摘要
本文研究少自由度机器人机构一体化参数建模体系、理论与方法,并以开发航空大型结构件高速数控加工装备为工程背景,将研究成果用于一种新型三坐标并联动力头的设计。全文取得了如下创造性成果:
在一体化参数建模体系架构研究方面,创造性地引入变分的概念,实现了对受约束刚体“许动”和“受限”微小运动在数学描述上的统一,使得在线性空间理论框架下建立不同类型的同维参数模型成为可能。
在一体化参数建模理论研究方面,以Lie代数、螺旋理论和线性空间理论为数学工具,定义了受约束刚体的变分空间、力空间及其子空间,运用虚功原理首次揭示并严格证明了各子空间的内在联系,构造出各子空间基底的流程与算法,并据此提出少自由度机器人机构广义雅可比矩阵的概念与通用建模方法。
在一体化参数建模方法研究方面,以广义雅可比矩阵为核心,提出一套少自由度串联与并联运动链速度、加速度、精度、力/刚度、刚体动力学普适性建模方法,并在以下5个方面形成特色:
(1)速度建模。利用广义雅可比矩阵显式格式和坐标变换方法,构造出与系统自由度同维的无量纲速度雅可比矩阵,克服了前人在构造这类矩阵时必须进行大量繁复求导运算的困难。
(2)加速度建模。继承了影响系数法和“Accelerator”法的优点,采用Lie括号运算法则构造出具有显式格式的海塞矩阵,突破了以往方法难于得到这类矩阵显式表达的瓶颈,使其具有更好的可计算性。
(3)误差建模。将矩阵摄动理论与螺旋理论有机结合,首次构造出可将影响末端可补偿与不可补偿位姿精度的几何误差源有效分离的普适性误差模型,为采用适当手段改善系统位姿精度提供了重要的判据。
(4)刚度建模。利用广义雅可比矩阵的结构特征,首次构造出将系统刚度矩阵表示成驱动与约束刚度线性叠加形式的普适性刚度模型,为指导零部件的机械结构详细设计提供了重要的依据。以3-UPS&UP并联机构为例,提出一种考虑UP支链弹性的约束刚度矩阵构造方法,为计及动平台弹性变形的并联机构刚度建模提供了有效手段。
(5)刚体动力学建模。借助力螺旋表达格式,使得系统刚体动力学模型更具完备性,并可解算出目前商用软件无法得到的广义约束力。
在工程应用方面,以开发航空大型结构件高速数控加工装备为工程背景,发明了一种具有自主知识产权的新型三坐标并联动力头——A3头。结合工程样机开发,全程演义了其位置、速度、加速度、精度、刚度和刚体动力学一体化建模流程;完成了基于等刚度匹配准则的优化设计、几何误差源灵敏度分析,以及伺服电机参数预估等设计任务,并将研究成果成功地用于首台实物样机的开发。
本文研究成果对丰富和发展机器人机构学设计理论,推进并联机器人技术的工程应用具有重要的理论意义和实用价值。
This dissertation presents a complete theoretical package for unified parameter modeling of lower mobility robotic manipulators, and its application to the design of a novel 3-DOF PKM (Parallel Kinematic Machine) module that can be employed to configure a CNC manufacturing cell for large structural component machining in aircraft industry. The following contributions have been made.
A variational representation is proposed to describe the permitted and restricted instantaneous motions of a constrained body in the configuration space. This breakthrough idea leads to the possibility to formulate various models having the same dimensions. Mainly drawing on linear algebra, supported by screw theory and Lie algebra, the wrench/twist spaces and their subspaces associated with the actuation/constraint forces and the permitted/restricted infinitesimal motions of a constrained rigid body are defined and the commutative relationships amongst these subspaces have been identified, reflecting, in general, two sides of a coin, i.e. the mobility and immobility of a constrained mechanical system. Exploiting the properties of these subspaces, a general and systematic methodology for formulating the generalized Jacobian is proposed.
Based upon the generalized Jacobian, a complete package is presented that enables velocity, acceleration, accuracy, force/stiffness, and rigid body dynamics modeling of lower mobility serial and parallel manipulators to be integrated into a unified mathematical framework. The major merits can be summarized in brief.
(1) Velocity modeling. A general approach to formulate dimensionally homogeneous Jacobian of lower mobility parallel manipulators having coupled translational and rotational movement capabilities is proposed, with which the heavy computational burden due to partial derivative implementations can dramatically be released.
(2) Acceleration modeling. Thanks to the Lie bracket representation the Hessian matrix in an explicit and compact form is formulated in comparison with the existing influence coefficient method and“Accelerator”method available at hand.
(3) Error modeling. The proposed error model allows the geometrical source errors affecting the compensatable and uncompensatable pose accuracy to be identified in an explicit manner, providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration.
(4) Stiffness modeling. It has been observed that the overall stiffness matrix can be expressed as a superposition of the actuation and constraint stiffness matrices. This thereby provides the field engineers with a guideline to carry out the detailed mechanical design. Particularly, by taking 3-UPS&UP parallel mechanism as an example, an effective stiffness modeling method is presented to deal with the circumstances where the platform rigidity needs to be taken into account.
(5) Rigid body dynamics. With the aid of wrench representation, the proposed dynamic model can be employed to evaluate the generalized constraint forces imposed upon the system. These forces, however, can not be achieved by the existing commercial software available on market.
The proposed modeling theory and methodology have been used in the design of a novel 3-DOF parallel module, named the A3 head, which can be used to configure a manufacturing cell for large structural component machining in aircraft industry. The work in this phase involves stiffness optimization, sensitivity analysis of source errors on the uncompensatable pose accuracy, and servo motor parameter estimation. The outcome has been successfully employed for the development of a prototype machine built by Tianjin University.
引文
[1] Pollard W L G, Spray painting machine, US Patent 2213108, 1940
[2] Gough V E, Whitehall, S G, Universal tyre test machine, In: Proceedings of the FISITA Ninth International Technical Congress, 1962: 117-137
[3] Cappel K L, Motion simulator, US Patent 3295224, 1967
[4] Clavel R, Device for the movement and positioning of an element in space, US Patent 4976582, 1990
[5] Wahl J, Articulated tool head, US Patent 6431802, 2002
[6] Neumann K E, Robot, US Patent 4732525, 1988
[7] Pritschow G, Wurst K-H, Systematic design of hexapods and other parallel link systems, CIRP Annals Manufacturing Technology, 1997, 46 (1): 291-295
[8] Tsai L-W, Robot Analysis: The mechanics of serial and parallel manipulators, New York: Wiley-Interscience Publication, 1999
[9] Tsai L-W, Systematic enumeration of parallel manipulators, Parallel kinematic machine: theoretical aspects and industrial requirement, New York: Springer, 1999: 33-49
[10] Fang Y, Tsai L-W, Structure synthesis of a class of 4-DoF and 5-DoF parallel manipulators with identical limb structures, International Journal of Robotics Research, 2002, 21(9): 799-810
[11] Rey L, Clavel R, The Delta parallel robot, Parallel kinematic machine: theoretical aspects and industrial requirement, New York: Springer, 1999: 401-417
[12] Gao F, Li W M, Zhao X C, et al, New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs, Mechanism and Machine Theory, 2002, 37: 1395-1411
[13] Available at: http://www.iwu.fhg.de
[14] Available at: http://www.index-werke.de
[15] Tonshoff H K, Grendel H K R, Structure and Characteristics of the Hybrid Manipulator George V, Parallel kinematic machine: theoretical aspects and industrial requirement, New York: Springer, 1999: 365-376
[16] Huang T, Li M, Li Z X, A 2-DOF translational parallel robot with revolute joints, CN patent 1355087, Dec. 31, 2001
[17] Huang T, Li M, Zhang D W, et al, 4-DOF hybrid robot, CN Patent 143942, 2003
[18] Huang, T, Li M, Li Z X, et al, A 5-DOF hybrid robot, Patent Cooperation Treaty, Int. Appl. PCT/CN2004/000479, 2004
[19]黄田,刘海涛,李曚,五自由度机器人, ZL 200510014459.8, 2007
[20]黄田,刘海涛,一种具有两转动和一平动自由度的并联机构, ZL 200610013608.3, 2008
[21] Ball R S, A Treatise on the theory of screws, Cambridge: Cambridge University Press, 1900
[22] Hunt K H, Kinematic geometry of mechanisms, Oxford: Oxford University Press, 1978
[23] Kim D, Chung W K, Kinematic condition analysis of three-DOF pure translational parallel manipulators, ASME Journal of Mechanical Design, 2003, 125: 323-331
[24] Li Q C, Huang Z, Type synthesis of 4-DOF parallel manipulators, In: Proceedings of the 2003 IEEE ICRA, Taipei, Taiwan, September 14-19, 2003: 755-760
[25] Li Q C, Huang Z, Type synthesis of 5-DOF parallel manipulators, In: Proceedings of the 2003 IEEE ICRA, Taipei, Taiwan, September 14-19, 2003: 103-1208
[26] Fang Y F, Tsai L-W, Structure synthesis of a class of 3-DOF rotational parallel manipulators, IEEE Transaction on Robotics and Automation, 2004, 20(1): 117-121
[27] Fang Y F, Tsai L-W, Structure synthesis of a class of 4-DOF and 5-DOF parallel manipulators with identical limb structures, The International Journal of Robotics Research, 2002, 21(9): 799-810
[28] Kong X W, Gosselin C M, Type synthesis of 3-DOF translational parallel manipulators based on screw theory, ASME Journal of Mechanical Design, 2004, 126: 83-92
[29] Kong X W, Gosselin C M, Type synthesis of 3-DOF spherical parallel manipulators based of screw theory, ASME Journal of Mechanical Design, 2004, 126: 101-108
[30] Kong X W, Gosselin C M, Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory, IEEE Transaction on Robotics and Automation, 2004, 20(2): 181-190
[31] Kong X, Gosselin C M, Type synthesis of 3-DOF PPR-equivalent parallel manipulators based on screw theory and the concept of virtual chain, ASME Journal of Mechanical Design, 2005, 127(6): 1113-1121
[32] Kong X, Gosselin C M, Type synthesis of 4-DOF SP-equivalent parallel manipulators: a virtual chain approach, Mechanism and Machine Theory, 2006, 41(11): 1306-1319
[33]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
[34] Jin Q, Yang T L, Structural synthesis of a class of five-DOF parallel robot mechanisms based on single-opened-chain units, In: Proceedings of ASME DETC/CIE Conference, Pittsburgh, PA, Sept. 9-12, 2001, Paper DAC-21 153
[35]杨廷力,机器人机构拓扑结构学,北京:机械工业出版社, 2004
[36] HervéJ M, Sparacino F, Structural synthesis of parallel robots generating spatial translation, In: IEEE/ICRA on Advanced Robotics, Pisa, Italy, 1991, 1: 808-813
[37] Sparacino F, HervéJ M, Synthesis of parallel manipulators using Lie-groups Y-star and H-robot, In: Proceedings of IEEE/Tsukuba International Workshop on Advanced Robotics, Tsukuba, Japan, Nov. 8-9, 1993: 75-80
[38] Angeles J, The qualitative synthesis of parallel manipulators, ASME Journal of Mechanical Design, 2004, 126(4): 617-624
[39] Huynh P, HervéJ M, Equivalent kinematic chains of three degree-of-freedom tripod mechanisms with planar-spherical bonds, ASME Journal of Mechanical Design, 2005, 127(1): 95-102
[40] Lee C-C, HervéJ M, Translational parallel manipulators with doubly planar limbs, Mechanism and Machine Theory, 2006, 41(4): 433-455
[41] Li Q, Huang Z, HervéJ M, Type synthesis of 3R2T 5-DOF parallel mechanisms using the lie group of displacements, IEEE Transactions on Robotics and Automation, 2004, 20(2): 173-180
[42] HervéJ M, Lie group of rigid body displacements, a fundamental tool for mechanism design, Mechanism and Machine Theory, 1999, 34(5): 719-730
[43] 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
[44] Yu J, Dai J S, Liu X-J, et al, Type synthesis of 3-DOF translational parallel manipulators based on atlas of DOF characteristic matrix, In: Proceedings of the ASME Design Engineering Technical Conference, 2006, Code 68587
[45] Meng J, Liu G F, Li Z X, A geometric theory for analysis and synthesis of sub-6 DOF parallel manipulators, IEEE Transactions on Robotics, 2007, 23(4): 625-649
[46] Merlet J P, Jacobian, manipulability, condition number, and accuracy of parallel robots, ASME Journal of Mechanical Design, 2006, 128(1): 199-206
[47] Tahmasebi F, Tsai L W, Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators, ASME Design and Engineering Division, 1992, 47: 95-102
[48] Stoughton R S, Arai T, Modified Stewart platform manipulator with improved dexterity, IEEE Transaction on Robotics and Automation, 1993, 9(2): 166-172
[49] Wang J, Gosselin C M, Kinematic analysis and singularity representation of spatial five-degree-of-freedom parallel mechanisms, Journal of Robotic System, 1997, 14(12): 851-869
[50] Siciliano B, Tricept robot: inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm, Robotica, 1999, vol. 17(4): 437-445
[51] Hong K S, Kim J G, Manipulability analysis of a parallel machine tool: application to optimal link length design, Journal of. Robotic System, 2000, 17(8): 403-415
[52] 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 Transaction on Robotics and Automation, 2003, 19(2): 200-209
[53] Callegari M, Tarantini M, Kinematic analysis of a novel translational platform, ASME Journal of Mechanical Design, 2003, 125(2): 308-315
[54] Huang T, Li M,. Li Z, Chetwynd D G, Whitehouse D J, Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index, IEEE Transaction on Robotics and Automation, 2004, 20(3): 538-543
[55] Alici G, Shirinzadeh B, Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing, Robotica, 2004, 22(1): 97-108
[56] Liu C H, Cheng S, Direct singular positions of 3RPS parallel manipulators, ASME Journal of Mechanical Design, 2004, 126(6): 1006-1016
[57] Oh K K, Liu X J, Kang D S, Kim J, Optimal design of a micro parallel positioning platform Part I: kinematic analysis, Robotica, 2004, 22(6): 599-609
[58] Huang T, Li M,. Zhao X M, Mei J P, Chetwynd D G, Hu S J, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant—a novel 5-DOF reconfigurable hybrid robot, IEEE Transaction on Robotics, 2005, 21(3): 449-456
[59] Milutinovic D S, Glavonjic M, Kvrgic V, Zivanovic S, A new 3-DOF spatial parallel mechanism for milling machines with long X Travel, Annals of the CIRP, 2005, 54(1): 345-348
[60] Li M, Huang T, Zhang D, Zhao X, Hu S J, Chetwynd D G, Conceptual design and dimensional synthesis of a reconfigurable hybrid robot, ASME Journal Manufacturing Science and Engineering, 2005, 127(3): 647-653
[61] Liu X J, Wang J, Pritschow G, On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism, Mechanism and. Machine Theory, 2006, 41(9): 1111-1130
[62] Liu H , Huang T, Mei J, Zhao X, Chetwynd D G, Li M, Hu S J, Kinematic design of a 5-DOF hybrid robot with large workspace/limb-stroke ratio, ASME Journal of Mechanical Design, 2007, 129(5): 530-537
[63] Richard P L, Gosselin C M, Kong X, Kinematic analysis and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator, ASME Journal of Mechanical Design, 2007, 129(6): 611-616
[64] Liu X J, Guan L, Wang J, Kinematic and closed optimal design of a kind of PRRRP parallel manipulator, ASME Journal of Mechanical Design, 2007, 129(5): 558-563
[65] Angeles J, Fundamentals of robotic mechanical systems, theory, methods, and algorithms, Springer-Verlag, 2nd ed., New York., 2003
[66] Kumar V, Instantaneous kinematics of parallel-chain robotic mechanisms, ASME Journal of Mechanical Design, 1992, 114(9): 349-358
[67] Chen Y C, Walker I D, A consistent approach to the instantaneous kinematics of redundant, non-redundant and in-parallel manipulators, In: Proceedings of the IEEE International Conference on Robotics and Automation, 1994: 2172-2178
[68] Ling S H, Huang M Z, Kinestatic analysis of general parallel manipulators, ASME Journal of Mechanical Design, 1995, 117(12): 601-606
[69] Kim D, Chuan W, Youm Y, Analytic Jacobian of in-parallel manipulators, In: Proceedings of the IEEE International Conference on Robotics and Automation, 2000: 2376-2381
[70] Chan V K, Ebert-Uphoff I, Investigation of the deficiencies of parallel manipulators in singular configurations through the Jacobian nullspace, In: Proceedings of the IEEE International Conference on Robotics and Automation, 2001: 1313-1320
[71] Joshi S, Tsai L W, Jacobian analysis of limited-DOF parallel manipulators, ASME Journal of Mechanical Design, 2002, 124(2): 254-258
[72] Zlatanov D, Bonev I A, Gosselin C M, Constraint singularities of parallel mechanisms, In: Proceedings of IEEE International Conference on Robotics and Automation, 2002, 1: 496-502
[73] Zoppi M, Zlatanov D, Molfino R, On the velocity analysis of interconnected chains mechanisms, Mechanism and Machine Theory, 2006, 41(11): 1346-1358
[74] Hong M B, Choi Y J, Kinestatic analysis of nonsingular lower mobility manipulators, IEEE Transaction on Robotics, 2009, 25(4): 938-942
[75] Thomas M, Twsar D, Dynamic modeling of serial manipulator arms, ASME Journal of Mechanical Design, 1982, 104(9) 218-228
[76] Wang H B, Huang Z, Kinematic influence coefficient method of kinematic and dynamic analysis, Mechanism Machine Theory, 1990, 25(2):167-173
[77] Zhu S J, Huang Z, Ding H F, Forward/reverse velocity and acceleration analysis for a class of lower-mobility parallel mechanisms, ASME Journal Mechanical Design, 2007, 129(4): 390-396
[78] Lipkin H, Duffy J, Hybrid twist and wrench control for a robotic manipulator, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 1988, 110(2): 138-144
[79] Doty K, Melchiorri C, Bonevento C, A theory of generalized inverse applied to robotics, International Journal of Robotic Research, 1993, 12(1): 1-19
[80] Doty K, Melchiorri C, Schwartz E M, Bonevento C, Robot manipulability, IEEE Transaction on Robotics and Automation, 1995, 11: 462-468
[81] Ma O, Angeles J, Optimum architecture design of platform manipulators, In: The fifth International Conference on Advanced Robotics, 1991, 2: 1130-1135
[82] Tandirci M, Angeles J, Ranjbaran F, Characteristic point and the characteristic length of robotic manipulators, ASME Design and Engineering Division, 1992, 45: 203-208
[83] Angeles J, Ranjbaran F, Patel R V, On the design of the kinematic structure of seven-axes redundant manipulators for maximum conditioning, In: Proceedings of the IEEE International Conference Robotics and Automation, 1992: 494-499
[84] Angeles J, Kinematic isotropy in humans and machines, In: Proceedings of the IFToMM 9th World Congress, 1995, 2(1): XLII-XLIX
[85] Angeles J, Is there a characteristic length of a rigid-body displacement?, Mechanism and Machine Theory, 2006, 41(8): 884-896
[86] Khan W A, Angeles J, The kinetostatic optimization of robotic manipulators: the inverse and the direct problems, ASME Journal of Mechanical Design, 2006, 128(1): 168-178
[87] Gosselin C M, The optimum design of robotic manipulators using dexterity indices, Journal of Robotics and Automation System, 1992, 9(4): 213-226
[88] Kim S G, Ryu J, New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators, IEEE Transaction on Robotics and Automation, 2003, 19(4): 731-736
[89] Kong M, Zhang Y, Du Z, Sun L, A novel approach to deriving the unit-homogeneous Jacobian matrices of mechanisms, In: Proceedings of the IEEE International Conference on Mechatronics and Automation, 2007: 3051-3055
[90] Pond G, Carretero J A, Formulating Jacobian matrices for the dexterity analysis of parallel manipulators, Mechanism and Machine Theory, 2006, 41: 1505-1519
[91] Pond G, Carretero J A, Quantitative dexterous workspace comparison of parallel manipulators, Mechanism and Machine Theory, 2007, 42(10): 1388-1400
[92] Tsai L W, Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work, ASME Journal of Mechanical Design, 2000, 122(3): 3-9
[93] Khalil W, Guegan S, Inverse and direct dynamic Modeling of Gough–Stewart Robots, IEEE Transactions on Robotics, 2004, 20(4): 754-762
[94] Callegari M, Palpacelli M C, Principi M, Dyanmics modelling and control of the 3-RCC translational platform, Mechatronics, 2006, 16: 589-605
[95] Staicu S, Zhang D, A novel dynamic modelling approach for parallel mechanisms analysis, Robotics and Computer-Integrated Manufacturing, 2008, 24: 167-172
[96] Staicu S, Inverse dynamics of the 3-PRR planar parallel robot, Robotics and Autonomous Systems, 2009, 57: 556-563
[97] Huang Z, Modeling formulation of 6-dof multi-loop parallel mechanisms, In: Proceeding of the 4th IFToMM International Symposium on Lingkage and Computer Aided Design Methods, 1985, II-1: 155-162
[98] Huang Z, Modeling formulation of 6-dof multi-loop parallel mechanisms, In: Proceeding of the 4th IFToMM International Symposium on Lingkage and Computer Aided Design Methods, 1985, II-1: 163-170
[99] Zhu S J, Huang Z, Guo X J, Forward/reverse velocity and acceleration analyses for a class of lower-mobility parallel mechanisms, In: Proceedings ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2005: 949-955
[100] Fang Y, Huang Z, Kinematics of a three-degree-of-freedom in-parallel actuated manipulator mechanism, Mechanism and Machine Theory, 1997, 32(7): 789-796
[101] Lu Y, Using CAD variation geometry and analytic approach for solving kinematics of a novel 3-SPU/3-SPU parallel manipulator, ASME Journal of Mechanical Design, 2006, 128(5): 574-580
[102] Lu Y, Shi Y, Hu B, Kinematic analysis of two novel 3UPPU I and 3UPU II PKMs, Robotics and Autonomous Systems, 2008, 56: 296-305
[103] Lu Y, Hu B, Analyzing kinematics and solving active/constrained forces of a 3SPU+UPR parallel manipulator, Mechanism and Machine Theory, 2007, 42(10): 1298-1313
[104] Lu Y, Hu B, Unified solving Jacobian/Hessian matrices of some parallel manipulators with n SPS active legs and a passive constrained leg, ASME Journal of Mechanical Design, 2007, 129(11): 1161-1169
[105] Lu Y, Hu B, Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs, Mechanism and Machine Theory, 2008, 43(9): 1112-1128
[106] Sugimoto K, Existence criteria for overconstrained mechanisms: an extension of motor algebra, ASME Journal of Mechanical Design, 1990, 112(3):. 295-298
[107] Brand L, Vector and tensor analysis, John Wiley and Sons, New York, 1947
[108] Rico J M, Duffy J, An application of screw algebra to the acceleration analysis of serial chains, Mechanism and Machine Theory, 1996, 31(4): 445-457
[109] Rico J M, Duffy J, Forward and inverse acceleration analysis of in-parallel manipulator, ASME Journal of Mechanical Design, 2000, 122(9): 1161-1169
[110] Gallardo J, Rico J M, Frisoli A, Checcacci D, Bergamasco M, Dynamics of parallel manipulators by means of screw theory, Mechanism and Machine Theory, 2003, 38(11): 1113-1131
[111] Gallardo J, Rico J M, Alici G, Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory, Mechanism and Machine Theory, 2006, 41(9): 1113-1131
[112] Crane III C D, Duffy J, A synamic analysis of a spatial manipulator to determine the payload weight, Journal of Robotic Systems, 2003, 90(7): 355-371
[113] Schellekens P, Rosielle N, Vermeulen H, Vermeulen M, Wetzels S, Pril W, Design for precision: current status and trends, CIRP Annals - Manufacturing Technology, 1998, 47(2): 557-586
[114] Wurst K H, Linapod-machine tools as parallel link systems based on a modular design, In: Proceeding of the 1st European-American Forum on Parallel Kinematic Machines, Milan, Italy, 1998: 377-394
[115] Patel A J, Ehmann K F, Volumetric error of a Stewart platform-based machine tool, CIRP Annals-Manufacturing Technology, 1997, 46: 287-290
[116] Wang S M, Ehmann K F, Error model and accuracy analysis of a six-DOF Stewart platform, ASME Journal of Manufacturing Science and Engineering, 2002, 124(2): 286-295
[117] Ryu J, Cha J, Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators, Mechanism and Machine Theory, 2003, 38: 227-240
[118] Weck M, Staimer D, Parallel kinematic machine tools—current state and future potentials, CIRP Annals-Manufacturing Technology, 2002, 51(2): 671-683
[119] Denavit J, Hartenberg R S, Kinematic notation for lower-pair mechanisms based on matrices, ASME Journal of Applied Mechanics, 1955, 2: 211-215
[120] Wang J, Masonry O, On the accuracy of a Stewart platform Part I: the effect of manufacturing tolerances, In: Procceedings of International Conference on Robotics and Automation, 1993, 1: 114-120
[121] Maurine P, Dombre E., Calibration procedure for the parallel robot Delta 4, In: Proceedings of the IEEE International Conference on Robotics and Automation, 1996, 2: 975-980
[122] Wang Y, Pessi P, Wu H, Handroos H, Accuracy analysis of hybrid parallel robot for the assembling of ITER, Fusion Engineering and Design, 2009, 84(7-11): 1964-1968
[123] Zhuang H, Roth Z S, Hamano F, A complete and parametrically continuous kinematic model for robot manipulators, IEEE Transactions on Robotics and Automation, 1992, 8(4): 451-463
[124] Hayati S A, Mirmirani M, Improving the absolute positioning accuracy of robot manipulators, Journal of Robotic System, 1985, 2(4): 397-413
[125] Veitschegger W K, Wu C H, Robot accuracy analysis based on kinematics, IEEE Journal of Robotics and Automation, 1986, RA-2(3): 171-179
[126] Liu J, Zhang Y, Improving the positioning accuracy of a neurosurgical robot system, IEEE/ASME Transactions on Mechatronics, 2007, 12(5): 527-533
[127] Stone H W, Kinematic modeling, identification, and control of robotic manipulators, Kluwer Academic Publishers, Dordrecht, 1987
[128] Zhuang H, Roth Z S, Robot calibration using the CPC error model, Journal of Robotics and Computer Integrated Manufacturing, 1992, 9(3): 227-237
[129] Okamura K, Park F C, Kinematic calibration and the product of exponential formula, Robotica, 1996, 14: 415-421
[130] Chen I M, Yang G, Tan C T, Yeo S H, Local POE model for robot kinematic calibration, Mechanism and Machine Theory, 2001, 36: 1215-1239
[131] Iurascu C C, Park F C, Geometric algorithms for kinematic calibration of robots containing closed loops, ASME Journal of Mechanical Design, 2003, 125(3): 23-32
[132] Meng J, Li Z, A general approach for accuracy analysis of parallel manipulators with joint clearance, In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005, 790-795
[133] Jin Y, Chen I M, Effects of constraint errors on parallel manipulators with decoupled motion, Mechanism and Machine Theory, 2006, 41: 912-928
[134] Huang T, Whitehouse D J, Chetwynd D G, A unified error model for tolerance design, assembly and error compensation of 3-DOF parallel kinematic machines with parallelogram struts, CIRP Annals-Manufacturing Technology, 2002, 51(1): 297-301
[135] Huang T, Li Y, Tang G, Li S, Zhao X, Whitehouse D J, Chetwynd D G, Liu X, Error modeling, sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts, Science in China Series E: Technological Sciences, 2002, 45(5): 467-476
[136] Huang T, Chetwynd D G, Mei J P, Zhao X M, Tolerance design of 2-DOF overconstrained translational parallel robot, IEEE Transaction on Robotics, 2006, 22(1): 167-172
[137] Gosselin C M, Stiffness mapping for parallel manipulators, IEEE Transactions On Robotics and Automation, 1990, 6(3): 377-382
[138] 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
[139] Lee M K, Design of a high stiffness machining robot arm using double parallel mechanisms, In: Proceedings of the IEEE International Conference on Robotics and Automation, 1995, 1: 234-240
[140] 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
[141] Stoughton R S, Arai T, A modified Stewart platform with improved dexterity, IEEE Transaction on Robotics and Automation, 1993, 9(2): 166-172
[142] 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
[143] Bhattacharya H, et al, On the optimum design of Stewart platform type manipulators, Robotica, 1995, 13: 133-140
[144] 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
[145] 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
[146] Robert R G, Minimal realization of a spatial stiffness matrix with simple springs connected in parallel, In: Proceedings of IEEE International Conference on Robotics and Automation, 1999, 3: 2153-2158
[147] 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
[148] Huang S, Schimmels J M, The eigenscrew decomposition of spatial stiffness matrices, IEEE Transactions on Robotics and Automation, 2000, 16(2): 146-156
[149] 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
[150] 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
[151] 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
[152] Tsai L W, Walsh G, et al, Kinematics of a novel three DOF translational platform, In: Proceedings of the IEEE International Conference On Robotics and Automation, Minneapolis, USA, 1996, 4: 3446-3451
[153] Tsai L W, Joski S, Comparison study of architectures of four 3 degree-of-freedom translational parallel manipulators, In: Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea, 2001, 2: 1283-1288
[154] 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
[155] Goldsmith P B, Kinematics and stiffness of a symmetrical 3-UPU translational parallel manipulator, In: Proceedings of the IEEE International Conference on Robotics and Automation, Washington, USA, 2002, 4: 4102-4107
[156] Goldsmith P B, Design and kinematics of a three-legged parallel manipulator, IEEE Transactions of Robotics and Automation, 2003, 19(4): 726-731
[157] 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
[158] Majou F, Gosselin C, Wenger P, et al, Parametric stiffness analysis of the Orthoglide, Mechanism and Machine Theory, 2007, 42(3): 296-311
[159] Kim J, Park F C, Kim M, Geometric design tools for stiffness and vibration analysis of robotic mechanisms, In: Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, USA, 2000, 2: 1942-1947
[160] 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
[161] Koseki Y, Tanikawa T, Koyachi N, et al, Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method, In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, 2000, 1: 786-792
[162] Company C, Pierrot F, Modelling and design issues of a 3-axis parallel machine tool, Mechanism and Machine Theory, 2002, 37(11): 1325-1345
[163] Yoon W-K, Suehiro T, Tsumaki Y, et al, A method for analyzing parallel mechanism stiffness including elastic deformations in the structure, In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, 2002, 3: 2875-2880
[164] Yoon W-K, Suehiro T, Tsumaki Y, et al, A compact modified Delta parallel mechanism design based on a stiffness analysis, In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2003, 2: 1262-1267
[165] 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, In: Proceedings of the 12th World Congress in Mechanism and Machine Science, Besancon, France, 2007, 5: 623-628
[166] 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
[167]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
[168]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
[169]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
[170] 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
[171] Xu Q S, Li Y M, Stiffness modeling for an orthogonal 3-PUU compliant parallel micromanipulator, In: Proceedings of the IEEE International Conference on Mechatronics and Automation, 2006, 1: 124-129
[172] 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, 2008, 24(3): 402-414
[173] Dai J S, Ding X, Compliance analysis of a three legged rigidly connected platform, ASME Journal of Mechanical Design, 2006, 128(4): 755-764
[174] 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
[175] 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
[176] 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
[177] 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
[178] 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
[179] Zhang D, On stiffness improvement of the Tricept machine tool, Robotica, 2005, 23(3): 377-386
[180] 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
[181] 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
[182] 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
[183] 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
[184] 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
[185] 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
[186] 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
[187] 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
[188] Wang Y, Liu H, Huang T, Chetwynd D G, Stiffness modeling of the Tricept robot using the overall Jacobian matrix, ASME Journal of Mechanisms and Robotics, 2009, 1(2): 021002.1-021002.8
[189] Dasgupta B, Mruthyunjaya T S, A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator, Mechanism and Machine Theory, 1998, 33(8): 1135-1152
[190] Dasgupta B, Mruthyunjaya T S, Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach, Mechanism and Machine Theory, 1998, 33(7): 993-1012
[191] Dasgupta B, Choudhury P, General strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators, Mechanism and Machine Theory, 1999, 34(6): 801-824
[192] Pang H, Shahinpoor M, Inverse dynamics of a parallel manipulator, Journal of Robotic Systems, 1994, 11(8): 693-702
[193] Liu M J, Li C X, Li C N, Dynamics analysis of the Gough-Stewart platform manipulator, IEEE Transactions on Robotics and Automation, 2000, 16(1): 94-98
[194] Zhang C D, Song S M, Efficient method for inverse dynamics of manipulators based on the virtual work principle, Journal of Robotic Systems, 1993, 10(5): 605-627
[195] Tsai L-W, Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work, ASME Journal of Mechanical Design, 2000, 122(1): 3-9
[196] Wang J, Gosselin C M, A new approach for the dynamic analysis of parallel manipulators, Multibody System Dynamics, 1998, 2(3): 317-334
[197] Lee K M, Shah D K, Dynamic analysis of a three-degrees-of-freedom in-parallel actuated manipulator, IEEE Transactions on Robotics and Automation, 1988, 4(3): 361-367
[198] Dasgupta B, Mruthyunjaya T S, Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach, Mechanism and Machine Theory, 1998, 33(7): 993-1012
[199] Tsai L W, Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work, ASME Journal of Mechanical Design, 2000, 122(3): 3-9
[200] Huang T, Zhao X, Wang Y, Mei J, Ni Y, Determination of servomotor parameters of a tripod-based parallel kinematic machine, Progress of Natural Science, 2001, 11(8): 612-621
[201] Cheng H, Yiu Y K, Dynamics and control of redundantly actuated parallel manipulators, IEEE/ASME Transactions on Mechanics, 2003, 8(4): 483-491
[202] Wisama K, Sylvain G, Inverse and direct dynamic modeling of Gough–Stewart robots, IEEE Transactions on Robotics, 2004, 20(4): 754-762
[203] Gregorio R D, Vincenzo P C, Dynamics of a class of parallel wrists, ASME Journal of Mechanical Design, 2004, 126(3): 436-441
[204] Huang T, Mei J P, Li Z X, Zhao X M, Chetwynd D G, A method for estimating servomotor parameters of a parallel robot for rapid pick-and-place operations, ASME Journal of Mechanical Design, 2005, 127(4): 596-601
[205] Li M, Huang T, Mei J P, Zhao X M, Chetwynd D G, Hu S J, Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable PKMs—the Tricept and the TriVariant, ASME Journal of Mechanical Design, 2005, 127(6): 1129-1136
[206] Zhu Z, Li J, Gan Z, Zhang H, Kinematic and dynamic modelling for real-time control of Tau parallel robot, Mechanism and Machine Theory, 2005, 40(9): 1051-1067
[207] Callegari M, Palpacelli M C, Principi M, Dynamics modelling and control of the 3-RCC translational platform, Mechatronics, 2006, 16(10): 589-605
[208] Sokolov A, Xirouchakis P, Dynamics analysis of a 3-DOF parallel manipulator with R–P–S joint structure, Mechanism and Machine Theory, 2007, 42(5): 541-557
[209] Liu H, Mei J, Zhao X, Huang T, Chetwynd D G, Inverse dynamics and servomotor parameter estimation of a 2-DOF spherical parallel mechanism, Science in China, Series E: Technological Science, 2008, 51(3): 288-301
[210] Nidal F, Vicente M, Alvaro P, Francisco V, Identification of dynamic parameters of a 3-DOF RPS parallel manipulator, Mechanism and Machine Theory, 2008, 43(1): 1-17
[211] Staicu S, Zhang D, A novel dynamic modelling approach for parallel mechanisms analysis, Robotics and Computer-Integrated Manufacturing, 2008, 24(1): 167-172
[212] Staicu S, Dynamics analysis of the Star parallel manipulator, Robotics and Autonomous Systems, 2009, 57(1): 1-10
[213] Staicu, S., Inverse dynamics of the 3-PRR planar parallel robot, Robotics and Autonomous Systems, 2009, 57(5): 556-563
[214] Geike T, McPhee J, Inverse dynamic analysis of parallel manipulators with full mobility, Mechanism and Machine Theory, 2003, 38(6): 549-562
[215] Murray R, Li Z X, Sastry S, A mathematical introduction to robotic manipulation, Boca Raton, FL: CRC, 1994
[216] Hogben L, Handbook of linear algebra, Chapman & Hall/CRC, 2007
[217]张贤达,矩阵分析与应用,清华大学出版社, 2004
[218]华罗庚,高等数学引论(第四册),高等教育出版社, 2008
[219] Carretero J A, Podhorodeski R P, Nahon M A, Gosselin C M, Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator, ASME Journal of Mechanical Design, 2000, 122, (1): 17-24
[220] Dai J S, Jones J R, A linear algebraic procedure in obtaining reciprocal screw systems, Journal of Robotic System, 2003, 20(7): 401-412
[221] Available at: http://www.exechon.com
[222] Huang T, Liu H, A parallel device having double rotation freedoms and one translation freedom, PCT WO 2007/124637, 2007
[223] Lipkin H, Time derivatives of screws with applications to dynamics and stiffness, Mechanism and Machine Theory, 2005, 40(3): 259-273
[224]熊有伦,丁汉,刘恩沧,机器人学,机械工业出版社,1993
[225] Li Y, Liu H, Zhao X, Huang T, Design of a 3-DOF PKM module for large structural component machining, Mechanism and Machine Theory, accepted
[226]文怀兴,夏田,数控机床系统设计,化学工业出版社工业装备与信息工程出版中心,2005