摘要
本文紧密结合新型可重构5自由度混联机器人TriVariant-B的样机开发,系统研究了一类少自由度球坐标型并联构型装备的静刚度解析和半解析建模、有限元分析、性能指标评价及灵敏度分析等相关理论与方法。论文取得了如下创造性成果:
以Tricept和TriVariant系列5自由度混联机器人为例,利用摄动法提出一种构造可描述含恰约束主动/从动支链球坐标型并联机构全变形雅可比矩阵的建模方法,利用该矩阵可有效地分离出上述并联机构操作空间变形与关节空间变形在驱动和约束空间中的映射关系,进而为后续整机静刚度分析奠定了坚实的运动学基础。
利用全变形雅可比矩阵和变形叠加原理,系统研究了少自由度球坐标型并联机构静刚度解析建模方法。该方法利用静态凝聚技术和变形协调条件,有效地解决了恰约束支链弯曲刚度的精准建模问题,修正了前人所提出的结论。研究结果表明,利用全变形雅可比矩阵建立的刚度模型具有列式简洁,物理意义明确,通用性强等优点,并充分体现了速度与刚度模型在数学层面上的内在联系。
以TriVariant-B机器人为例,提出一种计及复杂机架柔性的并联构型装备整机静刚度半解析建模方法。该方法基于结构力学中的子结构综合思想,首先将整机系统分解为机构和机架两个子系统,然后建立各子系统的刚度矩阵,最后利用线性叠加原理构造整机系统的刚度模型。在机架子系统刚度建模中,提出一种采用商用有限元软件及静态凝聚技术构造机架子系统界面刚度模型的有效方法,大幅度提高了计算效率。利用这种建模方法,可在概念设计阶段实现整个工作空间中的整机刚度快速预估,进而为指导系统的详细机械设计提供了有力的工具。
借助商用有限元软件ANSYS的参数化设计语言,系统研究了并联构型装备中各种常用铰链的有限元精确建模技术。提出一种可在不同位形下快速建立整机有限元模型的建模策略与实施方法,有效地提高了计算效率。在此基础上,构造出计及复杂机架柔性的TriVariant-B混联机器人整机刚度有限元模型,并对机架及连架虎克铰等关键零部件的优化设计做了有益的探讨。
以TriVariant-B机器人为例,利用整机系统柔度矩阵的最大奇异值,提出一种可评价并联构型装备线刚度和角刚度性能的评价指标。利用该指标并借助灵敏度分析方法,系统考察了该机器人关键部件弹性对整机刚度的贡献,并揭示出机构子系统无约束主动支链中的铰链拉压刚度和恰约束支链本体扭转刚度是影响整机刚度的薄弱环节。另外,利用该指标并采用多目标遗传算法研究了该机器人机构尺度参数对整机刚度的影响,并据此提出了改进方案。
开展了TriVariant-B机器人物理样机的静刚度实验研究工作。业已证明,由本文提出的半解析模型和有限元分析所得计算结果与实验结果具有良好的一致性,进而验证了它们的有效性。
本文研究成果已成功地应用于新型火焰切割加工装备TriVariant-B机器人的结构设计和开发,同时对其它类似并联构型装备的相关研究提供了有益的借鉴。
This dissertation presents a theoretical package for stiffness modeling, analysis, performance evaluation and optimization of a class of spherical coordinate parallel kinematic machines (PKM) using analytical and semi-analytical approaches. The outcome has been employed for the development of a 5-DOF hybrid robot known as the TriVariant. The following contributions have been made.
By taking the Tricept and the TriVariant robots as examples, the overall deflection Jacobian of the parallel mechanisms having a properly constrained active/passive limb is formulated. In the overall deflection Jacobian, the topological characteristics in the actuations and constraints can be explicitly separated.
Using the overall deflection Jacobian and linear superposition, two analytical approaches for the stiffness modeling of the PKM having a properly constrained active/passive limb are proposed by simultaneously taking into account the component compliances in both actuations and constraints. In the modeling process, the precise bending compliance of the properly constrained limb is formulated with the static condensation and loop-closure compatibility conditions. The use of the overall deflection Jacobian allows the stiffness model to be formulated in a more effective and compact manner, and the underlying relationship between the velocity and the stiffness mapping functions to be revealed.
By taking the TriVariant-B robot as an example, a semi-analytical approach is developed for the stiffness modeling of the PKM having complex machine frame geometry. In this approach, the PKM is decomposed into two subsystems associated with the parallel mechanism and the machine frame by assuming one of them is rigid. The stiffness model of entire system is then achieved by linear superposition using the interface compatibility conditions. This approach enables the stiffness distributions throughout the workspace to be time-effectively examined.
By means of ANSYS parametric design language (APDL), the finite element analysis model of the TriVariant-B is formulated by taking into account the compliance of machine frame. Particular attentions are placed upon: (1) precise FEA formulation of different type of joints, and (2) the development of an effective modeling strategy for the rapid rigidity estimation associated with different configurations in order to avoid FEA model re-meshing.
On the basis of singular value decomposition, two global indices are proposed for evaluating the translational and rotational rigidities of the TriVariant-B robot. Utilizing these indices, the contributions of the component compliances in the parallel mechanism and the machine frame to the translational and rotational compliances of the system are investigated by sensitivity analysis. It has been found that the joints compliance has significant impact on the translational stiffness of system while the torsional compliance of the properly constrainted passive limb has significant impact on the rotational stiffness. These findings provide engineers with informative guidelines for the detailed mechanical design. In the end, the global rigidity performance indices of the TriVariant-B are also optimized using multiple-object genetic algorithm.
The experimental investigation is carried out on a TriVariant-B prototype machine. It shows that the experiment results have a good match with those obtained by the FEA and theoretical analysis.
The outcome of this thesis has been employed to the design of a TriVariant-B prototype machine for frame cutting and would be useful for the development of other similar parallel kinematic machines.
引文
[1]汪劲松,黄田,并联机床——机床行业面临的机遇与挑战,中国机械工程,1999,10(10):1103-1107
[2] Merlet J P, Parallel manipulators: State of the art and perspectives, Journal of Advanced Robotics, 1994, 8 (6): 589
[3] Martin Eastman, Will Hexapods go from show floor to shop floor, Cutting Tool Engineering, 1995, 6: 102-110
[4] Pritschow G, Wurst K H, Systematic design of Hexapods and other parallel link systems, Annals of CIRP, 1997, 46 (1): 291-295
[5] http://www.roboticsonline.com/public/articles/archivedetails.cfm?id=797
[6] Lee M K, Shah D K, Kinematic analysis of a three-degrees-of-freedom manipulator, IEEE Transaction on Robotics and Automation, 1988, 4 (3): 354- 360
[7] Waldron K J, Raghavan M, et al, Kinematics of a hybrid series-parallel manipulation system, ASME Journal of Mechanisms, Transmissions and Automation in Design, 1989, 111 (6): 211-221
[8] Pierrot F, Chiaccchio P, Evaluation of velocity capabilities for redundant parallel robot, Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, 1997, 1: 774-779
[9] Tsai L W, Tahmasebi F, Synthesis and analysis of a new class of six-degree-of-freedom parallel minimanipulators, Journal of Robotic Systems, 1993, 10 (5): 561-580
[10] Pritschow G, Parallel kinematic machines (PKM)-limitations and new solutions, Annals of CIRP, 2000, 49 (1): 275-280
[11] Clavel R, Delta, a fast robot with parallel geometry, Proceedings of the 18th International Symposium On Industrial Robots(ISIR’98), 1988: 91-100
[12] Hunt K H, Structural kinematics of in-parallel-actuated robot-arms, ASME Journal of Mechanism, Transmission and Automation in Design, 1983, 105 (4): 705-712
[13] Carretero J A, Podhorodeski RP, Nahon M A, et al. Kinematic analysis and optimization of a new 3-DOF spatial parallel manipulator, ASME Journal of Mechanical Design, 2000, 122 (1): 17-24
[14] Neumann K E, Robot, US Patent, No. 4732525, 1988-05
[15] Neumann K E, Tricept application, In: The 3rd Chemnitz Parallel Kinematics Seminar, Germany, 2002: 547~551
[16] Huang T, Li M, Wu M L, et al, The Criteria for conceptual design of reconfigurable PKM modules—theory and application, Chinese Journal of Mechanical Engineering (In Chinese), 2005, 41 (8): 36-41
[17] Thornton G S, The GEC Tetrabot-a new serial-parallel assembly robot, IEEE International Conference on Robotics and Automation, 1988, 1: 437-439
[18] Dwolatzky B, Thornton G S, The GEC Tetrabot-a serial-parallel topology robot: control design aspects, International Conference on Control, 1988: 426-431
[19] Cezary Z, Krzysztof M, Kazimierz N, Wojciech S, A prototype robot for polishing and milling large objects, The Industrial Robot, 2003, 30 (1): 66-76
[20] Tonshoff H K, Grendel H K R, Structure and characteristics of the hybrid manipulator George V, In: Boer, C. R., Molinari-Tosatti, L. and Smith, K. S., Parallel Kinematic Machines, Springer-Verlag, London, 1999: 365-376
[21] Jovane F, Negri S P, Fassi I, et al, Design issue for reconfigurable PKMs, In: The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002, 17-47
[22] Wurst K H, Peting U, PKM concept for reconfigurable machine tools, In: The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002, 63-66
[23] Neumann K E, Tricept application, In: The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002, 547-551
[24] Gronbach H, Tricenter-a universal milling machine with hybrid kinematic, In: The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002, 595-608
[25] Marinized Tricept robot cuts cost and risk of welding underwater, Offshore, 2004, 64(7): 58
[26] Available at: http://www.pkmtricept.com
[27] Huang, T, Li M, Li Z X, et al, A 5-DOF hybrid robot, Patent Cooperation Treaty, Int. Appl. PCT/CN2004/000479, 2004-05
[28] Li M, Huang T, et al, Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable PKM—the Tricept and the TriVariant, ASME Journal of Mechanical Design, 2005, 127 (6): 1129-1136
[29] Huang T, Li M, Zhao X M, et al, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant—a novel 5-DOF reconfigurable hybrid robot, IEEE Transactions of Robotics and Automation, 2005, 21 (3): 449-456
[30]李曚,可重构混联机械手??TriVariant的设计理论与方法:[博士学位论文],天津;天津大学,2005
[31]黄田,刘海涛,李曚,五自由度机器人,国家发明专利,公开号:CN1709657,2005-12
[32] Liu H T, Huang T, Zhao X M, et al, Optimal design of the TriVariant robot to achieve a nearly axial symmetry of kinematic performance, Mechanism and Machine Theory, 2007, 42 (12): 1643-1652
[33] Liu H T, Huang T, Mei J P, et al, Kinematic Design of a 5-DOF hybrid robot with large workspace/limb-stroke ratio, ASME Journal of Mechanical Design, 2007, 129 (5): 530-537
[34] Tsai L W, Robot Analysis: The mechanics of serial and parallel manipulators, New York, USA, Wiley-Interscience Publication, 1999
[35] Gosselin C M, Stiffness mapping for parallel manipulators, IEEE Transactions On Robotics and Automation, 1990, 6 (3): 377-382
[36] Lee M K, Aujunan S, A Three-Degrees-of-Freedom micromotion in-parallel actuated manipulator, IEEE Translations On Robotics and Automation, 1991, 7 (5): 634-641
[37] Lee M K, Design of a high stiffness machining robot arm using double parallel mechanisms, Proceedings of the IEEE International Conference on Robotics and Automation, 1995, 1: 234-240
[38] Tahmasebi F, Tsai L W, Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators, Design Engineering Division of American Society of Mechanical Engineers, 1992, 47: 95-102
[39] Stoughton R S, Arai T, A modified Stewart platform with improved dexterity, IEEE Transaction on Robotics and Automation, 1993, 9 (2): 166-172
[40] Ferraresi C, Pastorelli S, Sorli M, et al, Static and dynamic behavior of a high stiffness Stewart platform-based force/torque sensor, Journal of Robotic Systems, 1995, 12 (12): 883-893
[41] Bhattacharya H, et al, On the optimum design of Stewart platform type manipulators, Robotica, 1995, 13: 133-140
[42] EI-Khasawneh B S, Ferreira P M, Computation of stiffness and stiffness bounds for parallel link manipulators, International Journal of Machine Tools and Manufacture, 1999, 39 (2): 321-342
[43]高峰,金振林,一种新型6自由度正交并联机器人机构的柔度分析,机械设计与研究,2001, 17 (2):38-41
[44]金振林,高峰,新型机器人6维力/力矩传感器结构的刚度性能指标分析,中国机械工程,2001,12 (10):1092-1094
[45]金振林,赵现朝,高峰,新型并联机床的柔度指标及其在工作空间内分布研究,中国机械工程,2002,13 (3):1092-1094
[46]金振林,赵现朝,范文刚,新型正交并联机器人静力学分析,燕山大学学报,2002,26 (4):308-311
[47]金振林,高峰,李金良,并联3-2-1结构新型微操作手及其承载能力分析,中国机械工程,2002,13 (2):1092-1094
[48] Clinton C M, Zhang G M, Wavering A J, Stiffness modeling of a Stewart-Platform-Based Milling Machine, Transaction of NAMRI/SME, 1997, 115: 335-340
[49] Ceccarelli M, Carbone G, A stiffness analysis for CaPaMan (Cassino Parallel Manipulator), Mechanism and Machine Theory, 2002, 37 (5): 427-439
[50] Ceccarelli M, Ottaviano E, Galvagno M, A 3-DOF parallel manipulator as earthquake motion simulator, Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision, 2002, 944-949
[51] Ottaviano E, Ceccarelli M, Carbone G, Experimental results of a 3-DOF parallel manipulator as an earthquake motion simulator, Proceedings of the ASME Design Engineering Technical Conference, 2004, 2: 215-222
[52] Ottaviano E, Ceccarelli M, Application of a 3-DOF parallel manipulator for earthquake simulations, IEEE/ASME Transactions on Mechatronics, 2006, 11 (2): 240-246
[53] Goldsmith P B, Kinematics and stiffness of a symmetrical 3-UPU translational parallel manipulator, Proceedings of the IEEE International Conference on Robotics and Automation, Washington, USA, 2002, 4: 4102-4107
[54] Goldsmith P B, Design and kinematics of a three-legged parallel manipulator, IEEE Transactions of Robotics and Automation, 2003, 19 (4): 726-731
[55] Deblaise D, Hernot X, Maurine P, A systematic analytical method for PKM stiffness matrix calculation, Proceedings of IEEE International Conference on Robotics and Automation, 2006, 4: 4213-4219
[56] Robert R G, Minimal Realization of a Spatial Stiffness Matrix with Simple Springs Connected in Parallel, Proceedings of IEEE International Conference on Robotics and Automation, 1999, 3: 2153-2158
[57] Robert R G, Minimal Realization of an arbitrary spatial stiffness matrix with a parallel connection of simple and complex springs, IEEE Transactions on Robotics and Automation, 2000, 16 (5): 603-608
[58] Huang S, Schimmels J M, The Eigenscrew Decomposition of Spatial Stiffness Matrices, IEEE Transactions on Robotics and Automation, 2000, 16 (2): 146-156
[59] Huang S, Schimmels J M, The Duality in spatial stiffness and compliance as realized in parallel and serial elastic mechanisms, ASME Journal of Dynamic Systems, Measurement and Control, 2002, 124 (1): 76-84
[60] Huang S, Schimmels J M, Realization of Those Elastic Behavious that Have Compliant Axis in Compact Elastic Mechanisms, Journal of Robotic Systems, 2002, 19 (3): 143-154
[61] Ciblak N, Lipkin H, Synthesis of Cartesian Stiffness for Robotic Applications, Proceedings of IEEE International Conference on Robotics and Automation, Detroit, USA, 1999, 3: 2147-2152
[62]韩书葵,方跃法,槐创锋,4自由度并联机器人刚度分析,机械工程学报,2006,S1:35-38
[63]陈文凯,刘平安,3-RSR并联机器人静力学和刚度的研究,机械设计与制造,2006,9:113-115
[64]黄真,赵永生,赵铁石,高等空间机构学,北京:高等教育出版社,2006
[65]黄真,孔令富,方跃法,并联机器人机构学理论及控制,北京:机械工业出版社,1997
[66] Zefran M, Kumar V, Affine connections for the Cartesian stiffness matrix, Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, NM, 1997, 2: 1376-1381
[67] Tsai L W. Kinematics of a three DOF platform with three extensible limbs, In Recent Advances in Robot Kinematics, Kluwer Academic Publishers,1996: 401-410
[68] Tsai L W, Walsh G, et al, Kinematics of a novel three DOF translational platform, Proceedings of the IEEE International Conference On Robotics and Automation, Minneapolis, USA, 1996, 4: 3446-3451
[69] Tsai L W, Joski S, Comparison study of architectures of four 3 Degree-of-Freedom translational parallel manipulators, Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea, 2001, 2: 1283-1288
[70] Tsai L W, Joski S, Kinematic analysis of 3-DOF position mechanisms for use in hybrid kinematic machines, ASME Journal of Mechanical Design, 2002, 124 (2): 245-253
[71] Li J F, Wang X H, Fei R Y, et al, Performance analysis and kinematic design of pure translational parallel mechanism with vertical guide-ways, Chinese Journal of Mechanical Engineering, 2006, 19 (2): 300-306
[72] Majou F, Gosselin C, Wenger P, et al, Parametric stiffness analysis of the Orthoglide, Mechanism and Machine Theory, 2007, 42 (3): 296-311
[73] Kim J, Park F C, Kim M, Geometric design tools for stiffness and vibration analysis of robotic mechanisms, Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, USA, 2000, 2: 1942-1947
[74] Kim J, Park F C, Ryu S J, et al, Design and analysis of a redundantly actuated parallel mechanism for rapid machining, IEEE Transactions on Robotics and Automation, 2001, 17 (4): 423-434
[75] Koseki Y, Tanikawa T, Koyachi N, et al, Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method, Proceedings of the IEEE International Conference on Intelligent Robots and Systems, 2000, 1: 786-792
[76] Company C, Pierrot F, Modelling and design issues of a 3-axis parallel machine-tool, Mechanism and Machine Theory, 2002, 37 (11): 1325-1345
[77] Yoon W-K, Suehiro T, Tsumaki Y, et al, A method for analyzing parallel mechanism stiffness including elastic deformations in the structure, IEEE International Conference on Intelligent Robots and Systems, 2002, 3: 2875-2880
[78] Yoon W-K, Suehiro T, Tsumaki Y, et al, A compact modified Delta parallel mechanism design based on a stiffness analysis, Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2003, 2: 1262-1267
[79] Rizk R, Munteanu M G, Fauroux J C, Gogu G, A semi-analytical stiffness model of parallel robots from the Isoglide family via the sub-structuring principle, Proceedings of the 12th World Congress in Mechanism and Machine Science, Besancon, France, 2007, 5: 623-628
[80] Cai G Q, Wang Q M, Hu M, et al, A study on the kinematics and dynamics of a 3-DOF parallel machine tool, Journal of Materials Processing Technology, 2001, 111: 269-272
[81]蔡光起,原所先,胡明等,三自由度虚拟轴机床静力学及动力学的若干研究,中国机械工程,1999,10 (10):1108-1111
[82]李嘉,陈恳,董怡,并联柔性铰机器人的静刚度研究,清华大学学报,1999,36(8):16-20
[83] Joshi S, Tsai L W, Jacobian analysis of Limited-DOF parallel manipulators, ASME Journal of Mechanical Design, 2002, 124 (2): 254-258
[84] Xu Q S, Li Y M, Kinematic analysis and optimization of a new compliant parallel micromanipulator, International Journal of Advanced Robotic Systems, 2006, 3 (4): 351-358
[85] Xu Q S, Li Y M, Stiffness modeling for an orthogonal 3-PUU compliant parallel micromanipulator, Proceedings of the IEEE International Conference on Mechatronics and Automation, 2006, 1: 124-129
[86] Xu Q S, Li Y M, An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory, Robotics and Computer-Integrated Manufacturing, 2007, In Press
[87] Dai J S, Ding X, Compliance analysis of a three legged rigidly connected platform, ASME Journal of Mechanical Design, 2006, 128 (4): 755-764
[88] Joshi S, Tsai L W, A Comparison study of two 3-DOF parallel manipulators: one with three and the other with four supporting legs, IEEE Transactions on Robotics and Automation, 2003, 19 (2): 200-209
[89] Gosselin C M, Zhang D, Stiffness analysis of parallel mechanisms using a lumped model, International Journal of Robotics and Automation, 2002, 17 (1): 17-27
[90] Zhang D, Gosselin C M, Kinetostatic modeling of N-DOF parallel mechanisms with a passive constraining leg and prismatic actuators, ASME Journal of Mechanical Design, 2001, 123 (3): 375-384
[91] Zhang D, Gosselin C M, Kinetostatic modeling of parallel mechanisms with a passive constraining leg and revolute actuators, Mechanism and Machine Theory, 2002, 37 (6): 599-617
[92] Zhang D, Gosselin C M, Kinetostatic analysis and design optimization of the Tricept machine tool family, ASME Journal of Manufacturing Science and Engineering, 2002, 124 (3): 725-733
[93] Zhang D, On stiffness improvement of the Tricept machine tool, Robotica, 2005, 23 (3): 377-386
[94] Zhang D, Xi F, Mechefske C M, et al, Analysis of parallel kinematic machine with kinetostatic modeling method, Robotics and Computer-Integrated Manufacturing, 2004, 20 (2): 151-165
[95] Xi F, Zhang D, Xu Z, Mechefske C M, A comparative study on tripod units for machine tools, International Journal of Machine Tools and Manufacture, 2003, 43 (7): 721-730
[96] Xi F, Zhang D, Xu Z, et al, Global kinetostatic modelling of tripod-based parallel kinematic machine, Mechanism and Machine Theory, 2004, 39 (4): 357-377
[97] Zhang D, Xu Z, Mechefske C M, Xi F, Optimum design of parallel kinematic tool heads with genetic algorithms, Robotica, 2004, 22 (1): 77-84
[98] Zhang D, Wang L H, Conceptual development of an enhanced tripod mechanism for machine tool, Robotics and Computer-Integrated Manufacturing, 2005, 21 (4-5): 318-327
[99] Zhang D, Wang L H, Lang S Y T, Parallel kinematic machines design, analysis and simulation in an integrated virtual environment, ASME Journal of Mechanical Design, 2005, 127: 580-588
[100] Zhang D, Wang L H, Esmailzadeh E, PKM capabilities and applications exploration in a collaborative virtual environment, Robotics and Computer-Integrated Manufacturing, 2006, 22 (4): 384-395
[101] Bi Z M, Lang S Y T, Zhang D, et al, Integrated design toolbox for tripod-based parallel kinematic machines, ASME Journal of Mechanical Design, 2007, 129: 799-807
[102] Huang T, Zhao X Y, Whitehouse D J, Stiffness estimation of a tripod-based parallel kinematic machine, IEEE Transactions of Robotics and Automation, 2002, 18 (1): 50-58
[103] Huang T, Mei J P, Zhao X Y, et al, Stiffness estimation of a tripod-based parallel kinematic machine, Proceedings of the IEEE International Conference on Robotics & Automation, 2001, 4: 3280-3285
[104] Li Y W, Wang J S, Wang L P, Stiffness analysis of a Stewart platform-based parallel kinematic machine, Proceedings of the IEEE International Conference on Robotics & Automation, 2002, 4: 3672-3677
[105]张华,李育文,王立平等,龙门式混联机床的静刚度分析,清华大学学报,2004,44 (2):182-185
[106]陈俊,王立平,张华等,平面2自由度并联构型静刚度分析和设计,机械工程学报, 2005,41 (7):158-163
[107]饶寿期,有限元法和边界元法基础,北京:北京航空航天大学,1990
[108]许尚贤,机械设计中的有限元法,北京:高等教育出版社,1990
[109] Bathe K J等著,罗恩等译,有限元分析中的数值方法,北京:科学出版社,1991
[110] Bathe K J等著,傅子智等译,工程分析中的有限元法,北京:机械工业出版社,1991
[111] Ross C T F著,吴德心译,结构力学的有限元法,北京:人民交通出版社,1991
[112]张策,黄永强,王子良等,弹性连杆机构的分析与设计,北京:机械工业出版社,1997
[113]赵经文,王宏钰,结构有限元分析,北京:科学出版社,2001
[114]马爱军,周传月,王旭,Patran和Nastran有限元分析专业教程,北京:清华大学出版社,2005
[115]博嘉科技,有限元分析软件—ANSYS融会与贯通,北京:中国水利水电出版社,2002
[116]倪栋等,通用有限元分析ANSYS 7.0实例精解,北京:电子工业出版社,2003
[117]博弈创作室,APDL参数化有限元分析技术及其应用实例,北京:中国水利水电出版社,2004
[118]张亚欧等,ANSYS 7.0有限元分析实用教程,北京:清华大学出版社,2004
[119]东方人华,ANSYS 7.0入门与提高,北京:清华大学出版社,2004
[120]张洪武,关振群,李云鹏等,有限元分析与CAE技术基础,北京:清华大学出版社,2004
[121]小飒工作室,最新经典ANSYS及Workbench教程,北京:电子工业出版社,2004
[122]赵海峰,蒋迪,ANSYS 8.0工程结构实例分析,北京:中国铁道出版社,2004
[123]胡仁喜,王庆五,闫石等,ANSYS 8.2机械设计高级应用实例,北京:机械工业出版社,2005
[124] Huang D T-Y, Lee J-J, On obtaining machine tool stiffness by CAE techniques, International Journal of Machine Tools and Manufacture, 2001, 41 (8): 1149-1163
[125] Portman V T, Sandler B-Z, Zahavi E, Rigid 6×6 parallel platform for precision 3-D micromanipulation theory and design application, IEEE Transactions on Robotics and Automation, 2000, 16 (6): 629-643
[126] Long C S, Snyman J A, Groenwold A A, Optimal structural design of a planar parallel platform for machining, Applied Mathematical Modelling, 2003, 27 (8): 581-609
[127]李兵,王知行等,新型并联机床的刚度计算模型,机械设计,1999,16 (3):14-16
[128]徐礼钜,范守文,一种新型并联机床的刚度和固有特性的有限元分析,2003,1,102-103
[129]魏永庚,王知行,并联机床结构静刚度的有限元分析,哈尔滨工业大学,机械与电子,2004,1:16-19
[130] Zhou L H, Huang T, et al, Stiffness analysis of the main module for parallel machine tools by finite element analysis, Transactions of Tianjin University, 2001, 7 (1): 30-35
[131]李育文,张华等,6-UPS并联机床静刚度的有限元分析和实验研究,中国机械工程,2004,15 (2):112-115
[132]刘悦,汪劲松,王立平,重型混联机床XNZH2430的静刚度优化,清华大学学报,2006,46(8):1418-1421
[133]邢问训,谢金星,现代优化计算方法,北京:清华大学出版社,1999
[134]王安麟,机械工程现代最优化设计方法与应用,上海:上海交通大学出版社,2000
[135]周继惠,曹青松,宋京伟等,传统机械优化设计方法和遗传算法的比较,华东交通大学学报,2002,19 (4):65-69
[136]邓少康,遗传算法在解决结构静动力逆问题中的应用:[硕士学位论文],西安;西北工业大学,2002
[137]雷英杰,张善文,李续武等,MATLAB遗传算法工具箱及应用,西安:西安电子科技大学出版社,2005
[138] Abdel-Malek K, Paul B, Criteria for the design of manipulator arms for a high stiffness to weight ratio, SME Journal of Manufacturing Systems, 1998, 17 (3): 209-220
[139] Liu X J, Jin Z L, Gao F, Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices, Mechanism and Machine Theory, 2000, 35 (9): 1257-1267
[140] Liu X J, Wang J S, Pritschow G, Performance atlases and optimum design of planar 5R symmetrical parallel mechanisms, Mechanism and Machine Theory, 2006, 41(2): 119-144
[141] Liu X J, Wang J S, Pritschow G, Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms, Mechanism and Machine Theory, 2006, 41(2): 145-169
[142]刘辛军,并联机器人机构尺寸与性能关系分析及其设计理论研究:[博士学位论文],秦皇岛:燕山大学,1999
[143] Tlusty J, Ziegert J, Ridgeway S, Fundamental comparison of the use of serial and parallel kinematics for machine tools, Annuals of CIRP, 1999, 48 (1): 351-356
[144] Chen J S, Hsu W Y, Design and analysis of a tripod machine tool with an integrated Cartesian guiding and metrology mechanism, Precision Engineering, 2004, 28 (1): 46-57
[145] Merlet J P, Jacobian, manipulability, condition number and accuracy of parallel robots, ASME Journal of Mechanical Design, 2006, 128 (1): 199-206