L. Howell. Compliant Constant-force Mechanism and Devices Formed Therein, U.S. Patent 5, 649, 454, 1995
16 G. K. Ananthasuresh, S. Kota. Designing Compliant Mechanisms, Mechanical Engineering. 1995,117(11):93～96
17 B. D. Jensen, L. L. Howell, L. G. Salmon. Design of Two-link, In-plane, Bistable Compliant Micro-mechanisms. ASME Trans. on Mechanical Design. 1999,121(3):416～423
18 M. S. Baker, S. M. Lyon, L. L. Howell. A Linear Displacement Bistable Micromechanism. Proceedings of the 26th Biennial Mechanisms and Robotics Conference, 2000:76～90
19 S. M. Lyon, M. S. Evans, P. A. Erickson, et al. Predication of the First Modal Frequency of Compliant Mechanism Using the Pseudo-Rigid-Body Model. ASME Trans. on Mechanical Design. 1999,121(3):309～313
20 C. Boyle, L. L. Howell, S. P. Magleby, et al. Dynamic Modeling of Compliant Constant-ForceCompression Mechanisms. Mechanism and Machine Theory. 2003,38: 1469～1487
21陈知泰,余跃庆,杜兆才等.柔顺机构的频率特性分析.机械设计与研究. 2005,21(6): 24～26
22 A. Midha, L. L. Howell. On the Nomenclature, Classification and Compliant Mechanism. ASME Trans. on Mechanical Design. 1994,116(2):270～279
23 G. K. Ananthasuresh, L. L. Howell. Case Studies and a Note on the Degrees-of-Freedom in Compliant Mechanisms. ASME Trans. on Transmissions and Automation. 1996,182(3):1～12
24谢先海,罗峰武,廖道训.柔顺机构自由度的一种计算方法.华中理工大学学报. 2000,28(2):40～41
25李团结.柔性机构的结构拓扑特征及其自由度分析.机械科学与技术. 2003,22(1):107～109
26 L. L. Howell, A. Midha. A Method for the Design of Compliant Mechanism With Small-Length Flexural Pivots. ASME Trans. on Mechanical Design. 1994,116(1):280～289
27 L. L. Howell, A. Midha. Evaluation of Equivalent Spring Stiffness for Use in a Pseudo Rigid Body Model of Large Deflection Compliant Mechanisms. ASME Trans. on Mechanical Design. 1996,118(1):126～140
28 L. L. Howell, A. Midha. Parametric Deflection Approximations for End Loaded Large Deflection Beams in Compliant Mechanisms. ASME Trans. on Mechanical Design. 1995,117(3):156～165
29 S. M. Lyon, L. L. Howell, G. M. Roach. Modeling Flexible Segments with Force and Moment End Loads via the Pseudo-Rigid-Body Model. Proceedings of the 2000 Design Engineering Technical Conferences, 2000:124～138
30 B. T. Edwards, B. D. Jensen, L. L. Howell. A Pseudo-Rigid-Body Model for Initially-Curved Pinned-Pinned Segments Used in Compliant Mechanisms. ASME Trans. on Mechanical Design. 2001,123(3):466～472
31 A. Midha, L. L. Howell. Limit Position of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept. Mechanism and Machine Theory. 2000,35:99～115
32李海燕,张宪民,彭惠青.大变形柔顺机构驱动特性研究.机械科学与技术. 2004,23(9):1040～1043
33 B. D. Jensen, L. L. Howell. Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints. ASME Trans. on Mechanical Design. 2004,126(1): 657～665
34 Nicolae Lobontiu, Ephrahim Garcia. Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms. ASME Trans. on Mechanical Design. 2005,127(4):766～773
35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.机械工程学报. 2002,16(2):75～78
36于靖军,毕树生,宗光华.空间全柔性机构位置分析的刚度矩阵法.北京航空航天大学学报. 2002,28(3):323～326
37 A. Saxena, G. K. Ananthasuresh. Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications. ASME Trans. on Mechanical Design. 2001,123(1):33～42
38 A. Saxena. Synthesis of Compliant Mechanisms for Path Generation Using Genetic Algorithm. ASME Trans. on Mechanical Design. 2005,127(4):745～752
39 B. W. Pedersen, T. Buhl, O. Sigmund. Topology Synthesis of Large-Displacement Compliant Mechanisms. Int. J. Numer. Mech. Engng. 2001, 50(1):2683～2705
40 Kang Tai, Guang Yu Cui, Tapabrata Ray. Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape. ASME Trans. on Mechanical Design. 2002,124(3):492～500
41邱丽芳,南铁玲,翁海珊.柔性铰链运动性能多目标优化设计.北京科技大学学报. 2008,30(2):189～192
42 L. L. Howell, A. Midha. A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms. ASME Trans. on Mechanical Design. 1996,118(1):121～125
43邱丽芳,翁海珊,柳林,南铁玲.不完全分布柔度的全柔性机构的研究.北京科技大学学报. 2007,29(增刊2):156～158
44邱丽芳,翁海珊,柳林,南铁玲.全柔性四杆机构伪刚体模型分析计算方法的改进.农业机械学报. 2008,29(5):142～145
45 S. X. Ping, S. Henty, S. Yang. Design of Compliant Microleverage Mechanisms. Sensors and Actuators. 2001,87(3):146～156
46李海燕.柔顺机构的分析及基于可靠性的优化设计.汕头大学硕士论文. 2004:40～46
47刘少芳.柔顺机构的动态拓扑优化设计.汕头大学硕士论文. 2004:14～26
48李海燕,张宪民,彭惠青.柔顺机构的疲劳可靠性优化设计.中国机械工程. 2004, 15(23):2130～2133
49 J. A. Hetrik, S. Kota. An Energy Formulation for Parametric Size and Shape Optimation of Compliant Mechanisms. ASME Trans. on Mechanical Design. 1999,121(3):229～233
50 G. K. Ananthasuresh, S. Kota, N. Kikuchi. Strategies for Systematic Synthesis of Compliant Mechanisms. ASME Trans. on Dynamic Systems and Control Division. 1994,116(2):677～686
51 M. I. Frecker, G. K. Ananthasuresh, S. Nishiwaki, et al. Topological Synthesis of Compliant Mechanisms Using Multi-Criterion Optimization. ASME Trans. on Mechanical Design. 1997, 119(1):238～245
52 O. Sigmund. Design of Multi-Physics Actuators Using Topology Optimization-PartⅠ: One-Material Structures. Comput. Methods Appl. Mech. Engrg. 2001,190(2):6577～6604
53 O. Sigmund. Design of Multi-Physics Actuators Using Topology Optimization-PartⅡ: Two-Material Structures. Comput. Methods Appl. Mech. Engrg. 2001, 190(2):6605～6627
54 Larsen, O. Sigmund. Design and Fabrication of Compliant Micro-Mechanisms and Structures with Negative Poisson’s Ratio. Journal of Microelectromechanical Systems. 1997,6(2):99～106
55 A. Saxena, G. K. Ananthasuresh. On an Optimal Property of Compliant Topologies. Structure and Multidisciplinary Optimization. 2000,19(3):36～49
56 G. K. Lau, H. Du, M. K. Lim, Use of Functional Specifications as Objective Functions in Topological Optimization of Compliant Mechanism. Comput. Methods Appl. Mech. Engrg. 2001,190(2):4421～4433
57 O. Sigmund. Design of Compliant Mechanisms Using Topology Optimization. Mechanics of Structures and Machines. 1997,25(4):495～526
58 N. Kikuchi, S. Nishiwaki, Fonseca, et al. Design Optimization Method for Compliant Mechanisms and Material Microstructure. Comput. Methods Appl. Mech. Engrg. 1998,151(1):401～417
59谢先海,廖道训.基于均匀化方法的柔顺机构的设计.中国机械工程. 2003,14(11):953～955
60罗峰武,谢先海,廖道训.柔顺机构的机械效益.湘潭矿业学院学报. 2000,15(3):41～45
61孙宝元,杨桂玉,李震.拓扑优化方法及其在微型柔性结构设计中的应用.纳米技术与精密工程. 2003,1(1):24～30
62杨桂玉.拓扑优化方法及其在微型柔性机构设计中应用的研究.大连理工大学硕士学位论文. 2004:1～14
63 G. K. Ananthasuresh, L. Yin. A Novel Topology Design Scheme for the Multi-Physics Problems of Electro-Thermally Actuated Compliant Micromechanisms. Sensors and Actuators, 2002:599～609
64刘震宇.微型及小型柔性机械结构的拓扑优化设计方法.大连理工大学博士学位论文. 2000:1～9
65梅玉林.拓扑优化的水平集方法及其在刚性结构、柔性机构和材料设计中的应用.大连理工大学博士学位论文. 2003:1～13
66李团结,曹炎,李世俊,等.平面双稳态柔性微机构的优化设计.机械科学与技术. 2004,23(6):709～711
67李团结,朱超,周小勇,等.定常力输出柔性滑块机构的优化综合.机械科学与技术. 2004,23(3):22～324
68陈永健,刘少芳.以柔顺机构作位移放大器的拓扑优化设计.汕头大学学报. 2004,19(3): 53～56
69 M. I. Frecker, G. K. Ananthasuresh, S. Nishiwaki, et al. Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization. ASME Trans. on Mechanical Design. 1997,119(4):38～245
70 A. Saxena, G. K. Ananthasuresh, On an Optimal Property of Compliant Topologies. Struct. Multidisc. Optim. 2000,19(3):36～49
71 M. L. Scott, L. L. Howell. Dynamic Response of Compliant Mechanisms Using the Pseudo-Rigid-Body Model. Proceedings of DETC 97 ASME Design Engineering Technical Conference, 1997 ,Sacramento California:78～91
72 Y. Q. Yu, L. L. Howell, Y. Yue, et al. Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model. ASME Trans. on Mechanical Design. 2005,127(4):760～765
73陈知泰.柔顺机构的动力学研究.北京工业大学硕士学位论文. 2005:1～30
74 Z. Li, S. Kota. Dynamic Analysis of Compliant Mechanisms. Proceedings of ASME 2002 Design Engineering Technical Conferences, 2002,California:1～11
75谢先海,廖道训.基于多刚体离散元模型的柔顺机构动力分析新方法.机械工程学报. 2003,39(5):953～955
76黄进,谢先海.平行导向柔顺机构的加工制造与性能测试.实验技术与管理.2000,6(1):7～9
77张策,黄永强,王子良,等.弹性连杆机构的分析与设计(第二版).机械工业出版社. 1997:59～88
78刘宏昭,曹惟庆.关于多柔体动力学与弹性机构动力学的讨论.机械设计. 1994,1(4):26～31
79 J. N. Bricout , J. C. Debus , Picheau. A Finite Element Model for the Dynamics of Flexible Manipulators. Mechanism and Machine Theory .1990,25:119～128
80 A. Q. Erdman, G. N. Sandor. A General Method for Kineto-elastodynamic Analysis and Synthesis of Mechanisms. ASME Trans. on Engineering for Industry. 1972,94(4):1193～1205
81 I. Imam, G. N. Sandor, S. N. Kramer. Deflection and Stress Analysis of High-speed Mechanisms with Elastic Links. ASME Trans. on Engineering for Industry. 1973,95(3):541～548
82 I. Imam, G. N. Sandor. A General Method of Kineto-elastodynamic Design of High-speed Mechanisms. Mechanism and Machine Theory. 1973,8:497～516
83 B. M. Bahgat, K. D. Willmert. Finite Element Vibrational Analysis of Planar Mechanism. Mechanism and Machine Theory. 1976,11:47～71
84 A. Midha, A. G. Erdman, D. A. Frohrib. Finite Element Approach to Mathematical Modeling of High-speed Elastic Linkages. Mechanism and Machine Theory. 1978,13:603～618
85 P. K. Nath, A Ghosh. Steady State Response of Mechanisms with Elastic Links by Finite Element Method. Mechanism and Machine Theory. 1980,15:199～211
86 D. A. Turcic, A. Midha. Generalized equations of motion for the dynamic analysis of elastic mechanism systems. ASME Trans. on Dynamic Systems Measurement and Control. 1984,106(3):243～248
87 D. A. Turcic, A. Midha. Dynamic Analysis of Elastic Mechanism Systems. PartⅡ: Applications. ASME Trans. on Dynamic Systems Measurement and Control. 1984,106(3):249～254
88 W. L. Cleghorn, R. G. Fenton, B. Tabarrok. Steady-state Vibration Response of High-speed Mechanisms. Mechanism and Machine Theory. 1984,19:417～423
89 J. Lieh. Dynamic Modeling of a Slider-crank Mechanism with Coupler and Joint Flexibility. Mechanism and Machine Theory. 1994,29:139～147
90 B. Fallahi, S. Lai, C. Venkat. A Finite Element Formulation of a Flexible Slider-crank Mechanism Using Local Coordinate. ASME Trans. on Mechanical Design. 1995,117(3): 329～338
91 J. N. Bricout, J. C. Debus, P. Micheau. A Finite Element Model for The Dynamics of FlexibleManipulators. Mechanism and Machine Theory. 1990,25:119～128
92商大中,曹承佳,李宏亮.考虑刚体运动与弹性运动耦合影响的旋转叶片振动有限元分析.计算力学报. 2000,17(3):330～338
93 S. M. Lin. Dynamic Analysis of Rotating Nonuiform Timoshenko Beams With an Elastically Restrained Root. ASME Trans. on Applied Mechanics. 1999,66(3):742～749
94 P. W. Links. Finite Element Appendage Equations For Hybrid Coordinate Dynamic Analysis. International Journal of Solids and Structures. 1972,8(1):709～731
95 P. W. Links. Dynamic Analydid of a System of Hinge-connected Rigid Bodies with Nonrigid Appendages. International Journal of Solids and Structures. 1973,9(2):1473～1487
96 L. Meirovitch, H. D. Nelson. High Spin Motion of Satellite Containing Elastic Parts. Journal of Spaceraft and Rocket. 1966,13(5):1597～1602
97 V. J. Modi. Attitude Dynamics of Satellite with Flexible Appendages. Journal of Spacecraft. 1972,10(9):734～751
98 C. S. Bodly. A Digital Computer Program for the Dynamic Interaction Simulation of Controls And Structure. NASA TP-1219,1978
99 H. P. Frisch. A Vector-dyadic Development of The Equations of Motion For Ncoupled Flexible Bodies and Point Mass. NASA TND-8047, 1975
100 L. Meirovitch. Dynamics and Control of Large Flexible Spacecraft. Proceedings of a Symposium Held in Blacksburg, 1977, 688～695
101 L. Meirovitch. Dynamics and Control of Large Flexible Spacecraft. Proceedings of a Symposium Held, 1977, Blacksburg:688～695
102 T. R. Kane, D. A. Levinson. Formulation of Equation of Motion for Complex Spacecrafe. Journal of Guidance Control and Dynamics. 1980,3(2):99～112
103 H. B. Hablani. Constrained and Unconstrained Mode: Some Modeling Aspects of Flexible Spacecraft. Journal of Guidance Control and Dynamics. 1982,5(2):164～198
104 P. A. Meehan, S. F. Asokanthan. Chaotic Motion in Spinning Spacecraft with Circumferential Nutational Damper. Nonlinear Dynamics. 1997,12(2):69～87
105 R. E. Roberson, R. F. Schwertassek. Dynamics of Multibody Systems. Springer-Verlag, 1988: 46～75
106林健,黄琳.大型空间结构的动力学建模与控制.力学进展. 1991,21(3):333～341
107 Z. L. Wang, J. G. Xu. On The Stability and Control of Dynamical System with Flexible Structure. Science in China. 1993,36(1):27～34
108 G. Naganathan, A. H. Soni. Nonlinear Modeling of Kinematic and Flexibility Effects in Manipulator Design. ASME Trans. on Automation in Design. 1988,110(4):243～254
109 S. G. Yue, Y. Q. Yu, S. X. Bai. Flexible Robot Beam Element for the Manipulators with Jointand Link Flexibility. Mechanism and Machine Theory. 1997,32:209～219
110王照林,王大力.多弹性连杆机器人的建模与控制.上海交通大学出版社. 1992:23～45
111 J. M. Paros, L. Weisboro. How to Design Flexure Hinges. Machine Design. 1965,37(27):151～157
112吴鹰飞,周兆英.柔性铰链的应用.中国机械工程. 2002,13(18):1615～1618
113吴鹰飞,周兆英.柔性铰链的设计计算.工程力学. 2002,19(6):136～140
114普齐米尼斯基,王德荣等译.矩阵结构分析理论.国防工业出版社. 1975:19～45
115张策,王子良等.提高连杆机构KED分析计算效率的若干问题.唐山工程技术学院学报. 1986:61～71
116 K. E. Bisshopp, D. C. Drucker. Large Deflection of Cantilever Beams. Quarterly of Applied Mathematics. 1945,3(3):272～275
117 B. A. Coulter, R. E. Miller. Numerical Analysis of a Generalized Plane Elastic with Non-linear Material Behavior. International Journal for Numerical Methods in Engineering. 1988,26(8):617～630
118 R. Frisch-Fay. Flexible Bars. Butterworth. Washington. DC. 1962:49～93
119 W. Gorski. A Review of Literature and a Bibliography on Finite Elastic Deflections of Bars. Trans. on the Institution of Engineers. 1976,18(2):74～85
120 H. B. Harrison. Post-buckling Analysis of Non-uniform Elastica Columns. International Journal for Numerical Methods in Engineering. 1973,7(7):195～210
121 K. Mattiasson. Numerical Results From Large Deflection Beam and Frame Problems Analyzed by Means of Elliptic Integrals. International Journal for Numerical Methods in Engineering. 1981,17(6):145～153
122 R. E. Miller. Numerical Analysis of a Generalized Plane Elastica. International Journal for Numerical Methods in Engineering. 1980,15(3):325～332
123 P. F. Byrd, M. D. Friedman. Handbook of Elliptic Integrals for Engineers and Physicists. Springer-Verlag. 1954:31～65
124 L. V. King. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge University Press.1924:5～67
125 H. Hancock. Elliptic Integral. Dover. New York. 1958:17～37
126 A. G. reenhill. The Applications of Elliptic Functions. Dover. New York. 1959:32～79
127吴鹰飞,周兆英.柔性铰链的应用.中国机械工程. 2002,13(18):1615～1618
128邵忍平.机械系统动力学.机械工业出版社, 2005:68～72
129余跃庆,李哲.现代机械动力学.北京工业大学出版社, 1998:230～301
130刘惟信.机械可靠性分析.清华大学出版社, 1996:268～270
131 S. Nishiwaki, M. Frecker. Topology Optimization of Compliant Mechanisms Using theHomogenization Method. Internal Journal for Numerical Methods in Engineering. 1998,42(3):535～559
2 L. L. Howell. Compliant Mechanisms. John Wiley & Sons, 2001:1～100
3 I. Her. Methodology for Compliant Mechanisms Design. Ph.D. dissertation. Purdue University. West Lafayette. IN. 1986:19～26
4 G. M. Roach, S. M. Lyon, L. L. Howell. A Compliant Overrunning Ratchet and Pawl Clutch With Centrifugal Throw-out. Proceedings of the ASME Design Engineering Technical Conferences, 1998,Istenbul:214～226
5 G. M. Roach, L. L. Howell. Compliant Overrunning Clutch With Centrifugal Throw-out. U.S. Patent 6, 148, 979, 2000
6 R. N. Motsinger. Flexural Devices in Measurement Systems. Measurement Engineering. Phoenix, AZ, 1964
7 S. B. Tuttle. Semifixed Flexural Mechanisms, Mechanisms for Engineering Design. Wiley, 1967:40～75
8 J. M. Derderian. The Pseudo-Rigid-Body Model Concept and Its Application to Micro Compliant Mechanisms. M.S. Thesis of Brigham Young University. 1996:20～42
9 B D Jensen, L L Howell, D B Gunyan, et al. The Design and Analysis of Compliant MEMS Using the Pseudo-Rigid-Body Model. ASME international Mechanical Engineering Congress and Exposition, 1997:119～126
10 G. K. Ananthasuresh, S. Kota, Y. Gianchandani. A Methodical Approach to the Design of Compliant Micromechanisms, Solid-State Sensor and Actuator Workshop. Hilton Head Island. 1994:189～192
11 V. D. Larsen, O. Sigmund, S. Bouwstra. Design and Fabrication of Compliant Micromechanisms and Structures with Negative Poisson’s Ratio. Proceeding of the 9th Annual International Workshop on Micro Electro Mechanical Systems, 1996,San Diego: 365～371
12 D. Clements. Implementing Compliant Mechanisms in Micro-Electro-Mechanical Systems (MEMS). M. S. Thesis of Brigham Young University. 2000:61～89
13 M. B. Parkinson, B. D. Jensen, G. M. Roach, Optimization-Based Design of a Fully-Compliant Bistable Micromechanism. Proceedings of the 26th Biennial Mechanisms and Robotics Conference, 2000:146～159
14 L. G. Salmon, D. B. Gunyan, J. M. Derderian, et al. Use of the Pseudo-Rigid-Body Model toSimplify the Description of Compliant Micromechanisms. Solid-State Sensor and Actuator Workshop, 1994:136～139
15 A. Midha, M. D. Murphy, L. L. Howell. Compliant Constant-force Mechanism and Devices Formed Therein, U.S. Patent 5, 649, 454, 1995
16 G. K. Ananthasuresh, S. Kota. Designing Compliant Mechanisms, Mechanical Engineering. 1995,117(11):93～96
17 B. D. Jensen, L. L. Howell, L. G. Salmon. Design of Two-link, In-plane, Bistable Compliant Micro-mechanisms. ASME Trans. on Mechanical Design. 1999,121(3):416～423
18 M. S. Baker, S. M. Lyon, L. L. Howell. A Linear Displacement Bistable Micromechanism. Proceedings of the 26th Biennial Mechanisms and Robotics Conference, 2000:76～90
19 S. M. Lyon, M. S. Evans, P. A. Erickson, et al. Predication of the First Modal Frequency of Compliant Mechanism Using the Pseudo-Rigid-Body Model. ASME Trans. on Mechanical Design. 1999,121(3):309～313
20 C. Boyle, L. L. Howell, S. P. Magleby, et al. Dynamic Modeling of Compliant Constant-ForceCompression Mechanisms. Mechanism and Machine Theory. 2003,38: 1469～1487
21陈知泰,余跃庆,杜兆才等.柔顺机构的频率特性分析.机械设计与研究. 2005,21(6): 24～26
22 A. Midha, L. L. Howell. On the Nomenclature, Classification and Compliant Mechanism. ASME Trans. on Mechanical Design. 1994,116(2):270～279
23 G. K. Ananthasuresh, L. L. Howell. Case Studies and a Note on the Degrees-of-Freedom in Compliant Mechanisms. ASME Trans. on Transmissions and Automation. 1996,182(3):1～12
24谢先海,罗峰武,廖道训.柔顺机构自由度的一种计算方法.华中理工大学学报. 2000,28(2):40～41
25李团结.柔性机构的结构拓扑特征及其自由度分析.机械科学与技术. 2003,22(1):107～109
26 L. L. Howell, A. Midha. A Method for the Design of Compliant Mechanism With Small-Length Flexural Pivots. ASME Trans. on Mechanical Design. 1994,116(1):280～289
27 L. L. Howell, A. Midha. Evaluation of Equivalent Spring Stiffness for Use in a Pseudo Rigid Body Model of Large Deflection Compliant Mechanisms. ASME Trans. on Mechanical Design. 1996,118(1):126～140
28 L. L. Howell, A. Midha. Parametric Deflection Approximations for End Loaded Large Deflection Beams in Compliant Mechanisms. ASME Trans. on Mechanical Design. 1995,117(3):156～165
29 S. M. Lyon, L. L. Howell, G. M. Roach. Modeling Flexible Segments with Force and Moment End Loads via the Pseudo-Rigid-Body Model. Proceedings of the 2000 Design Engineering Technical Conferences, 2000:124～138
30 B. T. Edwards, B. D. Jensen, L. L. Howell. A Pseudo-Rigid-Body Model for Initially-Curved Pinned-Pinned Segments Used in Compliant Mechanisms. ASME Trans. on Mechanical Design. 2001,123(3):466～472
31 A. Midha, L. L. Howell. Limit Position of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept. Mechanism and Machine Theory. 2000,35:99～115
32李海燕,张宪民,彭惠青.大变形柔顺机构驱动特性研究.机械科学与技术. 2004,23(9):1040～1043
33 B. D. Jensen, L. L. Howell. Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints. ASME Trans. on Mechanical Design. 2004,126(1): 657～665
34 Nicolae Lobontiu, Ephrahim Garcia. Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms. ASME Trans. on Mechanical Design. 2005,127(4):766～773
35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.机械工程学报. 2002,16(2):75～78
36于靖军,毕树生,宗光华.空间全柔性机构位置分析的刚度矩阵法.北京航空航天大学学报. 2002,28(3):323～326
37 A. Saxena, G. K. Ananthasuresh. Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications. ASME Trans. on Mechanical Design. 2001,123(1):33～42
38 A. Saxena. Synthesis of Compliant Mechanisms for Path Generation Using Genetic Algorithm. ASME Trans. on Mechanical Design. 2005,127(4):745～752
39 B. W. Pedersen, T. Buhl, O. Sigmund. Topology Synthesis of Large-Displacement Compliant Mechanisms. Int. J. Numer. Mech. Engng. 2001, 50(1):2683～2705
40 Kang Tai, Guang Yu Cui, Tapabrata Ray. Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape. ASME Trans. on Mechanical Design. 2002,124(3):492～500
41邱丽芳,南铁玲,翁海珊.柔性铰链运动性能多目标优化设计.北京科技大学学报. 2008,30(2):189～192
42 L. L. Howell, A. Midha. A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms. ASME Trans. on Mechanical Design. 1996,118(1):121～125
43邱丽芳,翁海珊,柳林,南铁玲.不完全分布柔度的全柔性机构的研究.北京科技大学学报. 2007,29(增刊2):156～158
44邱丽芳,翁海珊,柳林,南铁玲.全柔性四杆机构伪刚体模型分析计算方法的改进.农业机械学报. 2008,29(5):142～145
45 S. X. Ping, S. Henty, S. Yang. Design of Compliant Microleverage Mechanisms. Sensors and Actuators. 2001,87(3):146～156
46李海燕.柔顺机构的分析及基于可靠性的优化设计.汕头大学硕士论文. 2004:40～46
47刘少芳.柔顺机构的动态拓扑优化设计.汕头大学硕士论文. 2004:14～26
48李海燕,张宪民,彭惠青.柔顺机构的疲劳可靠性优化设计.中国机械工程. 2004, 15(23):2130～2133
49 J. A. Hetrik, S. Kota. An Energy Formulation for Parametric Size and Shape Optimation of Compliant Mechanisms. ASME Trans. on Mechanical Design. 1999,121(3):229～233
50 G. K. Ananthasuresh, S. Kota, N. Kikuchi. Strategies for Systematic Synthesis of Compliant Mechanisms. ASME Trans. on Dynamic Systems and Control Division. 1994,116(2):677～686
51 M. I. Frecker, G. K. Ananthasuresh, S. Nishiwaki, et al. Topological Synthesis of Compliant Mechanisms Using Multi-Criterion Optimization. ASME Trans. on Mechanical Design. 1997, 119(1):238～245
52 O. Sigmund. Design of Multi-Physics Actuators Using Topology Optimization-PartⅠ: One-Material Structures. Comput. Methods Appl. Mech. Engrg. 2001,190(2):6577～6604
53 O. Sigmund. Design of Multi-Physics Actuators Using Topology Optimization-PartⅡ: Two-Material Structures. Comput. Methods Appl. Mech. Engrg. 2001, 190(2):6605～6627
54 Larsen, O. Sigmund. Design and Fabrication of Compliant Micro-Mechanisms and Structures with Negative Poisson’s Ratio. Journal of Microelectromechanical Systems. 1997,6(2):99～106
55 A. Saxena, G. K. Ananthasuresh. On an Optimal Property of Compliant Topologies. Structure and Multidisciplinary Optimization. 2000,19(3):36～49
56 G. K. Lau, H. Du, M. K. Lim, Use of Functional Specifications as Objective Functions in Topological Optimization of Compliant Mechanism. Comput. Methods Appl. Mech. Engrg. 2001,190(2):4421～4433
57 O. Sigmund. Design of Compliant Mechanisms Using Topology Optimization. Mechanics of Structures and Machines. 1997,25(4):495～526
58 N. Kikuchi, S. Nishiwaki, Fonseca, et al. Design Optimization Method for Compliant Mechanisms and Material Microstructure. Comput. Methods Appl. Mech. Engrg. 1998,151(1):401～417
59谢先海,廖道训.基于均匀化方法的柔顺机构的设计.中国机械工程. 2003,14(11):953～955
60罗峰武,谢先海,廖道训.柔顺机构的机械效益.湘潭矿业学院学报. 2000,15(3):41～45
61孙宝元,杨桂玉,李震.拓扑优化方法及其在微型柔性结构设计中的应用.纳米技术与精密工程. 2003,1(1):24～30
62杨桂玉.拓扑优化方法及其在微型柔性机构设计中应用的研究.大连理工大学硕士学位论文. 2004:1～14
63 G. K. Ananthasuresh, L. Yin. A Novel Topology Design Scheme for the Multi-Physics Problems of Electro-Thermally Actuated Compliant Micromechanisms. Sensors and Actuators, 2002:599～609
64刘震宇.微型及小型柔性机械结构的拓扑优化设计方法.大连理工大学博士学位论文. 2000:1～9
65梅玉林.拓扑优化的水平集方法及其在刚性结构、柔性机构和材料设计中的应用.大连理工大学博士学位论文. 2003:1～13
66李团结,曹炎,李世俊,等.平面双稳态柔性微机构的优化设计.机械科学与技术. 2004,23(6):709～711
67李团结,朱超,周小勇,等.定常力输出柔性滑块机构的优化综合.机械科学与技术. 2004,23(3):22～324
68陈永健,刘少芳.以柔顺机构作位移放大器的拓扑优化设计.汕头大学学报. 2004,19(3): 53～56
69 M. I. Frecker, G. K. Ananthasuresh, S. Nishiwaki, et al. Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization. ASME Trans. on Mechanical Design. 1997,119(4):38～245
70 A. Saxena, G. K. Ananthasuresh, On an Optimal Property of Compliant Topologies. Struct. Multidisc. Optim. 2000,19(3):36～49
71 M. L. Scott, L. L. Howell. Dynamic Response of Compliant Mechanisms Using the Pseudo-Rigid-Body Model. Proceedings of DETC 97 ASME Design Engineering Technical Conference, 1997 ,Sacramento California:78～91
72 Y. Q. Yu, L. L. Howell, Y. Yue, et al. Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model. ASME Trans. on Mechanical Design. 2005,127(4):760～765
73陈知泰.柔顺机构的动力学研究.北京工业大学硕士学位论文. 2005:1～30
74 Z. Li, S. Kota. Dynamic Analysis of Compliant Mechanisms. Proceedings of ASME 2002 Design Engineering Technical Conferences, 2002,California:1～11
75谢先海,廖道训.基于多刚体离散元模型的柔顺机构动力分析新方法.机械工程学报. 2003,39(5):953～955
76黄进,谢先海.平行导向柔顺机构的加工制造与性能测试.实验技术与管理.2000,6(1):7～9
77张策,黄永强,王子良,等.弹性连杆机构的分析与设计(第二版).机械工业出版社. 1997:59～88
78刘宏昭,曹惟庆.关于多柔体动力学与弹性机构动力学的讨论.机械设计. 1994,1(4):26～31
79 J. N. Bricout , J. C. Debus , Picheau. A Finite Element Model for the Dynamics of Flexible Manipulators. Mechanism and Machine Theory .1990,25:119～128
80 A. Q. Erdman, G. N. Sandor. A General Method for Kineto-elastodynamic Analysis and Synthesis of Mechanisms. ASME Trans. on Engineering for Industry. 1972,94(4):1193～1205
81 I. Imam, G. N. Sandor, S. N. Kramer. Deflection and Stress Analysis of High-speed Mechanisms with Elastic Links. ASME Trans. on Engineering for Industry. 1973,95(3):541～548
82 I. Imam, G. N. Sandor. A General Method of Kineto-elastodynamic Design of High-speed Mechanisms. Mechanism and Machine Theory. 1973,8:497～516
83 B. M. Bahgat, K. D. Willmert. Finite Element Vibrational Analysis of Planar Mechanism. Mechanism and Machine Theory. 1976,11:47～71
84 A. Midha, A. G. Erdman, D. A. Frohrib. Finite Element Approach to Mathematical Modeling of High-speed Elastic Linkages. Mechanism and Machine Theory. 1978,13:603～618
85 P. K. Nath, A Ghosh. Steady State Response of Mechanisms with Elastic Links by Finite Element Method. Mechanism and Machine Theory. 1980,15:199～211
86 D. A. Turcic, A. Midha. Generalized equations of motion for the dynamic analysis of elastic mechanism systems. ASME Trans. on Dynamic Systems Measurement and Control. 1984,106(3):243～248
87 D. A. Turcic, A. Midha. Dynamic Analysis of Elastic Mechanism Systems. PartⅡ: Applications. ASME Trans. on Dynamic Systems Measurement and Control. 1984,106(3):249～254
88 W. L. Cleghorn, R. G. Fenton, B. Tabarrok. Steady-state Vibration Response of High-speed Mechanisms. Mechanism and Machine Theory. 1984,19:417～423
89 J. Lieh. Dynamic Modeling of a Slider-crank Mechanism with Coupler and Joint Flexibility. Mechanism and Machine Theory. 1994,29:139～147
90 B. Fallahi, S. Lai, C. Venkat. A Finite Element Formulation of a Flexible Slider-crank Mechanism Using Local Coordinate. ASME Trans. on Mechanical Design. 1995,117(3): 329～338
91 J. N. Bricout, J. C. Debus, P. Micheau. A Finite Element Model for The Dynamics of FlexibleManipulators. Mechanism and Machine Theory. 1990,25:119～128
92商大中,曹承佳,李宏亮.考虑刚体运动与弹性运动耦合影响的旋转叶片振动有限元分析.计算力学报. 2000,17(3):330～338
93 S. M. Lin. Dynamic Analysis of Rotating Nonuiform Timoshenko Beams With an Elastically Restrained Root. ASME Trans. on Applied Mechanics. 1999,66(3):742～749
94 P. W. Links. Finite Element Appendage Equations For Hybrid Coordinate Dynamic Analysis. International Journal of Solids and Structures. 1972,8(1):709～731
95 P. W. Links. Dynamic Analydid of a System of Hinge-connected Rigid Bodies with Nonrigid Appendages. International Journal of Solids and Structures. 1973,9(2):1473～1487
96 L. Meirovitch, H. D. Nelson. High Spin Motion of Satellite Containing Elastic Parts. Journal of Spaceraft and Rocket. 1966,13(5):1597～1602
97 V. J. Modi. Attitude Dynamics of Satellite with Flexible Appendages. Journal of Spacecraft. 1972,10(9):734～751
98 C. S. Bodly. A Digital Computer Program for the Dynamic Interaction Simulation of Controls And Structure. NASA TP-1219,1978
99 H. P. Frisch. A Vector-dyadic Development of The Equations of Motion For Ncoupled Flexible Bodies and Point Mass. NASA TND-8047, 1975
100 L. Meirovitch. Dynamics and Control of Large Flexible Spacecraft. Proceedings of a Symposium Held in Blacksburg, 1977, 688～695
101 L. Meirovitch. Dynamics and Control of Large Flexible Spacecraft. Proceedings of a Symposium Held, 1977, Blacksburg:688～695
102 T. R. Kane, D. A. Levinson. Formulation of Equation of Motion for Complex Spacecrafe. Journal of Guidance Control and Dynamics. 1980,3(2):99～112
103 H. B. Hablani. Constrained and Unconstrained Mode: Some Modeling Aspects of Flexible Spacecraft. Journal of Guidance Control and Dynamics. 1982,5(2):164～198
104 P. A. Meehan, S. F. Asokanthan. Chaotic Motion in Spinning Spacecraft with Circumferential Nutational Damper. Nonlinear Dynamics. 1997,12(2):69～87
105 R. E. Roberson, R. F. Schwertassek. Dynamics of Multibody Systems. Springer-Verlag, 1988: 46～75
106林健,黄琳.大型空间结构的动力学建模与控制.力学进展. 1991,21(3):333～341
107 Z. L. Wang, J. G. Xu. On The Stability and Control of Dynamical System with Flexible Structure. Science in China. 1993,36(1):27～34
108 G. Naganathan, A. H. Soni. Nonlinear Modeling of Kinematic and Flexibility Effects in Manipulator Design. ASME Trans. on Automation in Design. 1988,110(4):243～254
109 S. G. Yue, Y. Q. Yu, S. X. Bai. Flexible Robot Beam Element for the Manipulators with Jointand Link Flexibility. Mechanism and Machine Theory. 1997,32:209～219
110王照林,王大力.多弹性连杆机器人的建模与控制.上海交通大学出版社. 1992:23～45
111 J. M. Paros, L. Weisboro. How to Design Flexure Hinges. Machine Design. 1965,37(27):151～157
112吴鹰飞,周兆英.柔性铰链的应用.中国机械工程. 2002,13(18):1615～1618
113吴鹰飞,周兆英.柔性铰链的设计计算.工程力学. 2002,19(6):136～140
114普齐米尼斯基,王德荣等译.矩阵结构分析理论.国防工业出版社. 1975:19～45
115张策,王子良等.提高连杆机构KED分析计算效率的若干问题.唐山工程技术学院学报. 1986:61～71
116 K. E. Bisshopp, D. C. Drucker. Large Deflection of Cantilever Beams. Quarterly of Applied Mathematics. 1945,3(3):272～275
117 B. A. Coulter, R. E. Miller. Numerical Analysis of a Generalized Plane Elastic with Non-linear Material Behavior. International Journal for Numerical Methods in Engineering. 1988,26(8):617～630
118 R. Frisch-Fay. Flexible Bars. Butterworth. Washington. DC. 1962:49～93
119 W. Gorski. A Review of Literature and a Bibliography on Finite Elastic Deflections of Bars. Trans. on the Institution of Engineers. 1976,18(2):74～85
120 H. B. Harrison. Post-buckling Analysis of Non-uniform Elastica Columns. International Journal for Numerical Methods in Engineering. 1973,7(7):195～210
121 K. Mattiasson. Numerical Results From Large Deflection Beam and Frame Problems Analyzed by Means of Elliptic Integrals. International Journal for Numerical Methods in Engineering. 1981,17(6):145～153
122 R. E. Miller. Numerical Analysis of a Generalized Plane Elastica. International Journal for Numerical Methods in Engineering. 1980,15(3):325～332
123 P. F. Byrd, M. D. Friedman. Handbook of Elliptic Integrals for Engineers and Physicists. Springer-Verlag. 1954:31～65
124 L. V. King. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge University Press.1924:5～67
125 H. Hancock. Elliptic Integral. Dover. New York. 1958:17～37
126 A. G. reenhill. The Applications of Elliptic Functions. Dover. New York. 1959:32～79
127吴鹰飞,周兆英.柔性铰链的应用.中国机械工程. 2002,13(18):1615～1618
128邵忍平.机械系统动力学.机械工业出版社, 2005:68～72
129余跃庆,李哲.现代机械动力学.北京工业大学出版社, 1998:230～301
130刘惟信.机械可靠性分析.清华大学出版社, 1996:268～270
131 S. Nishiwaki, M. Frecker. Topology Optimization of Compliant Mechanisms Using theHomogenization Method. Internal Journal for Numerical Methods in Engineering. 1998,42(3):535～559
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |