6-SPS并联机器人运动学及工作空间的仿真研究
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摘要
6-SPS并联机器人相对于串联机器人来说是一种全新的机器人，具有刚度大、承载能力强、误差小、精度高及运动性能好等优点。而并联机器人是一种闭环机构，导致了其运动学和工作空间分析较为困难。因此，研究6-SPS并联机器人的运动学和工作空间具有重要意义，也有助于并联机器人的研究、应用和推广。
根据6-SPS并联机器人反解容易、正解较难的特点，本论文基于位置反解方程，通过杆长逐次逼近的思路建立了位置正解模型，并对该方法进行了实例验证。运用运动影响系数法及刚体运动原理推导了6-SPS并联机器人速度和加速度的正反解模型，并研究了其运动可视化的问题。在分析了影响并联机器人工作空间的约束前提下，通过边界数值搜索的方法，得到了工作空间的形状及其大小。
由已建立的运动学和工作空间的数学模型，采用参数化设计和人机交互相结合的方法，设计了6-SPS并联机器人运动学和工作空间的仿真系统，该仿真系统对提高并联机器人的设计效率具有一定的价值。
最后，根据仿真得到的结果，对6-SPS并联机器人的运动学和工作空间进行了分析研究。
The 6-SPS parallel robot is a new kind of robots in comparision to conventional serial robots. It has more advantages over serial robots in terms of stiffness, high load/wight ratio, precision, velocity, and low error. However, it is rather difficult to analyze the kinematics and workspace of parallel manipulators due to its specific closed-loop. So, the research will be of great significance, and can help to promote its research, application and spread too.
Based on inverse equation, the forward solution model of position is presented in this thesis through method of successive approximation, for parallel robots possess characteristic of easy inverse solution and difficult direct solution. The method is proved to be highly effective by simulation example. The direct and inverse models of velocity and acceleration are founded by approach of influence coefficient and principle of rigid body moving, and furthermore, studies its movement-viewed problem. Given multiple restrictions of workspace, the shape and volume of workspace are gained through method of boundary numerical search.
Under mathematics model of kinematics and workspace, the simulation system of kinematics and workspace are developed through the method that combines parametic design with interactive design. It is valuable for the simulation system to improve designing efficiency.
Finally, the kinematics and workspace of 6-SPS parallel manipulator are analyzed and researched by simulation results.
根据6-SPS并联机器人反解容易、正解较难的特点，本论文基于位置反解方程，通过杆长逐次逼近的思路建立了位置正解模型，并对该方法进行了实例验证。运用运动影响系数法及刚体运动原理推导了6-SPS并联机器人速度和加速度的正反解模型，并研究了其运动可视化的问题。在分析了影响并联机器人工作空间的约束前提下，通过边界数值搜索的方法，得到了工作空间的形状及其大小。
由已建立的运动学和工作空间的数学模型，采用参数化设计和人机交互相结合的方法，设计了6-SPS并联机器人运动学和工作空间的仿真系统，该仿真系统对提高并联机器人的设计效率具有一定的价值。
最后，根据仿真得到的结果，对6-SPS并联机器人的运动学和工作空间进行了分析研究。
The 6-SPS parallel robot is a new kind of robots in comparision to conventional serial robots. It has more advantages over serial robots in terms of stiffness, high load/wight ratio, precision, velocity, and low error. However, it is rather difficult to analyze the kinematics and workspace of parallel manipulators due to its specific closed-loop. So, the research will be of great significance, and can help to promote its research, application and spread too.
Based on inverse equation, the forward solution model of position is presented in this thesis through method of successive approximation, for parallel robots possess characteristic of easy inverse solution and difficult direct solution. The method is proved to be highly effective by simulation example. The direct and inverse models of velocity and acceleration are founded by approach of influence coefficient and principle of rigid body moving, and furthermore, studies its movement-viewed problem. Given multiple restrictions of workspace, the shape and volume of workspace are gained through method of boundary numerical search.
Under mathematics model of kinematics and workspace, the simulation system of kinematics and workspace are developed through the method that combines parametic design with interactive design. It is valuable for the simulation system to improve designing efficiency.
Finally, the kinematics and workspace of 6-SPS parallel manipulator are analyzed and researched by simulation results.
引文
[1] Hunt. K H. Kinematic Geometry of Mechanisms. Oxford: Clarendon Press,1978
[2] Mac Callion H, Phain D T. Proc. 3rd Congressvon TMM, 1979
[3] 刘宝顺．虚轴机床工作空间研究，天津大学研究报告，1997
[4] Grace K W, Colgate J E. A 6-DOF Micro-manipulator for Ophthalmic Surgery. IEEE. Conf. Rob&Aut, 1993,630～635
[5] 王洋．训练仿真器概论，信息与控制，1984(2)
[6] An C. H. Experimental Evalnation of Freedford and Computed Torque Control. IEEE. Conf. Robotics and Automation, 1987
[7] Innocenti C, Parenti-Castelli V. Forward Kinematic of the General 6-6 Fully Parallel Mechanism. Joumal of Mechanical Design, Transactions of the ASME, 1993, 115(4): 932～937
[8] Dasgupta B, Mruthyunjaya T S. A Constructive Predictor-Corrector Algorithm for the Direct Position Kinematics Problem for a General 6-6 Stewart Platform. Mechanism and Machine Theory, 1996, 31 (6): 799～811
[9] 陈永，严静．同伦迭代法及应用于一般6-SPS并联机器人机构位置正解问题，机械科学与技术，1997，16(2)：189～194
[10] 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
[11] Wampler C W. Mech. Mach. Theory, 1995, 31(3): 331～337
[12] Raghavan M. Stewart Platform of General Geometry has 40 Configurations. Journal of Mechanical Design, Transactions of the ASME, 1993, 115(2):277～281
[13] 梁崇高，荣辉．一种Stewart平台型机械手位移正解，机械工程学报，1991，27(2)：26～30
[14] Han K, Chung W, Youm Y. New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors. Joumal of Mechanical Design, Transactions of the ASME, 1996, 118(2): 214～21
[15] Geng Z, Haynes L. Neural Network Solution for the Forward Kinematics Problem of a Stewart Platform. Proceedings-IEEE International Conference on Robotics and Automation, 1991:2650～2655
[16] Fichter E E A Stewart Platform-Based Manipulator: General Theory and Practical Construction. Int J of Rob Res, 1986, 5(2): 157～182
[17] Merlet J P.C-Surface Applied to the Design of an Hybrid Force-Position Robot
Controller. INRIA Research Report, 1987:1055～1059
[18] Sugimoto K. Trans ASME, J Mech Transm Automn Des, 1989, 111:29～33
[19] Geng Z, Haynes L S, Lee J D. On the dynamic Model and Kinematic Analysis of a Class of Stewart Platforms. Robotics and Autonomous Systems, 1992, 9(4):237～254
[20] Liu K, Lewis F. Singularities and Dynamics of a Stewart Platform Manipulator. Joumal of Intelligent and Robotic Systems, 1993, 8(3): 287～308
[21] Do W Q D, Yang D C H. J Robot Sys, 1988, 5(3): 209～227
[22] Ji Z. Trans ASME, J Mech Des, 1994, 116:67～69
[23] Dasgupta B, Mruthyunjaya T S. Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator. Mechanism & Machine Theory, 1998, 33(8): 1135～1152
[24] Gosselin C M. Trans ASME, J Dyn Sys Meas Control, 1996, 118:22～28
[25] Merlet J P. Closed-Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors Data. Proc. of IEEE Int. Conf. on Rob Auto., 1993:200～204
[26] Gosselin C M, Angeles J. Singularity Analysis of Closed-Loop Kinematic Chains. IEEE Trans on Rob and Aut, 1990, 6(3): 281～290
[27] B Dasgupta. Comparision of an Exact and an Approximate in Platform Type Parallel Manipulators. Mechanism & Machine Theory, 1998, 33(7): 965～974
[28] Huang Tian, Wang Jin Song. Closed Form Solution to the position Workspace of Stewart Parallel Manipulators. Sience in China, 1998, 41(4): 393～403
[29] Gosselin C M, Lavoie E. Efficient Algorithm for the Graphical Representation of the Three-Dimensional Workspace of Parallel Manipulators. ASME, 1992, 45:323～328
[30] Masory O, Wang J. Workspace Evalution of Stewart Platforms. ASME, 1992, 45:337～345
[31] Merlet J P. Trajectory Verification in the Workspace for Parallel Manipulators. Int J Robt Res, 1994, 13(4): 326～333
[32] 黄真．空间机构学，北京：机械工业出版社，1991
[33] 尹小琴，马履中．基于影响系数的并联机器人机构运动分析，江苏大学学报(自然科学版)，2002
[34] 孙立宁，于晖等．机构影响系数和并联机器人雅可比矩阵的研究，哈尔滨工业大学学报，2002，34(6)：810～814
[35] 任宝生．理论力学，西安：西安交通大学出版社，1995
[36] 张万国．高等数学，上海：复旦大学出版社，2002
[37] 熊有伦，丁汉等，刘恩仓．机器人学，北京：机械工业出版社，1993
[38] 熊有伦，尹周平等．机器人操作，武汉：湖北科学技术出版社，2002
[39] 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
[40] Gosselin C M. Determination of the Workspace of 6-DOF Parallel Manipulators. Journal of Mechanical Design, 1990, 112(3): 331～336
[41] Kim D I, Chung W K. Geometrical Approach for the Workspace of 6-DOF Parallel Manipulators. Proceedings of the 1997 IEEE International Conference on Robotics and Automation, 1997:2986～2991
[42] Macro C, Massimo S. The Effects of Design Parameters on the Workspace of a Turin Parallel Robot. The International Journal of Robotics Research, 1998,17(8): 886～902
[43] Merlet J P. Designing a Parallel Manipulator for a Specific Workspace. The International Journal of Robotics Research. 1997, 16(4): 545～556
[44] 刘藻珍，魏华梁．系统仿真，北京：北京理工大学出版社，1998
[45] 薛定宇，陈阳泉．基于MATLAB／Simulink的系统仿真技术与应用，北京：清华大学出版社，2003
[46] 闻新，周露等．MATLAB科学图形构件基础与应用，北京：科学出版社，2002
[47] 姚东，王爱民等．MATLAB命令大全，北京：人民邮电出版社，2000
[48] 施晓红，周佳．精通GUI图形界面编程，北京：北京大学出版社，2003
[2] Mac Callion H, Phain D T. Proc. 3rd Congressvon TMM, 1979
[3] 刘宝顺．虚轴机床工作空间研究，天津大学研究报告，1997
[4] Grace K W, Colgate J E. A 6-DOF Micro-manipulator for Ophthalmic Surgery. IEEE. Conf. Rob&Aut, 1993,630～635
[5] 王洋．训练仿真器概论，信息与控制，1984(2)
[6] An C. H. Experimental Evalnation of Freedford and Computed Torque Control. IEEE. Conf. Robotics and Automation, 1987
[7] Innocenti C, Parenti-Castelli V. Forward Kinematic of the General 6-6 Fully Parallel Mechanism. Joumal of Mechanical Design, Transactions of the ASME, 1993, 115(4): 932～937
[8] Dasgupta B, Mruthyunjaya T S. A Constructive Predictor-Corrector Algorithm for the Direct Position Kinematics Problem for a General 6-6 Stewart Platform. Mechanism and Machine Theory, 1996, 31 (6): 799～811
[9] 陈永，严静．同伦迭代法及应用于一般6-SPS并联机器人机构位置正解问题，机械科学与技术，1997，16(2)：189～194
[10] 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
[11] Wampler C W. Mech. Mach. Theory, 1995, 31(3): 331～337
[12] Raghavan M. Stewart Platform of General Geometry has 40 Configurations. Journal of Mechanical Design, Transactions of the ASME, 1993, 115(2):277～281
[13] 梁崇高，荣辉．一种Stewart平台型机械手位移正解，机械工程学报，1991，27(2)：26～30
[14] Han K, Chung W, Youm Y. New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors. Joumal of Mechanical Design, Transactions of the ASME, 1996, 118(2): 214～21
[15] Geng Z, Haynes L. Neural Network Solution for the Forward Kinematics Problem of a Stewart Platform. Proceedings-IEEE International Conference on Robotics and Automation, 1991:2650～2655
[16] Fichter E E A Stewart Platform-Based Manipulator: General Theory and Practical Construction. Int J of Rob Res, 1986, 5(2): 157～182
[17] Merlet J P.C-Surface Applied to the Design of an Hybrid Force-Position Robot
Controller. INRIA Research Report, 1987:1055～1059
[18] Sugimoto K. Trans ASME, J Mech Transm Automn Des, 1989, 111:29～33
[19] Geng Z, Haynes L S, Lee J D. On the dynamic Model and Kinematic Analysis of a Class of Stewart Platforms. Robotics and Autonomous Systems, 1992, 9(4):237～254
[20] Liu K, Lewis F. Singularities and Dynamics of a Stewart Platform Manipulator. Joumal of Intelligent and Robotic Systems, 1993, 8(3): 287～308
[21] Do W Q D, Yang D C H. J Robot Sys, 1988, 5(3): 209～227
[22] Ji Z. Trans ASME, J Mech Des, 1994, 116:67～69
[23] Dasgupta B, Mruthyunjaya T S. Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator. Mechanism & Machine Theory, 1998, 33(8): 1135～1152
[24] Gosselin C M. Trans ASME, J Dyn Sys Meas Control, 1996, 118:22～28
[25] Merlet J P. Closed-Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors Data. Proc. of IEEE Int. Conf. on Rob Auto., 1993:200～204
[26] Gosselin C M, Angeles J. Singularity Analysis of Closed-Loop Kinematic Chains. IEEE Trans on Rob and Aut, 1990, 6(3): 281～290
[27] B Dasgupta. Comparision of an Exact and an Approximate in Platform Type Parallel Manipulators. Mechanism & Machine Theory, 1998, 33(7): 965～974
[28] Huang Tian, Wang Jin Song. Closed Form Solution to the position Workspace of Stewart Parallel Manipulators. Sience in China, 1998, 41(4): 393～403
[29] Gosselin C M, Lavoie E. Efficient Algorithm for the Graphical Representation of the Three-Dimensional Workspace of Parallel Manipulators. ASME, 1992, 45:323～328
[30] Masory O, Wang J. Workspace Evalution of Stewart Platforms. ASME, 1992, 45:337～345
[31] Merlet J P. Trajectory Verification in the Workspace for Parallel Manipulators. Int J Robt Res, 1994, 13(4): 326～333
[32] 黄真．空间机构学，北京：机械工业出版社，1991
[33] 尹小琴，马履中．基于影响系数的并联机器人机构运动分析，江苏大学学报(自然科学版)，2002
[34] 孙立宁，于晖等．机构影响系数和并联机器人雅可比矩阵的研究，哈尔滨工业大学学报，2002，34(6)：810～814
[35] 任宝生．理论力学，西安：西安交通大学出版社，1995
[36] 张万国．高等数学，上海：复旦大学出版社，2002
[37] 熊有伦，丁汉等，刘恩仓．机器人学，北京：机械工业出版社，1993
[38] 熊有伦，尹周平等．机器人操作，武汉：湖北科学技术出版社，2002
[39] 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
[40] Gosselin C M. Determination of the Workspace of 6-DOF Parallel Manipulators. Journal of Mechanical Design, 1990, 112(3): 331～336
[41] Kim D I, Chung W K. Geometrical Approach for the Workspace of 6-DOF Parallel Manipulators. Proceedings of the 1997 IEEE International Conference on Robotics and Automation, 1997:2986～2991
[42] Macro C, Massimo S. The Effects of Design Parameters on the Workspace of a Turin Parallel Robot. The International Journal of Robotics Research, 1998,17(8): 886～902
[43] Merlet J P. Designing a Parallel Manipulator for a Specific Workspace. The International Journal of Robotics Research. 1997, 16(4): 545～556
[44] 刘藻珍，魏华梁．系统仿真，北京：北京理工大学出版社，1998
[45] 薛定宇，陈阳泉．基于MATLAB／Simulink的系统仿真技术与应用，北京：清华大学出版社，2003
[46] 闻新，周露等．MATLAB科学图形构件基础与应用，北京：科学出版社，2002
[47] 姚东，王爱民等．MATLAB命令大全，北京：人民邮电出版社，2000
[48] 施晓红，周佳．精通GUI图形界面编程，北京：北京大学出版社，2003