基于修正自由度公式的并联机构型综合理论
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摘要
并联机构作为一类机器人机构,具有精度高、刚度大、速度快和承载能力强等优点。研究并联机器人机构的型综合问题,有利于在实际应用中获得新的并联机器人结构,为设计制造出实用的并联机器人打下基础,在理论上也有较高的价值,有利于逐步建立并联机器人型综合的一般方法。
本课题主要研究基于修正自由度计算公式的并联机构型综合问题,旨在针对含有过约束的并联机构,建立全面有效的型综合理论。主要研究内容包括以下几方面:
提出了运用系统连杆法和拓扑矩阵-图表法对含有过约束的并联机构进行型综合。采用系统连杆法得到众多空间并联机构的关联连杆;根据关联连杆并且应用拓扑矩阵-图表法,得到了各种并联机构拓扑胚图与拓扑图,为进一步研究型综合问题打下了基础。
基于几何约束和尺寸驱动技术,提出并联机器人模拟机构的计算机辅助几何法,研究了相关的基本理论;建立一些含有过约束的并联模拟机构,对模拟机构给定输入件的驱动尺寸,确定动平台的位置和姿态。证明了本论文得到的机构的自由度与可动性的正确性。
论文的工作为进一步研究并联机构的型综合问题奠定了一定的理论基础。
The parallel mechanism is a kind of robot structure. It has the characteristics of high accuracy, rigidity, speed, and large load carrying capability. Researching the problem of type synthesis of parallel mechanisms is propitious to obtaining new parallel robotic mechanisms in practical application, and lays the foundation for the design and manufacture practical parallel robot. On the other hand, it helps to work up a common technique of type synthesis and has a higher value theoretically.
This paper focuses on the synthesis of the parallel mechanisms based on modificatory Grubler’s formula and aims to establish a universal and effective theory for parallel mechanisms with overconstrained. The main contributions are as follows:
A systematic linkage technique and a topology matrix-graph approach are put forward for type synthesis of parallel mechanisms with consstrained. By using the systematic linkage technique, numerous acceptable associated linkages of parallel mechanism can be derived. From the acceptable associated linkage and by using the approach of topology matrix-graph, topology embryonic graphs and topology graphs of various parallel mechanisms can be derived ,as the foundation of studying the subject of type synthesis further.
Based on the geometric constraints and dimension driven techniques, a novel computer aided geometric approach is put forward for designing the computer simulation mechanisms of parallel manipulators. Some spacial parallel simulation mechanisms with overconstrained are configurate. When the driving dimensions of driving limbs are modified, the configuration of the simulation mechanisms are varied correspondingly. The correctness of the DOF and movability of parallel mechanisms synthesized in this paper can be validated.
The research work of this dissertation establishes theoretical basis for the further research of type synthesis of parallel mechanisms.
本课题主要研究基于修正自由度计算公式的并联机构型综合问题,旨在针对含有过约束的并联机构,建立全面有效的型综合理论。主要研究内容包括以下几方面:
提出了运用系统连杆法和拓扑矩阵-图表法对含有过约束的并联机构进行型综合。采用系统连杆法得到众多空间并联机构的关联连杆;根据关联连杆并且应用拓扑矩阵-图表法,得到了各种并联机构拓扑胚图与拓扑图,为进一步研究型综合问题打下了基础。
基于几何约束和尺寸驱动技术,提出并联机器人模拟机构的计算机辅助几何法,研究了相关的基本理论;建立一些含有过约束的并联模拟机构,对模拟机构给定输入件的驱动尺寸,确定动平台的位置和姿态。证明了本论文得到的机构的自由度与可动性的正确性。
论文的工作为进一步研究并联机构的型综合问题奠定了一定的理论基础。
The parallel mechanism is a kind of robot structure. It has the characteristics of high accuracy, rigidity, speed, and large load carrying capability. Researching the problem of type synthesis of parallel mechanisms is propitious to obtaining new parallel robotic mechanisms in practical application, and lays the foundation for the design and manufacture practical parallel robot. On the other hand, it helps to work up a common technique of type synthesis and has a higher value theoretically.
This paper focuses on the synthesis of the parallel mechanisms based on modificatory Grubler’s formula and aims to establish a universal and effective theory for parallel mechanisms with overconstrained. The main contributions are as follows:
A systematic linkage technique and a topology matrix-graph approach are put forward for type synthesis of parallel mechanisms with consstrained. By using the systematic linkage technique, numerous acceptable associated linkages of parallel mechanism can be derived. From the acceptable associated linkage and by using the approach of topology matrix-graph, topology embryonic graphs and topology graphs of various parallel mechanisms can be derived ,as the foundation of studying the subject of type synthesis further.
Based on the geometric constraints and dimension driven techniques, a novel computer aided geometric approach is put forward for designing the computer simulation mechanisms of parallel manipulators. Some spacial parallel simulation mechanisms with overconstrained are configurate. When the driving dimensions of driving limbs are modified, the configuration of the simulation mechanisms are varied correspondingly. The correctness of the DOF and movability of parallel mechanisms synthesized in this paper can be validated.
The research work of this dissertation establishes theoretical basis for the further research of type synthesis of parallel mechanisms.
引文
1 Pollard and W.L.G. Spray painting machine. US Patent, 1940, 213(2): 12-58
2 Gough, V.E. and Whitehall, S.G. Universal type test machine. Proceedings of the FISITA Ninth International Technical Congress, 1962, May: 117-137
3 Stewart, D. A platform with six degrees of freedom. Proceedings of the IMechE, 1965, 180(15): 371-385
4 K. H. Hunt. Kinematic Geometry of Mechanisms. Oxford: Oxford University Press, UK, 1990: 78-99
5 E.F.Fichter. A Stewart platform-based manipulator: general theory and practice construction. Intt .J of Robot Research, 1986, 59(2): 157-182
6 J. P. Merlet. Still a long way to go on the road for parallel mechanisms. A keynote speech to be presented at the ASME 2002 DETC Conference, Montréal, 2002: 1-5
7 J.P.Merlet.“Parallel robot: Open problems,”in Proc. 9th Int. Symp.Robotics Research, Snowbird, UT, 1999, October: 9-12
8黄真.并联机器人机构学基础理论的研究[J].机器人技术与应用, 2001, 6: 11-14
9黄真.并联机器人及其机构学理论[J].燕山大学学报, 1998-1, 22(1): 13-17
10文福安,杨光.并联机器人机构概述[J].机械科学与技术, 2000, 19(1): 69-80
11朱煌,汪劲松,张永忠,等.并联机床设计理论、技术与设计环境[J].中国矿业大学学报(自然科学版), 2001, 30(3): 301-306
12黄真,丁华锋.机构的结构类型综合综述.燕山大学学报, 2003, 27(3): 189-192
13 Huang, Z. and Li, Q.C. On the Type Synthesis of Lower Mobility Parallel Mechanisms. Proceedings of Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec City, 2002, October 3-4: 272-283
14 Z. Huang, Q.C. Li. General Methodology for Type Synthesis of Lower-Mobility Symmetrical Parallel Manipulators and Several Novel Manipulators. International Journal of Robotics Research, 2002, 21(2): 131-146
15 Z. Huang, Q.C. Li. Some Novel Lower-Mobility Parallel Mechanisms. ASMEand 5-DOF parallel manipulator designs. Mechanism and Machine Theory, 2002, 37(4): 1395-1411
41 F.Gao etal. New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator Designs. Mechanism and Machine Theory, 2002, 37(11): 395–1411
42刘辛军,汪劲松,高峰,等.并联机器人机构新构型设计的探讨.中国机械工程, 2001, 12(12): 1339-1342
43王海东.并联机器人机构构型与性能分析. [燕山大学工学硕士学位论文]. 2001: 32-34
44 Yi Lu, Tatu Leinonen. Type synthesis of unified planar–spatial mechanisms by systematic linkage and topology matrix-graph technique. Mechanism and Machine Theory, 2005, 40: 1145–1163
45 Merlet J-P. Determination of 6d workspaces of Gough-type parallel manipulator and comparison between different geometries. Int. J. of Robotics Research, 1999, 18(9): 902-916
46张曙, U. Heisel.并联运动机床.北京:机械工业出版社, 2003:1-255
47 R. Kamra, D. Kohli, A.K. Dhingra. Forward displacement analysis of a six-dof parallel manipulator actuated by 3R3P and 4R2P chains. Mechanism and Machine Theory, 2002, 37: 619-637
48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, 89(5): 25-29
49 C. Innocenti and V. P. Castelli. Direct Position Analysis of the Stewart Platform Mechanism. Mechanism and Machine Theory, 1990, 25(6): 611-621
50刘学杰,张峰,杨建鸣,等. 6-SPS并联机构运动学数值分析.包头钢铁学院学报, 2000, 19(4): 309-313
51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
52 W. Lin, J. Duffy and M. Griffis. Forward Displacement Analysis of the 4-4 Stewart Platform. ASME J. of Mechanical Design, 1992, 114: 444-450
53 C. Innocenti. Direct Kinematics in Analytical Form of the 6-4 Fully ParallelMechanism. ASME J. of Mechanical Design, 1995, 117: 89-95
54 K. Cleary and T. Arai. A Prototype Parallel Manipulator: Kinematics Construction, Software, Workspace Results and Singularity analysis. In IEEE Int. Conf. on Robotics and Automation, Sacramento, USA, 1991: 566-571
55 E. F. Fichter. A Stewart Platform Based Manipulator: General Theory and Practical Construction. Int. J. of Robotics Research, 1986, 5(2): 157-181
56 J. P. Merlet. Parallel manipulators, Part 1, theory. Rapport de Recherche 646, INRIA, 1987: 143-160
57 C. Gosselin. Determination of the Workspace of 6-DOF Parallel Manipulators. In ASME Design Automation Conf., Montreal, Canada, 1989: 321-326
58 O. Masory and J. Wang. Workspace Evaluation of Stewart Platforms. In 22nd Biennial Mechanisms Conf., Scottsdale, USA, 1992: 337-346
59 Feng gao, Xinjun liu, Xu Chen. The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators. Mechnism and Machine Theory, 2001, 36: 205-220
60于晖,孙立宁,张秀峰,等.虎克铰工作空间研究及其在6-HTRT并联机器人中的应用.中国机械工程, 2002, 13(21): 1830-1834
61刘辛军,汪劲松,李剑锋,等.一种新型空间3自由度并联机构的正反解及工作空间分析.中国机械工程, 2001, 37(10): 36-39
62王奇志,谭民,徐心和.一类具有对称结构并联机器人的工作空间.机器人, 2001, 23(4): 322-325
63金振林,王军,高峰.新型6-PSS并联机器人工作空间分析.中国机械工程, 2002, 13(13): 14-16
64张立杰,刘辛军.球面三自由度并联机器人可达工作空间的研究.中国机械工程, 2001, 12(10): 1122-1124
65李宏.两种少自由度并联机器人的某些运动特性研究. [燕山大学工学硕士学位论文]. 2002: 34-44
66 M. Thomas and D. Tesar, Dynamic Modeling of Serial Manipulator Arms. J. of Dyn. Sys, Meas. and Cont., 1982, 104(9): 218-227
67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, 1997:28-29, 65-99
68赵铁石.空间少自由度并联机器人机构分析与综合的理论研究. [燕山大学工学博士学位论文]. 2000: 82-91
69 Shao-Chi Wang, Hiromitsu Hikita, Hiroshi Kubo, et al. Kinematics and dynamics of a 6 degree-of-freedom fully parallel manipulator with elastic joints. Mechnism and Machine Theory, 2003, 38: 439-461
70乔雨,王波兴,向文.基于自由度分析的三维几何约束推理求解.计算机辅助设计与图形学学报, 2002, 14(6): 557-561
71 Tian Huang, etal. Design of Hexapod-Based machine tools with specified orientation capability and well-conditioned dexterity. The 10th World Congress for Theory of Machines and Mechanisms, Oulu, Finland. 1999(7): 40-45
72 Kenneth H. Pittens, Ron P. Podhorodeski. A family of Stewart platforms with optimal dexterity. Journal of Robotic Systems, 1993, 10(4): 463-479
73 Hongrui Wang, F. Gao, Zhen Huang. Design of 6-Axis Force/Forquw Sensor Based on Stewart Platform Related to Isotropy. Chinese Journal of Mechanical Engineering (English Edition), 1998, 11(3): 217-222
74 Morizono T.,Kawamura S.Analysis and control of a force display system driven by parallel wire mechanism [J]. Robotics, 1998, 16(5): 551-563
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2 Gough, V.E. and Whitehall, S.G. Universal type test machine. Proceedings of the FISITA Ninth International Technical Congress, 1962, May: 117-137
3 Stewart, D. A platform with six degrees of freedom. Proceedings of the IMechE, 1965, 180(15): 371-385
4 K. H. Hunt. Kinematic Geometry of Mechanisms. Oxford: Oxford University Press, UK, 1990: 78-99
5 E.F.Fichter. A Stewart platform-based manipulator: general theory and practice construction. Intt .J of Robot Research, 1986, 59(2): 157-182
6 J. P. Merlet. Still a long way to go on the road for parallel mechanisms. A keynote speech to be presented at the ASME 2002 DETC Conference, Montréal, 2002: 1-5
7 J.P.Merlet.“Parallel robot: Open problems,”in Proc. 9th Int. Symp.Robotics Research, Snowbird, UT, 1999, October: 9-12
8黄真.并联机器人机构学基础理论的研究[J].机器人技术与应用, 2001, 6: 11-14
9黄真.并联机器人及其机构学理论[J].燕山大学学报, 1998-1, 22(1): 13-17
10文福安,杨光.并联机器人机构概述[J].机械科学与技术, 2000, 19(1): 69-80
11朱煌,汪劲松,张永忠,等.并联机床设计理论、技术与设计环境[J].中国矿业大学学报(自然科学版), 2001, 30(3): 301-306
12黄真,丁华锋.机构的结构类型综合综述.燕山大学学报, 2003, 27(3): 189-192
13 Huang, Z. and Li, Q.C. On the Type Synthesis of Lower Mobility Parallel Mechanisms. Proceedings of Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec City, 2002, October 3-4: 272-283
14 Z. Huang, Q.C. Li. General Methodology for Type Synthesis of Lower-Mobility Symmetrical Parallel Manipulators and Several Novel Manipulators. International Journal of Robotics Research, 2002, 21(2): 131-146
15 Z. Huang, Q.C. Li. Some Novel Lower-Mobility Parallel Mechanisms. ASMEand 5-DOF parallel manipulator designs. Mechanism and Machine Theory, 2002, 37(4): 1395-1411
41 F.Gao etal. New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator Designs. Mechanism and Machine Theory, 2002, 37(11): 395–1411
42刘辛军,汪劲松,高峰,等.并联机器人机构新构型设计的探讨.中国机械工程, 2001, 12(12): 1339-1342
43王海东.并联机器人机构构型与性能分析. [燕山大学工学硕士学位论文]. 2001: 32-34
44 Yi Lu, Tatu Leinonen. Type synthesis of unified planar–spatial mechanisms by systematic linkage and topology matrix-graph technique. Mechanism and Machine Theory, 2005, 40: 1145–1163
45 Merlet J-P. Determination of 6d workspaces of Gough-type parallel manipulator and comparison between different geometries. Int. J. of Robotics Research, 1999, 18(9): 902-916
46张曙, U. Heisel.并联运动机床.北京:机械工业出版社, 2003:1-255
47 R. Kamra, D. Kohli, A.K. Dhingra. Forward displacement analysis of a six-dof parallel manipulator actuated by 3R3P and 4R2P chains. Mechanism and Machine Theory, 2002, 37: 619-637
48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, 89(5): 25-29
49 C. Innocenti and V. P. Castelli. Direct Position Analysis of the Stewart Platform Mechanism. Mechanism and Machine Theory, 1990, 25(6): 611-621
50刘学杰,张峰,杨建鸣,等. 6-SPS并联机构运动学数值分析.包头钢铁学院学报, 2000, 19(4): 309-313
51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
52 W. Lin, J. Duffy and M. Griffis. Forward Displacement Analysis of the 4-4 Stewart Platform. ASME J. of Mechanical Design, 1992, 114: 444-450
53 C. Innocenti. Direct Kinematics in Analytical Form of the 6-4 Fully ParallelMechanism. ASME J. of Mechanical Design, 1995, 117: 89-95
54 K. Cleary and T. Arai. A Prototype Parallel Manipulator: Kinematics Construction, Software, Workspace Results and Singularity analysis. In IEEE Int. Conf. on Robotics and Automation, Sacramento, USA, 1991: 566-571
55 E. F. Fichter. A Stewart Platform Based Manipulator: General Theory and Practical Construction. Int. J. of Robotics Research, 1986, 5(2): 157-181
56 J. P. Merlet. Parallel manipulators, Part 1, theory. Rapport de Recherche 646, INRIA, 1987: 143-160
57 C. Gosselin. Determination of the Workspace of 6-DOF Parallel Manipulators. In ASME Design Automation Conf., Montreal, Canada, 1989: 321-326
58 O. Masory and J. Wang. Workspace Evaluation of Stewart Platforms. In 22nd Biennial Mechanisms Conf., Scottsdale, USA, 1992: 337-346
59 Feng gao, Xinjun liu, Xu Chen. The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators. Mechnism and Machine Theory, 2001, 36: 205-220
60于晖,孙立宁,张秀峰,等.虎克铰工作空间研究及其在6-HTRT并联机器人中的应用.中国机械工程, 2002, 13(21): 1830-1834
61刘辛军,汪劲松,李剑锋,等.一种新型空间3自由度并联机构的正反解及工作空间分析.中国机械工程, 2001, 37(10): 36-39
62王奇志,谭民,徐心和.一类具有对称结构并联机器人的工作空间.机器人, 2001, 23(4): 322-325
63金振林,王军,高峰.新型6-PSS并联机器人工作空间分析.中国机械工程, 2002, 13(13): 14-16
64张立杰,刘辛军.球面三自由度并联机器人可达工作空间的研究.中国机械工程, 2001, 12(10): 1122-1124
65李宏.两种少自由度并联机器人的某些运动特性研究. [燕山大学工学硕士学位论文]. 2002: 34-44
66 M. Thomas and D. Tesar, Dynamic Modeling of Serial Manipulator Arms. J. of Dyn. Sys, Meas. and Cont., 1982, 104(9): 218-227
67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, 1997:28-29, 65-99
68赵铁石.空间少自由度并联机器人机构分析与综合的理论研究. [燕山大学工学博士学位论文]. 2000: 82-91
69 Shao-Chi Wang, Hiromitsu Hikita, Hiroshi Kubo, et al. Kinematics and dynamics of a 6 degree-of-freedom fully parallel manipulator with elastic joints. Mechnism and Machine Theory, 2003, 38: 439-461
70乔雨,王波兴,向文.基于自由度分析的三维几何约束推理求解.计算机辅助设计与图形学学报, 2002, 14(6): 557-561
71 Tian Huang, etal. Design of Hexapod-Based machine tools with specified orientation capability and well-conditioned dexterity. The 10th World Congress for Theory of Machines and Mechanisms, Oulu, Finland. 1999(7): 40-45
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