具有3-2-1并联结构地震模拟器的关键技术研究
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摘要
地震模拟器系统是地震工程研究工作中的重要试验设备之一。并联结构的振动台具有刚度大、对称性好、速度高、机构紧凑、动力学性能好等优点。本文提出一种应用于地震模拟器的具有3-2-1结构的冗余驱动并联机构，并对此机构的构型、运动学、静力学、工作空间、空间模型等方面进行了比较全面的研究，具体内容为：
1．建立了机构的位置反解方程，并利用对反解方程进行求导的方法，得到了机构的逆雅可比矩阵J~(-1)的解析表达式，这个表达式是分析机构各种性能指标的基础。
2．在机构位置反解和速度雅可比矩阵的基础上，利用数值迭代的方法对机构进行了正解求解，每次可以求得机构的一组正解。
3．建立了机构的静力学模型，得到了力与力矩传递矩阵G的解析表达式，并根据虚功原理导出了G与J的关系：G=(J~T)~(-1)。
4．建立了机构的空间模型，为今后的优化设计奠定了基础。
5．用解析和数值两种方法对机构的工作空间进行了详细的分析，得到在z=860附近可达工作空间截面积最大，在z=807附近灵活工作空间截面积最大。
6．利用机构的空间模型，分析了机构工作空间的大小与其结构参数的关系，得到了为获得最大工作空间r_1、r_2、r_3、r_4的最佳取值。
The earthquake simulator is one of the most important test equipment in the research of the earthquake engineering. The earthquake simulator with parallel structure shows several advantages, such as, higher stiffness, better symmetry, higher velocity, better dynamics and compact structure. In this dissertation, a new redundant activate parallel mechanism with 3-2-1 structure applied in the earthquake simulator is presented and studied in many fields, such as structure, kinematics, statics, workspace, physical model of the solution space and so on.
1. Drive the inverse position equation. Based on the differentiation to the inverse position equation, we get the analytic expression of the inverse jacobian matrix' J-1', the expression is the foundation of the research in many performance indexes.
2. Based on the inverse position equation and the jacobian matrix, the solution of direct position is obtained through the numerical iteration method.
3. The statics equation and the force/moment transmission matrix 'G' are obtained, then base on the principle of virtual work, the relationship between the two matrix 'G' and 'J' is obtained.
4. The physical model of the solution space are established and that grounds the foundation for the optimum design.
5. Detailed analysis in workspace is made by two means: numerical and analytic method. The conclusion is: The sectional view of reachable workspace reach its maximum area when z = 860, The sectional view of dexterous workspace reach its maximum area when z = 807.
6. Based on the physical model of the solution space, analyze the relationship between the workspace and the parameters of the manipulator, the optimal value of the parameters is obtained.
1．建立了机构的位置反解方程，并利用对反解方程进行求导的方法，得到了机构的逆雅可比矩阵J~(-1)的解析表达式，这个表达式是分析机构各种性能指标的基础。
2．在机构位置反解和速度雅可比矩阵的基础上，利用数值迭代的方法对机构进行了正解求解，每次可以求得机构的一组正解。
3．建立了机构的静力学模型，得到了力与力矩传递矩阵G的解析表达式，并根据虚功原理导出了G与J的关系：G=(J~T)~(-1)。
4．建立了机构的空间模型，为今后的优化设计奠定了基础。
5．用解析和数值两种方法对机构的工作空间进行了详细的分析，得到在z=860附近可达工作空间截面积最大，在z=807附近灵活工作空间截面积最大。
6．利用机构的空间模型，分析了机构工作空间的大小与其结构参数的关系，得到了为获得最大工作空间r_1、r_2、r_3、r_4的最佳取值。
The earthquake simulator is one of the most important test equipment in the research of the earthquake engineering. The earthquake simulator with parallel structure shows several advantages, such as, higher stiffness, better symmetry, higher velocity, better dynamics and compact structure. In this dissertation, a new redundant activate parallel mechanism with 3-2-1 structure applied in the earthquake simulator is presented and studied in many fields, such as structure, kinematics, statics, workspace, physical model of the solution space and so on.
1. Drive the inverse position equation. Based on the differentiation to the inverse position equation, we get the analytic expression of the inverse jacobian matrix' J-1', the expression is the foundation of the research in many performance indexes.
2. Based on the inverse position equation and the jacobian matrix, the solution of direct position is obtained through the numerical iteration method.
3. The statics equation and the force/moment transmission matrix 'G' are obtained, then base on the principle of virtual work, the relationship between the two matrix 'G' and 'J' is obtained.
4. The physical model of the solution space are established and that grounds the foundation for the optimum design.
5. Detailed analysis in workspace is made by two means: numerical and analytic method. The conclusion is: The sectional view of reachable workspace reach its maximum area when z = 860, The sectional view of dexterous workspace reach its maximum area when z = 807.
6. Based on the physical model of the solution space, analyze the relationship between the workspace and the parameters of the manipulator, the optimal value of the parameters is obtained.
引文
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2. Stewart D A. Platform with 6-DoF Proc. on Institution of Mechanical Engineering. 1965, 18(1): 371-386
3. K.H. Hunt. Structural Kinematics of In-Parallel-Actuated Robot Arm. Trans. ASME J. Mechanisms, rransmissions, and Automation in Design, 1983,105: 705-712
4．邱志成，谈大龙，赵明扬．并联机器人研究现状．研究开发，2000，38(4)：27-29
5．曲义远，黄真．空间六自由度多回路机构位置的三维搜索方法．机器人，1989，Vol．3，No．5：24-29
6．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
7. Z. Geng, L.S. Haynes, j.D. Lee, R. L. Caroll. Robotics and Autonomous Systems 9(1992)237-254
8. C.M. Gosselin, Trans. ASME. J. Dyn. Sys. Meas. Control. 1996.118: 22-28
9．王洪瑞．液压6-DOF并联机器人操作手运动和力控制研究．保定：河北大学出版社，2001
10. J. K. Salisbury, and J. J. Craig. Articulated hands: force control and kinematic issues. Int. J. Robot, 1982, Res. 1(1):4-12
11. T. Yoshikawa. Analysis and control of robot manipulators with redundancy. 1st International Symposium on Robotics Research. MIT Press, 1984:pp. 735-747,
12．李庆扬，数值分析，华中理工大学出版社，1986
13. Strang. Linear algebra and its application. Academic Press, New York, 1976
14. Gosselin and J. Angeles. A global performance index for the kinematic optimization of robotic manipulators. Transaction of the ASME, Journal of Mechanical Design, Sep. 1991, Vol.113: pp220-226
15. Feng Gao, Xin-Jun Liu and W.A. Gruver. The global condition index in the solution space of two-DOF planar parallel wrists. IEEE SMC' 95, Canada, 1995
16．刘辛军．并联机器人机构性能与尺寸关系分析及其设计理论研究．燕山大学，博士学位论文，1999
17. M.V. Kircanski. Robotic isotropy and optimal robot design of planar manipulators. IEEE, 1994: 1100-1105
18. C. Gosselin. Kinematic analysis, optimization and programming of parallel robotic manipulators. PH.D. thesis, McGill University, Montreal, Quebec, Canada, 1988
19. R. Kerr. Analysis, Properites, and Design of a Stewart-Platform Transducer. ASME J. Mech. Transm. Autom. Des., Vol. 111, pp. 25-28, 1989
20. Farhad Tahmasedbi, and Lung-Wen Tsai. On the stiffness of a novel six-degree-of-freedom parallel minimanipulator. Journal of Robotic Systems, 1995, Vol. 12, No. 12: 845-856
21．李敏霞，杨泽群，陈建秋．地震模拟振动台技术的开发与应用．世界地震工程，1996(2)：49-54
22．胡宝生．我国自行研制的第一个大型三向地震模拟振动台．世界地震工程，1995(4)：44-46
23．韩俊伟，李玉亭，胡宝生．大型三向六自由度地震模拟振动台．地震学报，1998，20(3)：327-331
24．孟吉复，杨国平，陈安元．模拟地震振动台的动力特性试验及分析．武汉水利电力学院学报，1990，23(6)：25-31
25．中国水利水电科学研究院工程抗震研究中心
26．方重．模拟地震振动台的近况及其发展．世界地震工程，1999，15(2)：89-91，96
27. Innocenti. C, Parenti-Castelli. V. Forward kinematics of the general 6-6 fully parallel mechanism: an exhaustive numerical approach via a mono-dimensional-search algorithm. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, v45, Robotics, Spatial Mechanisms, and Mechanical Systems, 1992: 545-552
28. Innocenti. C, Parenti-Castelli. V. Direct kinematics of the reverse Stewart platform mechanism. IFAC Symposia Series, n7, 1992: 75
29. Ait-Ahmed M, Renaud M, Vidyasagar M(Ed.). Proc Int Symp IntelRobot, Intelligent robotics, Tara McGraw-Hill, New DeL hi, 1993, 13-24
30. Innocenti C, Parenti-Castelli Forward kinematics of the general 6-6 fully parallel mechanism: an exhaustive numerical approach via a mono-dimensional-search algorithm Trans ASME, J Mech Des, 1993, 115: 932-937
31. Dasgupta B, Mruthyunjaya T S. Mech. Mach. Theory, 1996, 31 (6): 799-811
32．黄真，孔宪文．6-SPS并联机器人机构运动分析．东北重型机械学院学报，1992，16(4)：283-289
33．陈永，严静．同伦迭代法及应用于一般6-SPS并联机器人机构正位置问题．机械科学与技术，1997，16(2)：189-194
34．李维嘉．六自由度并联运动机构正向解的研究．华中理工大学学报，1997，25(4)：38-40
35．刘安心，杨廷力．求一般6-SPS并联机器人机构的全部位置正解．机械科学与技术，1996，15(4)：543-546
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