一种新型五自由度并联机床的性能分析
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摘要
本文对一种新型五自由度并联立式数控机床的运动学、灵巧度、奇异位形、精度几个方面进行了比较全面和系统的分析。
介绍了这种新型并联机床机构的组成及其特点，利用自由度公式和反螺旋两种方法计算了该机床机构的自由度。对中间约束支链和五驱动支链分别进行了运动学分析，并求出五驱动支链的反解。
导出此并联机床的速度雅克比矩阵和力雅克比矩阵。通过分析雅克比矩阵的条件数来判断关节空间和目标空间的速度传递性和力传递性，利用Matlab工具软件进行具体计算，并画出性能的三维图形来使分析可视化。把性能优化作为判断灵活工作空间的一个判据，考察灵活工作空间边界的各向同性。又由于线速度和角速度的量纲不同，采用分别考虑的方法，并综合考虑速度和力的传递性，优化结构参数。
本文在灵活工作空间内以雅克比矩阵的行列式值作为评价指标，验证当定平台和动平台都是均布时机构是否处于奇异位形，并在整个工作空间中搜索大大减少对并联机床奇异位形分析的工作量。
通过对国内外误差建模方法的综述分析，本文采用了矩阵法建立了并联机床机构的误差模型。利用蒙特卡洛技术模拟分析了驱动杆杆长误差和球铰(虎克铰)间隙对终端平台误差的影响。
The thesis analyses the kinematics, dexterity, singularity and accuracy of a 5 axis standing virtual CNC machine tool which is based on a novel 5-DOF parallel mechanism systematically.
The constitutes and characteristic of the PMT is introduced. The degree of freedom of the mechanism is calculated using formula of the degree of freedom and screw theory respectively. The kinematics analyses of the constraint limb and driving limbs are taken in. The inverse kinematics solution of the driving limbs is given.
Velocity Jacobian matrix and force Jacobian matrix of the PMT are educed. The condition numbers of the Jacobian matrix are analyzed to judge velocity transfer performance and force transfer performance between joint space and working space. The three dimensions drawings are drew by Matlab to make analysis visual. Judge flexible workspace using optimizing performance and checking isotropy of flexible workspace's boundary. Because the measurements of the linear velocity and the angular velocity are different, they are considered respectively. The velocity transfer performance and the force transfer performance are considered synthetically to optimize configuration parameters.
When the joints' distribution of the fixed platform and the moving platform are equal, judge the location is or not singularity. Regard the determinant values of the Jacobian matrix in flexible workspace as estimate guideline, which reduces extremely calculation that has been implemented in the singularity analyses of the 5-DOF parallel mechanism.
Analyze errors modeling methods at home and abroad, and erect errors model of the parallel mechanism using matrix methods. The influence of legs' tolerance and spherical joints' (Huke joints) clearance on errors of terminal platform is analyzed using Monte-Carlo technique.
介绍了这种新型并联机床机构的组成及其特点，利用自由度公式和反螺旋两种方法计算了该机床机构的自由度。对中间约束支链和五驱动支链分别进行了运动学分析，并求出五驱动支链的反解。
导出此并联机床的速度雅克比矩阵和力雅克比矩阵。通过分析雅克比矩阵的条件数来判断关节空间和目标空间的速度传递性和力传递性，利用Matlab工具软件进行具体计算，并画出性能的三维图形来使分析可视化。把性能优化作为判断灵活工作空间的一个判据，考察灵活工作空间边界的各向同性。又由于线速度和角速度的量纲不同，采用分别考虑的方法，并综合考虑速度和力的传递性，优化结构参数。
本文在灵活工作空间内以雅克比矩阵的行列式值作为评价指标，验证当定平台和动平台都是均布时机构是否处于奇异位形，并在整个工作空间中搜索大大减少对并联机床奇异位形分析的工作量。
通过对国内外误差建模方法的综述分析，本文采用了矩阵法建立了并联机床机构的误差模型。利用蒙特卡洛技术模拟分析了驱动杆杆长误差和球铰(虎克铰)间隙对终端平台误差的影响。
The thesis analyses the kinematics, dexterity, singularity and accuracy of a 5 axis standing virtual CNC machine tool which is based on a novel 5-DOF parallel mechanism systematically.
The constitutes and characteristic of the PMT is introduced. The degree of freedom of the mechanism is calculated using formula of the degree of freedom and screw theory respectively. The kinematics analyses of the constraint limb and driving limbs are taken in. The inverse kinematics solution of the driving limbs is given.
Velocity Jacobian matrix and force Jacobian matrix of the PMT are educed. The condition numbers of the Jacobian matrix are analyzed to judge velocity transfer performance and force transfer performance between joint space and working space. The three dimensions drawings are drew by Matlab to make analysis visual. Judge flexible workspace using optimizing performance and checking isotropy of flexible workspace's boundary. Because the measurements of the linear velocity and the angular velocity are different, they are considered respectively. The velocity transfer performance and the force transfer performance are considered synthetically to optimize configuration parameters.
When the joints' distribution of the fixed platform and the moving platform are equal, judge the location is or not singularity. Regard the determinant values of the Jacobian matrix in flexible workspace as estimate guideline, which reduces extremely calculation that has been implemented in the singularity analyses of the 5-DOF parallel mechanism.
Analyze errors modeling methods at home and abroad, and erect errors model of the parallel mechanism using matrix methods. The influence of legs' tolerance and spherical joints' (Huke joints) clearance on errors of terminal platform is analyzed using Monte-Carlo technique.
引文
1 J. M. Fithter. Application of the Stewart Platform as a Manufacturing Manipulator, SME Tech,1992,(1):199
2 J. M. Fithter. Evaluating the Stewart Platform for Manufacturing. Robotics Today,1993,6(1):1-3
3 Katsumi Suzumori. A Six-axis Motion Base and A Study of A Parallel Manipulators. Advanced Robotics. 1994,8(6):609-610
4 J. P. Merlet. Parallel Manipulators: State of the Art and Perspectives. Journal of Advanced Robotics,1994,8(6):589-596
5 G. Pritschow, K. H. Wurst. Systematic Design of Hexpods and Other Parallel Link System. Annals of CIRP,1997,46(1):291-295
6 李迎,龚光容,施祖康.虚拟轴机床的应用研究与发展趋势.机械设计与制造工程,1999,28(3):2-4
7 汪劲松,黄田.并联机床——机床行业面临的机遇与挑战.中国机械工程,1999,10(10):1103-1107
8 关浩,胡萍,于云满.21世纪新兴机床——虚拟轴并联机床.江苏机械制造与自动化,2001,(4):17-18
9 周凯.虚拟轴机床发展动态与应采取的对策.江苏机械制造与自动化,2000,(2):7-11
10 陈文家,王洪光,房立金,等.并联机床的发展现状与展望.机电工程,2001,18(4):5-8
11 杨建新,郁鼎又,王立平,等.并联机床研究现状与展望.机械设计与制造工程,2002,31(3):10-12
12 周凯.虚拟轴机床的发展趋势－混联机床.现代制造工程,2002,(3):5-7
13 黄田,汪劲松.并联机床设计基础理论研究进展.中国科协青年科学家论坛论文集.北京:航空工业出版社,1999:25-38
14 方跃法,黄真.并联机器人机构学研究进展.机器人,1995,18(4):221-225
15 黄真.空间机构学.北京:机械工业出版社,1991:97-141
16 黄真,孔令富,方跃法.并联机器人机构学及控制.北京:机械工业出版社,1997:12-268
17 黄真,高峰.从并联机器人研究看知识创新和技术创新.机械工程学报,2000,36(2):18-20
18 方跃法,黄真.三自由度3-RPS并联机器人操作器的瞬时独立运动分析.机械科学
与技术,1996,15(11):929-934
19 黄真,杜雄.3/6-SPS型Stewart机器人的一般线性丛奇异分析.中国机械工程,1998,(11):997-999
20 梁崇高,安辉.一种Stewart平台型机械手位移正解.机械工程学报, 1991,27(2):671-675
21 韩林,文福安,梁崇高.6-5平台型并联机构的位置正解.北京邮电大学学报,1998,21(2):33-37
22 L. Molinari Tosatti et al. An Integrated Methodology for the Design of Parallel Kinematic Machines. Annals of the CIRP,1997,46(2):341-345
23 Tian Huang et al. The Local Dexterity, Optimal Architecture and Design Criteria of Parallel Machine Tools. Annals of the CIRP,1998,47(1):347-351
24 Q.Y Wang et al. Design and Kinematics of a Parallel Manipulator for Manufacturing. Annals of the CIRP,1997,46(1):297-300
25 周凯.虚拟轴数控机床的虚实映射联动控制.中国机械工程,1998,9(3):16-18
26 杨向东,李铁民,魏永明,等.六自由度虚拟轴机床预处理算法及系统建模.中国机械工程,1998,9(5):82-86
27 刘文涛.并联杆系机床工作空间与精度分析.制造技术与机床,1998,(11):9-11
28 A. J Patel et al. Volumetric Error Analysis of a Stewart Platform Based Machine Tool. Annals of the CIRP,1997,46(1):287-290
29 Matthias Hebsacker.用六条腿机床实现高效铣削.制造技术与机床,1998,(10):20-22
30 倪雁冰,杨亚威,王辉,等.并联机床数控系统软件设计.制造业自动化,2002,24(8):10-13
31 李维嘉.Stewart运动平台的雅克比矩阵条件数的研究.华中理工大学学报,1997,25(11):33-35
32 金振林,高峰.一种正交并联机器人的灵巧度指标及其分布.机械设计,2001,(7):19-22
33 卢强,张友良.改型Stewart平台性能分析及优化.中国机械工程,2001,12(5):136-138
34 T. Yoshikawa. Analysis and Control of Robot Manipulators with Redundancy. Ist Int. Simp, Robotics Research, MIT press,1984:735-747
35 S. L. Chiu. Control of Redundant Manipulators for Task Compatibility. Proc. IEEE Int. Coference on Robotics and Automation,1987:1717-1724
36 蔡胜利,王秀彦,白师贤.3-TRS型机器人的操作能力分析.机械设计,1995(5):8-10
37 饶青,白师贤.6-6型Stewart机器人的可操作性分析及其定义.机器人,1994,16(6):345-349。
38 E. F. Fither. A Stewart Platform Based Manipulator: General Theory and Practical Construction. Int. J. Robotics Research,1986,5(2):57-182
39 C. M. Gosselin, J. Angeles. Singularity Analysis of Closed-Loop Kinematics Chain. IEEE Trans. on Robotics and Automation,1990,6 (3):281-290
40 O. Ma, J. Angeles. Architecture Singularities of Parallel Manipulators. Int J. Robotics and Automation,1992,7(1):23-29
41 J. P. Merlet. On the Infinitesimal Motion of a Parallel Manipulator in Singular Configurations. IEEE Proc. of Int. Conf. on Robotics and Automation,1992:320-325
42 J. P. Merlet. Singular Configurations of Parallel Manipulators and Grassmann Geometry. Int. J. Robotics Research,1990,8(5):45-56
43 N. Mouly, J. P. Merlet. Singular Configurations and Direct Kinematics of a New Parallel Manipulator. Proceeding of the IEEE International Conference on Robotics and Automation, Nice, France,1992:338-343
44 Y. Takeda, H. Funabashi. Kinematic and Static Characteristic of In-Parallel Actuated Manipulators at Singular Points and in Their Neighborhood. JSME International Journal(Series C),1996,39(1):85-93
45 D. Basu, A. Ghousal. Singularity Analysis of Platform-Type Multi-Loop Spatial Mechanisms. Mechanism and Machine Theory,1997,32(3):375-389
46 吴江宁,左爱秋,李世伦.并联六自由度平台机构机械误差分析与检测.中国机械工程,1999,(10):614-617
47 费业泰.精度来理论若干问题研究进展与未来.中国机械工程,2000,(11):255-256
48 阎华.机器人位姿误差建模方法综述.机床与液压,2000,(1):3-5
49 Oren Masory, Jian Wang, Hanqi Zhuang. Kinematic Modeling and Calibration for a Stewart Platform. Advanced Robotics, 1997,(5):519-539
50 孙昆鹏,杨向东,汪劲松.虚拟轴机床精度分析.第一届并联机器人及机床设计理论与关键技术研讨会论文.北京,1999:75-80
51 Ropponen, Timo, Arai. Accuracy Analysis of a Modified Stewart Platform Manipulator. Proceedings of the 1995 IEEE International Conference on Robotics and Automation, 1995,(1):521-525
52 苏玉鑫,段宝岩.六自由度Stewart平台运动精度分析.西安电子科技大学学报(自然科学版),2000,27(4):401-403
53 祃琳,黄田.面向制造的并联机床精度设计.中国机械工程,1999,(10):1114-1117
54 曾宪菁,黄田,曾子平.3-RRR型数控回转台的精度分析.机械工程学报,2001,37(11):42-45
55 H. Tajbakhsh, G.R. Fellow. Kinematic Error Estimation and Transmission Error Bounding for Stewart Platform Based Machine Tools. Transactions of NAMRI/SME, 1997:323-328
56 Han S. Kim, Yong J. Choi. The Kinematic Error Bound Analysis of the Stewart Platform. Journal of Robotic Systems,2000,17(1):63-73
57 吕崇耀,熊有伦.Stewart并联机构位姿误差分析.华中理工大学学报,1999,(8):4-6
58 卢强,张友良.Stewart平台误差的蒙特卡洛模拟.机械科学与技术,2001,20(4):543-544
2 J. M. Fithter. Evaluating the Stewart Platform for Manufacturing. Robotics Today,1993,6(1):1-3
3 Katsumi Suzumori. A Six-axis Motion Base and A Study of A Parallel Manipulators. Advanced Robotics. 1994,8(6):609-610
4 J. P. Merlet. Parallel Manipulators: State of the Art and Perspectives. Journal of Advanced Robotics,1994,8(6):589-596
5 G. Pritschow, K. H. Wurst. Systematic Design of Hexpods and Other Parallel Link System. Annals of CIRP,1997,46(1):291-295
6 李迎,龚光容,施祖康.虚拟轴机床的应用研究与发展趋势.机械设计与制造工程,1999,28(3):2-4
7 汪劲松,黄田.并联机床——机床行业面临的机遇与挑战.中国机械工程,1999,10(10):1103-1107
8 关浩,胡萍,于云满.21世纪新兴机床——虚拟轴并联机床.江苏机械制造与自动化,2001,(4):17-18
9 周凯.虚拟轴机床发展动态与应采取的对策.江苏机械制造与自动化,2000,(2):7-11
10 陈文家,王洪光,房立金,等.并联机床的发展现状与展望.机电工程,2001,18(4):5-8
11 杨建新,郁鼎又,王立平,等.并联机床研究现状与展望.机械设计与制造工程,2002,31(3):10-12
12 周凯.虚拟轴机床的发展趋势－混联机床.现代制造工程,2002,(3):5-7
13 黄田,汪劲松.并联机床设计基础理论研究进展.中国科协青年科学家论坛论文集.北京:航空工业出版社,1999:25-38
14 方跃法,黄真.并联机器人机构学研究进展.机器人,1995,18(4):221-225
15 黄真.空间机构学.北京:机械工业出版社,1991:97-141
16 黄真,孔令富,方跃法.并联机器人机构学及控制.北京:机械工业出版社,1997:12-268
17 黄真,高峰.从并联机器人研究看知识创新和技术创新.机械工程学报,2000,36(2):18-20
18 方跃法,黄真.三自由度3-RPS并联机器人操作器的瞬时独立运动分析.机械科学
与技术,1996,15(11):929-934
19 黄真,杜雄.3/6-SPS型Stewart机器人的一般线性丛奇异分析.中国机械工程,1998,(11):997-999
20 梁崇高,安辉.一种Stewart平台型机械手位移正解.机械工程学报, 1991,27(2):671-675
21 韩林,文福安,梁崇高.6-5平台型并联机构的位置正解.北京邮电大学学报,1998,21(2):33-37
22 L. Molinari Tosatti et al. An Integrated Methodology for the Design of Parallel Kinematic Machines. Annals of the CIRP,1997,46(2):341-345
23 Tian Huang et al. The Local Dexterity, Optimal Architecture and Design Criteria of Parallel Machine Tools. Annals of the CIRP,1998,47(1):347-351
24 Q.Y Wang et al. Design and Kinematics of a Parallel Manipulator for Manufacturing. Annals of the CIRP,1997,46(1):297-300
25 周凯.虚拟轴数控机床的虚实映射联动控制.中国机械工程,1998,9(3):16-18
26 杨向东,李铁民,魏永明,等.六自由度虚拟轴机床预处理算法及系统建模.中国机械工程,1998,9(5):82-86
27 刘文涛.并联杆系机床工作空间与精度分析.制造技术与机床,1998,(11):9-11
28 A. J Patel et al. Volumetric Error Analysis of a Stewart Platform Based Machine Tool. Annals of the CIRP,1997,46(1):287-290
29 Matthias Hebsacker.用六条腿机床实现高效铣削.制造技术与机床,1998,(10):20-22
30 倪雁冰,杨亚威,王辉,等.并联机床数控系统软件设计.制造业自动化,2002,24(8):10-13
31 李维嘉.Stewart运动平台的雅克比矩阵条件数的研究.华中理工大学学报,1997,25(11):33-35
32 金振林,高峰.一种正交并联机器人的灵巧度指标及其分布.机械设计,2001,(7):19-22
33 卢强,张友良.改型Stewart平台性能分析及优化.中国机械工程,2001,12(5):136-138
34 T. Yoshikawa. Analysis and Control of Robot Manipulators with Redundancy. Ist Int. Simp, Robotics Research, MIT press,1984:735-747
35 S. L. Chiu. Control of Redundant Manipulators for Task Compatibility. Proc. IEEE Int. Coference on Robotics and Automation,1987:1717-1724
36 蔡胜利,王秀彦,白师贤.3-TRS型机器人的操作能力分析.机械设计,1995(5):8-10
37 饶青,白师贤.6-6型Stewart机器人的可操作性分析及其定义.机器人,1994,16(6):345-349。
38 E. F. Fither. A Stewart Platform Based Manipulator: General Theory and Practical Construction. Int. J. Robotics Research,1986,5(2):57-182
39 C. M. Gosselin, J. Angeles. Singularity Analysis of Closed-Loop Kinematics Chain. IEEE Trans. on Robotics and Automation,1990,6 (3):281-290
40 O. Ma, J. Angeles. Architecture Singularities of Parallel Manipulators. Int J. Robotics and Automation,1992,7(1):23-29
41 J. P. Merlet. On the Infinitesimal Motion of a Parallel Manipulator in Singular Configurations. IEEE Proc. of Int. Conf. on Robotics and Automation,1992:320-325
42 J. P. Merlet. Singular Configurations of Parallel Manipulators and Grassmann Geometry. Int. J. Robotics Research,1990,8(5):45-56
43 N. Mouly, J. P. Merlet. Singular Configurations and Direct Kinematics of a New Parallel Manipulator. Proceeding of the IEEE International Conference on Robotics and Automation, Nice, France,1992:338-343
44 Y. Takeda, H. Funabashi. Kinematic and Static Characteristic of In-Parallel Actuated Manipulators at Singular Points and in Their Neighborhood. JSME International Journal(Series C),1996,39(1):85-93
45 D. Basu, A. Ghousal. Singularity Analysis of Platform-Type Multi-Loop Spatial Mechanisms. Mechanism and Machine Theory,1997,32(3):375-389
46 吴江宁,左爱秋,李世伦.并联六自由度平台机构机械误差分析与检测.中国机械工程,1999,(10):614-617
47 费业泰.精度来理论若干问题研究进展与未来.中国机械工程,2000,(11):255-256
48 阎华.机器人位姿误差建模方法综述.机床与液压,2000,(1):3-5
49 Oren Masory, Jian Wang, Hanqi Zhuang. Kinematic Modeling and Calibration for a Stewart Platform. Advanced Robotics, 1997,(5):519-539
50 孙昆鹏,杨向东,汪劲松.虚拟轴机床精度分析.第一届并联机器人及机床设计理论与关键技术研讨会论文.北京,1999:75-80
51 Ropponen, Timo, Arai. Accuracy Analysis of a Modified Stewart Platform Manipulator. Proceedings of the 1995 IEEE International Conference on Robotics and Automation, 1995,(1):521-525
52 苏玉鑫,段宝岩.六自由度Stewart平台运动精度分析.西安电子科技大学学报(自然科学版),2000,27(4):401-403
53 祃琳,黄田.面向制造的并联机床精度设计.中国机械工程,1999,(10):1114-1117
54 曾宪菁,黄田,曾子平.3-RRR型数控回转台的精度分析.机械工程学报,2001,37(11):42-45
55 H. Tajbakhsh, G.R. Fellow. Kinematic Error Estimation and Transmission Error Bounding for Stewart Platform Based Machine Tools. Transactions of NAMRI/SME, 1997:323-328
56 Han S. Kim, Yong J. Choi. The Kinematic Error Bound Analysis of the Stewart Platform. Journal of Robotic Systems,2000,17(1):63-73
57 吕崇耀,熊有伦.Stewart并联机构位姿误差分析.华中理工大学学报,1999,(8):4-6
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