3-RRR并联微动工作台研制及其误差分析
|
摘要
本文结合一种平面3-RRR并联微动工作台的研制，对其运动学、机构优化和精度问题进行了全面的研究。微动台采用免装配、无间隙和无摩擦的柔性铰链代替实际的转动副并且依靠压电陶瓷驱动器驱动，实现了工作台x向和y向的微米级位移以及在x—y平面内的微小转动。
论文提出了并联微动台伪刚体模型位姿反解、正解的方法，并进一步推导了微动条件下的线性运动学模型：常量雅各比矩阵法和铰链位移法，通过不同方法的比较得到了近似模型的理论精度。另外讨论了机构的各向同性指标以及利用Matlab软件对理论工作空间进行了仿真。
论文随后对微动工作台的静力学、动力学和柔性铰链进行了分析，得到了相应的计算公式。之后详细讨论了压电陶瓷驱动器的各项性能指标，针对迟滞性采用了Prcisach模型法消除，并通过实验对驱动器各项性能进行了测定。随后基于并联微动台各项性能指标对机构的参数进行了优化，得到了符合要求的结果。
论文还提出并建立合理的实验系统，通过实验对雅各比矩阵进行了标定，并且为之后的误差分析积累了必要的数据。最后，分析了影响并联微动平台精度的各项误差源，并通过实验数据对这些误差进行估计和综合。
With the development of a Planar 3-RRR parallel micro-motion stage, kinematic, structure optimization and precision of this stage is studied in this thesis. This micro-motion stage is constructed based on the compliant mechanism concept. It's a monolithic compliant mechanism utilizing flexure hinges. The micro-motion stage is actuated by three PZT stack actuators. The end-effector platform of the stage can translate along x, y-axis and rotate about the z-axis.
In this thesis, inverse and direct position analysis of the 3-RRR micro-motion stage is derived based on the pseudo-rigid-body model(PRBM). As a linear, effective kinematic model, constant-Jacobian method and loop closeure theory are presented. Isotropy and workspace capacity are also discussed.
The model of static, dynamic and flexure hinge stiffness matrix are formulated. Moreover, characteristics of PZT are investigated and measured by experiment. Especially, Preisach model method is derived to eliminate the hysteresis nonlinearity. Several defferent criteria are used to produce designs having optimum characteristics.
In addition, the experiment of the micro-motion stage is designed and studied which calibrate the Jacobian matrix and present essential data for error analysis. Finally, Analyze the sources of error and evaluate the main error quantity based on experiment data and obtain the synthesis of all error.
论文提出了并联微动台伪刚体模型位姿反解、正解的方法，并进一步推导了微动条件下的线性运动学模型：常量雅各比矩阵法和铰链位移法，通过不同方法的比较得到了近似模型的理论精度。另外讨论了机构的各向同性指标以及利用Matlab软件对理论工作空间进行了仿真。
论文随后对微动工作台的静力学、动力学和柔性铰链进行了分析，得到了相应的计算公式。之后详细讨论了压电陶瓷驱动器的各项性能指标，针对迟滞性采用了Prcisach模型法消除，并通过实验对驱动器各项性能进行了测定。随后基于并联微动台各项性能指标对机构的参数进行了优化，得到了符合要求的结果。
论文还提出并建立合理的实验系统，通过实验对雅各比矩阵进行了标定，并且为之后的误差分析积累了必要的数据。最后，分析了影响并联微动平台精度的各项误差源，并通过实验数据对这些误差进行估计和综合。
With the development of a Planar 3-RRR parallel micro-motion stage, kinematic, structure optimization and precision of this stage is studied in this thesis. This micro-motion stage is constructed based on the compliant mechanism concept. It's a monolithic compliant mechanism utilizing flexure hinges. The micro-motion stage is actuated by three PZT stack actuators. The end-effector platform of the stage can translate along x, y-axis and rotate about the z-axis.
In this thesis, inverse and direct position analysis of the 3-RRR micro-motion stage is derived based on the pseudo-rigid-body model(PRBM). As a linear, effective kinematic model, constant-Jacobian method and loop closeure theory are presented. Isotropy and workspace capacity are also discussed.
The model of static, dynamic and flexure hinge stiffness matrix are formulated. Moreover, characteristics of PZT are investigated and measured by experiment. Especially, Preisach model method is derived to eliminate the hysteresis nonlinearity. Several defferent criteria are used to produce designs having optimum characteristics.
In addition, the experiment of the micro-motion stage is designed and studied which calibrate the Jacobian matrix and present essential data for error analysis. Finally, Analyze the sources of error and evaluate the main error quantity based on experiment data and obtain the synthesis of all error.
引文
[1] Ellis G W.Piezoelectric Micromanipulators[J]. Science Instruments andTechniques, 138 1962 84-91.
[2] 贾庆轩，魏秋霜等 并联微动机器人的研究现状 山东理工大学学报 17(6) 2003．11
[3] 夏广岚，胡晓平等 并联机器人发展现状与展望 中国科技信息 2005．12
[4] 赵新华，赵连玉，温殿英，解宁 并联机器人运动学传动性能研究机械设计 2002．3
[5] 高峰 并联机器人设计理论及其关键应用技术研究 河北工业大学学报 2004．4
[6] PeterBaley. AMachine for the 21st Century [J]. Machinery and ProductionEngineering. 1995(1)
[7] BrnnoSiciliano. TheTricept robot: Inverse kinemaeics, manipulability analysisand closed-loop direct Kinematics algorithm [J]. Robotica. 1999,17(4)437-445
[8] ManfredWeck, MichaelDanmoer. Design, calculation and control of machinetools based on parallel kinematics[A]. In:Proc. Of the ASME[C]. MED-vol. 81998:715-721
[9] 王知行，李建生 BJ-1型并联机床 制造技术与机床 1999．9
[10] 蔡光起，戴炬，胡明等 机器人化三腿磨削机床的研制 制造技术与机 1998．10
[11] 邱志成，谈大龙，赵明扬 并联机器人研究现状研究开发 2000．4
[12] Hudgens J C, Tesar D.A Fully-parallel Six Degree-of-freedomMieromanipulator [J]. Kinematic Analysis and Dynamic Model. ASME,Mechanisms Conf.Mechanism Machines and Robotics 1998 15(3) 29-37.
[13] Chang-Soo Han, Jeffrey C. Hudgens, Delbert Tesar. Traver, Modeling,Synthesis, Analysis and Design of High Resolution Micromunipulator toEnhance Robot Accuracy[C]. IEEE/RSJ International Workshop on IntelligentRobot and Systems IROS/91 Osaka. 1991 3-5
[14] Pernette T,Henein S,et al.Design of Parallel Robots in Microrobotics[J] .Robotica, 1997.15 417-420.
[15] Pasi Kallio, Mikael Lind, Quan Zhou, et al. A 3DOF Piezohydraulic ParallelMicromanipulator[C]. IEEE International Conference on Robotics &Automation Leuven. 1998 566-570.
[16] Lee K.Arijunan M. A Three Degree of Freedom Micro-motion-in-parallel Actuated Manipulator[C]. IEEE Conf.On Robotics and Automation. 198928-37.
[17] Pernette Eric, Clavel Reymond. Parallel Robots and Microrobotics[C] .ISRAM, Montpellier 1996 535-540.
[18] Bi Shusheng, Zong Guanghua, Liu Rong, et al. Accuracy Analysis of theSerial-parallel Micromotion Manipulator. IEEE International Conference onRobotics and Automation. 1997 2258-2263.
[19] 毕树生，王守杰，宗光华 串并联微动机构的运动分析 机器人19(4)1997 247-251．
[20] Xudong Li, Guanghua Zong and Shusheng Bi. Development of Global VisionSystem. for Biologic Automatic Micro-Manipulation System. IEEEInternational Conference on Robotics & Automation, Seoul, 2001:127-132.
[21] 毕树生，宗光华 微操作机器人系统的研究开发 中国机械工程10(9)19991024-1027
[22] 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 183-186
[23] 于靖军，毕树生，宗光华 全柔性微位移放大机构的设计技术研究 航空学报 2004．1
[24] I. Her, J.C. Chang. A linear scheme for the displacement analysis ofmicropositioning stages with flexure hinges. Transactions of the ASME,Journal of Mechanical Design. 1(116) 1994 770-776
[25] 姜虹， 贾嵘等 六自由度并联机器人位置正解的数值解法 上海交通大学学报 2000．3
[26] Salisbury J K, Craig J J. Articulated hands: force control and kinematicissues[J]. J. of Robotic Research 1(1) 1982 4-12
[27] 方跃法，房海蓉，牟建斌 并联机器人误差敏感系数及其在工作空间内的分布 北方交通大学学报 2000．4
[28] Angeles J, Lopez-cajun C S. Kniematic isotropy and the conditioning index ofserial robotic manipulators [J]. J. of Robotic Research 11(6) 1992 560-571
[29] Gosselin C M. The optimum design of manipulators using dexterity indices [J] .Robotics and Automation Systems 1992.9:213-226
[30] Yuen Kuan Yong, Tien-Fu Lu, Daniel C. Loop Closure Theory in DerivingLinear and Simple Kinematic Model for a 3 DOF Parallel Micromanipulator.Proceedings of SPIE International Symposium on Device and ProcessTechnologies for Microelectronics, MEMS, and Photonics, Perth, Australia2003.12:10-12
[31] 李庆祥，王东生，李玉和等现代精密仪器设计 北京：清华大学出版社， 2004
[32] Do,W.Q.D and Yang, D.C.H. Inverse Dynamic Analysis and Simulation of aPlatform Type of Robot J. Robot. Syst. 1994.5 209-227
[33] Tsai, K.Y, Kohli.D. Modified Newton-Euler Computational Scheme forConfiguration Based on R-L Actuators. Proc. 1990 ASMW DesignEngineering Technical Conferences, Sacramento, CA. 1990
[34] Lebret, G., Liu, K., and Lewis, F.L., Dynamic Analysis and Control of aStewart Platform Manipulator, Robot[J]. 1993.7 507-534.
[35] Pang, H. Shahingpoor, M., Inverse Dynamics of a Parallel Manipulator.Robot[J] .1994.8 103-115.
[36] Codourey, A. and Burdet, E. A Body-oriented Method for Finding a LinearForm of the Dynamic Equation of Fully Parallel Robots. Proc. 1997 IEEEInternational Conference on Robotics and Automation, Albuquerque, NM,1997 1612-1618.
[37] Tsai, L. W. Solving the Inverse Dynamics of Parallel Manipulators by thePrinciple of Virtual Work. DETC98/MECH-5865, Proc. ASME DesignEngineering Technical Conferences, Atlanta, GA.
[38] 熊有伦 机器人技术基础 华中理工大学出版社1996
[39] 李国荣，陈大任，殷庆瑞 PZT系多层片式压电陶瓷微驱动器性能研究 无机材料学报 1999．6
[40] 张涛，孙立宁，蔡鹤翶 压电陶瓷基本特性研究 光学精密工程 1998．10
[41] 魏燕定，陶惠峰 压电驱动器迟滞特性的Preisach模型研究 压电与声光 2004
[42] NEW COMB C V. Improving the linearity of piezo-electricceramic actuators[J]. Elec Let 18(11) 1982 442-444.
[43] JUNG S B, KIM S W. Improvement of scanning accuracy of PZTpiezoelectric actuators by feed-forward model reference control[J]. PrecisionEngineering 16(1) 1994 49-55.
[44] 王建林，刘文晖，胡晓东等．压电微位移器在超微定位系统中的应用压电与声光19(2)1997 95-97
[45] PING Ge, M U SA Jouaneh. Generalized preisaeh model for hysteresisnonlinearity of piezoceramie actuators [J]. PrecisionEngineering. 20(2) 1997 99-111.
[46] 于靖军，周强等 基于动力学性能的全柔性机构优化设计 机械工程学报 2003．8 33
[47] 赵新华，张威 基于条件数的3-RTT并联机器人参数优化中国机械工程 2004．11 1903-1905
[48] 于靖军，周强 等基于动力学性能的全柔性机构优化设计 机械工程学报 2003．8
[49] 费业泰 误差理论与数据处理机械工业出版社 2000．5 95-103
[50] 张志涌，徐彦琴等 MATLAB教程：基于6.X版本北京航空航天大学出版社 2001．4
[51] 费业泰 误差理论与数据处理 机械工业出版社 2000．5 107-108
[2] 贾庆轩，魏秋霜等 并联微动机器人的研究现状 山东理工大学学报 17(6) 2003．11
[3] 夏广岚，胡晓平等 并联机器人发展现状与展望 中国科技信息 2005．12
[4] 赵新华，赵连玉，温殿英，解宁 并联机器人运动学传动性能研究机械设计 2002．3
[5] 高峰 并联机器人设计理论及其关键应用技术研究 河北工业大学学报 2004．4
[6] PeterBaley. AMachine for the 21st Century [J]. Machinery and ProductionEngineering. 1995(1)
[7] BrnnoSiciliano. TheTricept robot: Inverse kinemaeics, manipulability analysisand closed-loop direct Kinematics algorithm [J]. Robotica. 1999,17(4)437-445
[8] ManfredWeck, MichaelDanmoer. Design, calculation and control of machinetools based on parallel kinematics[A]. In:Proc. Of the ASME[C]. MED-vol. 81998:715-721
[9] 王知行，李建生 BJ-1型并联机床 制造技术与机床 1999．9
[10] 蔡光起，戴炬，胡明等 机器人化三腿磨削机床的研制 制造技术与机 1998．10
[11] 邱志成，谈大龙，赵明扬 并联机器人研究现状研究开发 2000．4
[12] Hudgens J C, Tesar D.A Fully-parallel Six Degree-of-freedomMieromanipulator [J]. Kinematic Analysis and Dynamic Model. ASME,Mechanisms Conf.Mechanism Machines and Robotics 1998 15(3) 29-37.
[13] Chang-Soo Han, Jeffrey C. Hudgens, Delbert Tesar. Traver, Modeling,Synthesis, Analysis and Design of High Resolution Micromunipulator toEnhance Robot Accuracy[C]. IEEE/RSJ International Workshop on IntelligentRobot and Systems IROS/91 Osaka. 1991 3-5
[14] Pernette T,Henein S,et al.Design of Parallel Robots in Microrobotics[J] .Robotica, 1997.15 417-420.
[15] Pasi Kallio, Mikael Lind, Quan Zhou, et al. A 3DOF Piezohydraulic ParallelMicromanipulator[C]. IEEE International Conference on Robotics &Automation Leuven. 1998 566-570.
[16] Lee K.Arijunan M. A Three Degree of Freedom Micro-motion-in-parallel Actuated Manipulator[C]. IEEE Conf.On Robotics and Automation. 198928-37.
[17] Pernette Eric, Clavel Reymond. Parallel Robots and Microrobotics[C] .ISRAM, Montpellier 1996 535-540.
[18] Bi Shusheng, Zong Guanghua, Liu Rong, et al. Accuracy Analysis of theSerial-parallel Micromotion Manipulator. IEEE International Conference onRobotics and Automation. 1997 2258-2263.
[19] 毕树生，王守杰，宗光华 串并联微动机构的运动分析 机器人19(4)1997 247-251．
[20] Xudong Li, Guanghua Zong and Shusheng Bi. Development of Global VisionSystem. for Biologic Automatic Micro-Manipulation System. IEEEInternational Conference on Robotics & Automation, Seoul, 2001:127-132.
[21] 毕树生，宗光华 微操作机器人系统的研究开发 中国机械工程10(9)19991024-1027
[22] 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 183-186
[23] 于靖军，毕树生，宗光华 全柔性微位移放大机构的设计技术研究 航空学报 2004．1
[24] I. Her, J.C. Chang. A linear scheme for the displacement analysis ofmicropositioning stages with flexure hinges. Transactions of the ASME,Journal of Mechanical Design. 1(116) 1994 770-776
[25] 姜虹， 贾嵘等 六自由度并联机器人位置正解的数值解法 上海交通大学学报 2000．3
[26] Salisbury J K, Craig J J. Articulated hands: force control and kinematicissues[J]. J. of Robotic Research 1(1) 1982 4-12
[27] 方跃法，房海蓉，牟建斌 并联机器人误差敏感系数及其在工作空间内的分布 北方交通大学学报 2000．4
[28] Angeles J, Lopez-cajun C S. Kniematic isotropy and the conditioning index ofserial robotic manipulators [J]. J. of Robotic Research 11(6) 1992 560-571
[29] Gosselin C M. The optimum design of manipulators using dexterity indices [J] .Robotics and Automation Systems 1992.9:213-226
[30] Yuen Kuan Yong, Tien-Fu Lu, Daniel C. Loop Closure Theory in DerivingLinear and Simple Kinematic Model for a 3 DOF Parallel Micromanipulator.Proceedings of SPIE International Symposium on Device and ProcessTechnologies for Microelectronics, MEMS, and Photonics, Perth, Australia2003.12:10-12
[31] 李庆祥，王东生，李玉和等现代精密仪器设计 北京：清华大学出版社， 2004
[32] Do,W.Q.D and Yang, D.C.H. Inverse Dynamic Analysis and Simulation of aPlatform Type of Robot J. Robot. Syst. 1994.5 209-227
[33] Tsai, K.Y, Kohli.D. Modified Newton-Euler Computational Scheme forConfiguration Based on R-L Actuators. Proc. 1990 ASMW DesignEngineering Technical Conferences, Sacramento, CA. 1990
[34] Lebret, G., Liu, K., and Lewis, F.L., Dynamic Analysis and Control of aStewart Platform Manipulator, Robot[J]. 1993.7 507-534.
[35] Pang, H. Shahingpoor, M., Inverse Dynamics of a Parallel Manipulator.Robot[J] .1994.8 103-115.
[36] Codourey, A. and Burdet, E. A Body-oriented Method for Finding a LinearForm of the Dynamic Equation of Fully Parallel Robots. Proc. 1997 IEEEInternational Conference on Robotics and Automation, Albuquerque, NM,1997 1612-1618.
[37] Tsai, L. W. Solving the Inverse Dynamics of Parallel Manipulators by thePrinciple of Virtual Work. DETC98/MECH-5865, Proc. ASME DesignEngineering Technical Conferences, Atlanta, GA.
[38] 熊有伦 机器人技术基础 华中理工大学出版社1996
[39] 李国荣，陈大任，殷庆瑞 PZT系多层片式压电陶瓷微驱动器性能研究 无机材料学报 1999．6
[40] 张涛，孙立宁，蔡鹤翶 压电陶瓷基本特性研究 光学精密工程 1998．10
[41] 魏燕定，陶惠峰 压电驱动器迟滞特性的Preisach模型研究 压电与声光 2004
[42] NEW COMB C V. Improving the linearity of piezo-electricceramic actuators[J]. Elec Let 18(11) 1982 442-444.
[43] JUNG S B, KIM S W. Improvement of scanning accuracy of PZTpiezoelectric actuators by feed-forward model reference control[J]. PrecisionEngineering 16(1) 1994 49-55.
[44] 王建林，刘文晖，胡晓东等．压电微位移器在超微定位系统中的应用压电与声光19(2)1997 95-97
[45] PING Ge, M U SA Jouaneh. Generalized preisaeh model for hysteresisnonlinearity of piezoceramie actuators [J]. PrecisionEngineering. 20(2) 1997 99-111.
[46] 于靖军，周强等 基于动力学性能的全柔性机构优化设计 机械工程学报 2003．8 33
[47] 赵新华，张威 基于条件数的3-RTT并联机器人参数优化中国机械工程 2004．11 1903-1905
[48] 于靖军，周强 等基于动力学性能的全柔性机构优化设计 机械工程学报 2003．8
[49] 费业泰 误差理论与数据处理机械工业出版社 2000．5 95-103
[50] 张志涌，徐彦琴等 MATLAB教程：基于6.X版本北京航空航天大学出版社 2001．4
[51] 费业泰 误差理论与数据处理 机械工业出版社 2000．5 107-108