新型三转动并联机构运动学综合与虚拟样机开发
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摘要
本文密切结合航空航天、智能机器人等领域对纯转动并联机构的重要需求,在国家自然科学基金项目资助下,深入研究了新型空间三转动自由度并联机构3-PUS&S的设计理论与方法,内容涉及运动学分析、工作空间分析、尺度综合、虚拟样机设计及静/动态特性预估等。主要研究成果如下:
1.运动学分析。根据该机构创成运动特点,采用倾斜角-扭转角法描述动平台姿态,借助螺旋理论建立机构正、逆位置分析模型与速度雅可比矩阵,并结合算例验证了上述模型的有效性。
2.工作空间分析。明确该机构可达/任务工作空间的数学定义,计及移动副位移、铰链转角及连杆干涉等工程约束,逆向搜索出机构可达工作空间,并揭示了尺度参数对工作空间的影响。
3.尺度综合。采用适宜的全域运动学性能评价指标,借助运动学性能图谱揭示了关键设计变量的影响程度与取值范围,并综合考虑相关的几何/工程约束,实现了机构的运动学优化设计。
4.虚拟样机设计与静/动态特性预估。结合工程需求开发出虚拟样机,经运动仿真与干涉检验,验证了运动学设计理论的有效性;针对典型姿态,预估虚拟样机的静刚度与动力学特性,并揭示出关键影响因素。
上述研究成果为该机构的物理样机开发奠定了坚实基础。
With the aid of NSFC Project, to meet the demand for the spatial rotational mechanism used in the field of aircraft industry and intelligent robot, this thesis investigates into the design theory and method of a novel three rotational parallel mechanism which is invented by Tianjin University. The following work has been accomplished.
1. Kinematic analysis. Referring to the kinematic characteristics of the three rotational parallel mechanism, the Tilt-and-Torsion angles are used to describe the orientation of the platform. Based on the screw theory, three equations involving driving parameters and pose parameters are formulated and proved by an example. And the Jacobian matrix is derived.
2. Workspace analysis. The reachable and task workspace definitions of the mechanism are proposed. Then the reachable workspace is searched based on the inverse position analysis with some constrained conditions such as the actuated journey, gemel angles and linkage interference. And the relationships between dimensional parameters and workspace are studied.
3. Dimensional synthesis. The influences and ranges of design variables are showed in the performance maps which describe the relationship between the global kinematic performance indexes and the design variables. Considered the geometry and engineering constraints, the kinematic optimization design is completed.
4. Virtual prototype design, and the static/dynamic characteristic estimation. The virtual prototype is set up according to the demand of the engineering. Based on this model, the motion simulation and interference checking are carried out and a finite element model is proposed with the aid of ANSYS software. The key parts which affect the static and dynamic characters of the mechanism are identified by the estimation of static stiffness and modal.
The above-mentioned outcomes lay a solid foundation for the development of the 3-PUS&S prototype.
1.运动学分析。根据该机构创成运动特点,采用倾斜角-扭转角法描述动平台姿态,借助螺旋理论建立机构正、逆位置分析模型与速度雅可比矩阵,并结合算例验证了上述模型的有效性。
2.工作空间分析。明确该机构可达/任务工作空间的数学定义,计及移动副位移、铰链转角及连杆干涉等工程约束,逆向搜索出机构可达工作空间,并揭示了尺度参数对工作空间的影响。
3.尺度综合。采用适宜的全域运动学性能评价指标,借助运动学性能图谱揭示了关键设计变量的影响程度与取值范围,并综合考虑相关的几何/工程约束,实现了机构的运动学优化设计。
4.虚拟样机设计与静/动态特性预估。结合工程需求开发出虚拟样机,经运动仿真与干涉检验,验证了运动学设计理论的有效性;针对典型姿态,预估虚拟样机的静刚度与动力学特性,并揭示出关键影响因素。
上述研究成果为该机构的物理样机开发奠定了坚实基础。
With the aid of NSFC Project, to meet the demand for the spatial rotational mechanism used in the field of aircraft industry and intelligent robot, this thesis investigates into the design theory and method of a novel three rotational parallel mechanism which is invented by Tianjin University. The following work has been accomplished.
1. Kinematic analysis. Referring to the kinematic characteristics of the three rotational parallel mechanism, the Tilt-and-Torsion angles are used to describe the orientation of the platform. Based on the screw theory, three equations involving driving parameters and pose parameters are formulated and proved by an example. And the Jacobian matrix is derived.
2. Workspace analysis. The reachable and task workspace definitions of the mechanism are proposed. Then the reachable workspace is searched based on the inverse position analysis with some constrained conditions such as the actuated journey, gemel angles and linkage interference. And the relationships between dimensional parameters and workspace are studied.
3. Dimensional synthesis. The influences and ranges of design variables are showed in the performance maps which describe the relationship between the global kinematic performance indexes and the design variables. Considered the geometry and engineering constraints, the kinematic optimization design is completed.
4. Virtual prototype design, and the static/dynamic characteristic estimation. The virtual prototype is set up according to the demand of the engineering. Based on this model, the motion simulation and interference checking are carried out and a finite element model is proposed with the aid of ANSYS software. The key parts which affect the static and dynamic characters of the mechanism are identified by the estimation of static stiffness and modal.
The above-mentioned outcomes lay a solid foundation for the development of the 3-PUS&S prototype.
引文
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[2] Neumann K E, Robot, US Patent 4732525, 1988
[3] Available at: http://www.ds-technologie.de
[4] Pierrot F, Company O, H4: a new family of 4-dof parallel robots, In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, 1999: 508-513
[5]黄田,李曚,李占贤,仅含转动副的二自由度平动并联机器人机构,中国发明专利,专利号: ZL01145160.2, 2001
[6]黄田,李曚,李占贤等,非对称空间5自由度混联机器人,中国发明专利,公开号: CN1524662, 2003
[7] Asada H, Granito J, Kinematic characterization of wrist joint and their optimal design, In: Proceedings of the IEEE International Conference on Robotics and Automation, St Louis, 1985: 244-250
[8] Gosselin C M, Angeles J, The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator, Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 11(2): 202-207
[9] Gosselin C M, Hamel J F, The agile eye: a high performance three-degree-of-freedom camera-orienting device, In: Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, 1994: 781-787
[10] Gosselin C M, Development and experimentation of a fast 3-dof camera-orienting device, The International Journal of Robotics Research, 1997,16(5): 619-630
[11] Bai S P, Hansen M R, Angeles J, A robust forward-displacement analysis of spherical parallel robots, Mechanism and Machine Theory, 2009, 44(12): 2204-2216
[12] Gosselin C M, Angeles J, Singularity analysis of closed-loop kinematic chains, Transactions on Robotics and Automation, 1990, 6(3): 281290
[13]黄田,曾宪菁,曾子平等,等顶锥角3自由度球面并联机构的全参数解析尺度综合,机械工程学报, 2000, 36(8): 15-19
[14] Gregorio R D, Kinematics of the 3-UPU wrist, Mechanism and Machine Theory, 2003, 38(3): 253-263
[15] Gregorio D R, A new family of spherical parallel manipulators, Robotica, 2002, 20(4): 353-358
[16] Fang Y F, Tsai L W, Structure synthesis of a class of 3-dof rotational parallel manipulators, Transactions on Robotics and Automation, 2004, 20(1): 117-121
[17] Tsai L W, Multi-degree-of-freedom mechanisms for machine tools and the like, US Patent 5656905, 1997
[18] Bonev I A, Gosselin C, Singularity loci of spherical parallel mechanisms, In: Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, 2005: 2957-2962
[19] Wang J, Gosselin C M, Singularity loci of a special class of spherical 3-dof parallel mechanisms with prismatic actuators, Journal of Mechanical Design, 2004, 126(3): 319-326
[20] Dai J S, Zhao T S, Sprained ankle physiotherapy based mechanism synthesis and stiffness analysis of a robotic rehabilitation device, Autonomous Robots, 2004,16(2):207-218
[21]黄田,赵学满,王攀峰,空间三转动自由度并联机构,中国发明专利,公开号: CN101244558A, 2008
[22] Karouia M, Herve J, Asymmetrical 3-dof spherical parallel mechanisms, European Journal of Mechanics -A/Solids, 2005, 24(1): 47-57
[23]杭鲁滨,王彦,吴俊等,三自由度并联机器人机型设计方法,中国机械工程, 2005, 16(9): 819-822
[24] Suh C H, Radcliffe C W, Kinematics and mechanisms design, New York: Wiley, 1978
[25] Murray R, Li Z X, Sastry S, A mathematical introduction to robotic manipulation, Florida: CRC, 1994
[26] Yang G L, Chen W H, Chen I M, et al, Design and kinematic analysis of modular reconfigurable parallel robots, In: SIMTech Technical Report, Singapore, 2001: 10/010/1-10/010/10
[27]勃拉涅茨,什梅格列夫斯基,四元数在刚体定位问题中的应用,北京:国防工业出版社, 1977
[28]刘惠林,张同庄, 3-RPR平面并联机构正解的吴方法,北京理工大学学报, 2000, 20(5): 565-569
[29]刘木兰, Grobner基理论及其应用,北京:科学出版社, 2000
[30]张可村,赵英良,数值计算的算法与分析,北京:科学出版社, 2003
[31]王则柯,高堂安,同伦方法引论,重庆:重庆出版社, 1990
[32]曾建潮,介婧,崔志华,微粒群算法,北京:科学出版社, 2004
[33]于靖军,刘辛军,丁希伦等,机器人机构学的数学基础,北京:机械工业出版社, 2008
[34]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
[35]黄真,空间机构学,北京:机械工业出版社, 1991
[36]高峰,并联机构设计与应用,见:现代机构学进展,北京:高等教育出版社, 2007: 129-144
[37] Gosselin C M, Determination of the workspace of 6-dof parallel manipulators, Journal of Mechanical Design, 1990, 112: 331-336
[38]黄田,汪劲松, Whitchouse D J,并联机器人位置空间解析.中国科学(E辑), 1998, 28(2): 136-145
[39]赵景山,冯敬之,褚福磊,机器人机构自由度分析理论,北京:科学出版社, 2009
[40] Miller K, Maximization of workspace volume of 3-dof spatial parallel manipulators, Journal of Mechanical Design, 2002, 124(6): 347-357
[41] Badescu M, Mavroidis C, Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints, Journal of Mechanical Design, 2004, 126(3): 291-300
[42] Salisbury J K, Craig J J, Articulated hand: force control of kinematic issues, The International Journal of Robotics Research, 1982, 1(1): 4-17
[43] Yoshikawa T, Manipulability of robotic mechanisms, The International Journal of Robotics Research, 1985, 4(2): 439-446
[44] Gosselin C, Angeles J, The optimum kinematic design of a spherical 3-dof parallel manipulator, Journal of Mechanism, Transmission, and Automation in Design, 1989, 112(2): 202-207
[45] Gosselin C, Angeles J, A globe performance index for the kinematic optimization of robotic manipulators, Journal of Mechanical Design, 1991, 113(3): 220-226
[46] Huang T, Li M, Zhao X Y, et al, Kinematic design of a reconfigurable miniature parallel kinematic machine, Chinese Journal of Mechanical Engineering, 2003, 16(1): 79-82
[47] 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
[48] Portman V T, Sandler B, Zahavi E, Rigid 6×6 parallel platform for precision 3-D micromanipulation theory and design application, Transactions on Robotics and Automation, 2000, 16(6): 629-643
[49]李兵,王知行,胡颖,新型并联机床的刚度计算模型,机械设计, 1999, 16(3): 14-16
[50]王友渔,一类球坐标型混联机器人静刚度建模理论与方法研究: [博士学位论文],天津:天津大学, 2008
[51] Dai J S, Huang Z, Lipkin H, Mobility of overconstrained parallel mechanisms, Journal of Mechanical Design, 2006, 128(1): 220-229
[52] Bonev I A, Ryu J, Orientation workspace analysis of 6-DOF parallel manipulators, In: Proceedings of the ASME Design Engineering Technical Conferences, Las Vegas: Nevada, 1999
[53]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, 168-170
[2] Neumann K E, Robot, US Patent 4732525, 1988
[3] Available at: http://www.ds-technologie.de
[4] Pierrot F, Company O, H4: a new family of 4-dof parallel robots, In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, 1999: 508-513
[5]黄田,李曚,李占贤,仅含转动副的二自由度平动并联机器人机构,中国发明专利,专利号: ZL01145160.2, 2001
[6]黄田,李曚,李占贤等,非对称空间5自由度混联机器人,中国发明专利,公开号: CN1524662, 2003
[7] Asada H, Granito J, Kinematic characterization of wrist joint and their optimal design, In: Proceedings of the IEEE International Conference on Robotics and Automation, St Louis, 1985: 244-250
[8] Gosselin C M, Angeles J, The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator, Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 11(2): 202-207
[9] Gosselin C M, Hamel J F, The agile eye: a high performance three-degree-of-freedom camera-orienting device, In: Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, 1994: 781-787
[10] Gosselin C M, Development and experimentation of a fast 3-dof camera-orienting device, The International Journal of Robotics Research, 1997,16(5): 619-630
[11] Bai S P, Hansen M R, Angeles J, A robust forward-displacement analysis of spherical parallel robots, Mechanism and Machine Theory, 2009, 44(12): 2204-2216
[12] Gosselin C M, Angeles J, Singularity analysis of closed-loop kinematic chains, Transactions on Robotics and Automation, 1990, 6(3): 281290
[13]黄田,曾宪菁,曾子平等,等顶锥角3自由度球面并联机构的全参数解析尺度综合,机械工程学报, 2000, 36(8): 15-19
[14] Gregorio R D, Kinematics of the 3-UPU wrist, Mechanism and Machine Theory, 2003, 38(3): 253-263
[15] Gregorio D R, A new family of spherical parallel manipulators, Robotica, 2002, 20(4): 353-358
[16] Fang Y F, Tsai L W, Structure synthesis of a class of 3-dof rotational parallel manipulators, Transactions on Robotics and Automation, 2004, 20(1): 117-121
[17] Tsai L W, Multi-degree-of-freedom mechanisms for machine tools and the like, US Patent 5656905, 1997
[18] Bonev I A, Gosselin C, Singularity loci of spherical parallel mechanisms, In: Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, 2005: 2957-2962
[19] Wang J, Gosselin C M, Singularity loci of a special class of spherical 3-dof parallel mechanisms with prismatic actuators, Journal of Mechanical Design, 2004, 126(3): 319-326
[20] Dai J S, Zhao T S, Sprained ankle physiotherapy based mechanism synthesis and stiffness analysis of a robotic rehabilitation device, Autonomous Robots, 2004,16(2):207-218
[21]黄田,赵学满,王攀峰,空间三转动自由度并联机构,中国发明专利,公开号: CN101244558A, 2008
[22] Karouia M, Herve J, Asymmetrical 3-dof spherical parallel mechanisms, European Journal of Mechanics -A/Solids, 2005, 24(1): 47-57
[23]杭鲁滨,王彦,吴俊等,三自由度并联机器人机型设计方法,中国机械工程, 2005, 16(9): 819-822
[24] Suh C H, Radcliffe C W, Kinematics and mechanisms design, New York: Wiley, 1978
[25] Murray R, Li Z X, Sastry S, A mathematical introduction to robotic manipulation, Florida: CRC, 1994
[26] Yang G L, Chen W H, Chen I M, et al, Design and kinematic analysis of modular reconfigurable parallel robots, In: SIMTech Technical Report, Singapore, 2001: 10/010/1-10/010/10
[27]勃拉涅茨,什梅格列夫斯基,四元数在刚体定位问题中的应用,北京:国防工业出版社, 1977
[28]刘惠林,张同庄, 3-RPR平面并联机构正解的吴方法,北京理工大学学报, 2000, 20(5): 565-569
[29]刘木兰, Grobner基理论及其应用,北京:科学出版社, 2000
[30]张可村,赵英良,数值计算的算法与分析,北京:科学出版社, 2003
[31]王则柯,高堂安,同伦方法引论,重庆:重庆出版社, 1990
[32]曾建潮,介婧,崔志华,微粒群算法,北京:科学出版社, 2004
[33]于靖军,刘辛军,丁希伦等,机器人机构学的数学基础,北京:机械工业出版社, 2008
[34]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
[35]黄真,空间机构学,北京:机械工业出版社, 1991
[36]高峰,并联机构设计与应用,见:现代机构学进展,北京:高等教育出版社, 2007: 129-144
[37] Gosselin C M, Determination of the workspace of 6-dof parallel manipulators, Journal of Mechanical Design, 1990, 112: 331-336
[38]黄田,汪劲松, Whitchouse D J,并联机器人位置空间解析.中国科学(E辑), 1998, 28(2): 136-145
[39]赵景山,冯敬之,褚福磊,机器人机构自由度分析理论,北京:科学出版社, 2009
[40] Miller K, Maximization of workspace volume of 3-dof spatial parallel manipulators, Journal of Mechanical Design, 2002, 124(6): 347-357
[41] Badescu M, Mavroidis C, Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints, Journal of Mechanical Design, 2004, 126(3): 291-300
[42] Salisbury J K, Craig J J, Articulated hand: force control of kinematic issues, The International Journal of Robotics Research, 1982, 1(1): 4-17
[43] Yoshikawa T, Manipulability of robotic mechanisms, The International Journal of Robotics Research, 1985, 4(2): 439-446
[44] Gosselin C, Angeles J, The optimum kinematic design of a spherical 3-dof parallel manipulator, Journal of Mechanism, Transmission, and Automation in Design, 1989, 112(2): 202-207
[45] Gosselin C, Angeles J, A globe performance index for the kinematic optimization of robotic manipulators, Journal of Mechanical Design, 1991, 113(3): 220-226
[46] Huang T, Li M, Zhao X Y, et al, Kinematic design of a reconfigurable miniature parallel kinematic machine, Chinese Journal of Mechanical Engineering, 2003, 16(1): 79-82
[47] 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
[48] Portman V T, Sandler B, Zahavi E, Rigid 6×6 parallel platform for precision 3-D micromanipulation theory and design application, Transactions on Robotics and Automation, 2000, 16(6): 629-643
[49]李兵,王知行,胡颖,新型并联机床的刚度计算模型,机械设计, 1999, 16(3): 14-16
[50]王友渔,一类球坐标型混联机器人静刚度建模理论与方法研究: [博士学位论文],天津:天津大学, 2008
[51] Dai J S, Huang Z, Lipkin H, Mobility of overconstrained parallel mechanisms, Journal of Mechanical Design, 2006, 128(1): 220-229
[52] Bonev I A, Ryu J, Orientation workspace analysis of 6-DOF parallel manipulators, In: Proceedings of the ASME Design Engineering Technical Conferences, Las Vegas: Nevada, 1999
[53]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, 168-170