连杆机构运动学几何代数求解综述

doi:10.13190/jbupt.201004.1.liaoqzh

北京邮电大学学报 ›› 2010, Vol. 33 ›› Issue (4): 1-11.doi: 10.13190/jbupt.201004.1.liaoqzh

• 综述 • 下一篇

连杆机构运动学几何代数求解综述

廖启征

北京邮电大学自动化学院

出版日期:2010-08-28 发布日期:2010-08-28
通讯作者: 廖启征(1947—)，男，教授，博士生导师， Email: qzliao@bupt.edu.cn.

Geometry Algebra Method for Solving the Kinematics of Linkage Mechanisms

Online:2010-08-28 Published:2010-08-28

摘要/Abstract

摘要：

介绍了连杆机构研究中涉及几何学的一些问题，包括平面、空间连杆机构；串联、并联机构的建模与求解；机构运动分析与综合等. 在建模和求解方面，主要介绍了目前对上述问题进行研究的一些新方法以及利用计算机对这些问题进行处理时出现的问题和应采取的措施.

关键词: 连杆机构, 几何代数, 运动分析与综合, 未知量消元

Abstract:

The problem discussed here is the research work of linkage mechanisms, which has relations with geometry. These works include planar and spatial mechanisms, series and parallel mechanisms, geometrical modeling of the mechanisms and equations solving. The kinematic analysis and synthesis of mechanisms are also discussed. Except traditional method, modern ones for solving these problems are outlined here. When computer is used, some special problems appear in the calculation and are also discussed.

Key words: linkage mechanisms, geometry algebra, kinematic analysis and synthesis, unknown elimination

廖启征. 连杆机构运动学几何代数求解综述[J]. 北京邮电大学学报, 2010, 33(4): 1-11.

参考文献

[1] Rooney J, Duffy J. On the closures of spatial mechanism//12^th ASME Mechanisms Conference. San Francisco: , 1972: 1-12.
[2] 杨廷力. 机械系统基本理论——结构学,运动学,动力学[M]. 北京: 机械工业出版社, 1996. Yang Tingli. Basic theory of mechanical systems——structural studies,kinematics, kinetics[M]. Beijing: China Machine Press, 1996.
[3] Duffy J, Crane C. A displacement analysis of the general spatial 7-link, 7R mechanism[J]. Mechanism and Machine Theory, 1980, 15: 153-169.
[4] Selig J. Geometrical method in robotics[M]. New York: Springer-Verlag, 1996.
[5] Raghavan M. The stewart platform of general geometry has 40 configurations[J]. ASME J Mech, 1993, 115: 277-282.
[6] Mourrain B. Enumeration problems in geometry, robotics and vision//Algorithms in Algebraic Geometry and Applications. Basel: Birkhauser, 1996: 285-306.
[7] Gao Xiaoshan. Generalized stewart platforms and their direct kinematics[J]. Mathematics Mechanization Research Preprints, 2003(22): 66-70.
[8] Freudenstein F. Kinematics, Past, Present and Future[J]. Mechanism and Machine Theory, 1973, 18(2): 151-161.
[9] 廖启征, 梁崇高, 张启先. 空间7R机构位移分析的新研究[J]. 机械工程学报, 1986, 22(3): 96-99. Liao Qizheng, Liang Chonggao, Zhang Qixian . Displacement analysis of spatial 7R new research institutions[J]. Journal of Mechanical Engineering, 1986, 22(3):96-99.
[10] 廖启征. 空间机构(无球面副)位移分析的酉交矩阵法. 北京: 北京航空航天大学, 1987.
[11] Liao Qizheng, Liang Chonggao, Zhang Qixian. Synthesizing spatial 7R mechanism with 16-assembly configurations[J]. Mechanism and Machine Theory, 1993, 28(5): 751-720.
[12] Qiao S, Liao Q, Wei S, et al. Inverse kinematic analysis of the general 6R serial robot mechanism based on double quaternion [J]. Mechanism and Machine Theory, 2010, 45(2): 193-199.
[13] Gan D, Liao Q, Dai J, et al. Dual quaternion based inverse kiverse kinematics of the general spatial 7R mechanism[J]. Proceedings IMechE, Part C: Journal Mechanical Engineering Science, 2008, 222(C8): 1593-1598.
[14] Hunt K H. Kinematic geometry of mechanisms[M]. : Oxford University Press,1978.
[15] Stewart D. A platform with six degree of freedom[J]. Proc Instn Mech Engrs, 1965, 180(15): 371-386.
[16] Lee Tae-Young, Shim Jae-Kyung. Forward kinematics of the general 6-6 Stewart platform using algebraic elimination[J]. Mechanism and Machine Theory, 2001, 36: 1073-1085.
[17] 黄昔光, 廖启征, 魏世民, 等. 基于法的一般6-6型台体并联机构位置正解[J]. 西安交通大学学报, 2008, 42(3): 300-303. Huang Xiguang, Liao Qizheng, Wei Shimin, et al. Mechanisms based on Groebner-Sylvester approach[J]. Journal of Xian Jiaotong University, 2008, 42(3): 300-303.
[18] Wen Fuan,Liang Chonggao. Displacement analysis of the 6-6 Stewart platform mechanisms[J]. Mechanism and Machine Theory, 1994, 29(4):547-557.
[19] Wu Wenda, Huang Yuzhen. The direct kinematic solution of the planar Stewart platform with coplanar ground points[J]. Mathematics Mechanization Research Preprints, 1994(12): 61-70.
[20] Huang Xiguang,Liao Qizheng, Wei Shimin, et al. Forward kinematics of the 6-6 Stewart platform with planar base and platform using algebraic elimination //2007 IEEE International Conference on Automation and Logistics. Jinan: , 2007: 18-21.
[21] Huang Yuzhen, Wu Wenda. Direct kinematic solutions of the Stewart platform[J]. Mathematics Mechanization Research Preprints, 1991(6): 94-101.
[22] Liao Qizheng, Seneviratne L, Earles S W E. Forward positional analysis for the general 4-6 in-parallel platform//Proc Instn Mech Engrs. 1995, 209: 55-67.
[23] 梁崇高, 荣辉. 一种Stewart平台型机械手位移正解[J]. 机械工程学报, 1991, 27(2): 26-30. Liang Chonggao, Rong Hui. A porward displayment solution to a stewart platform type manipulator[J]. Journal of Mechanical Engineering, 1991, 27(2) :26-30.
[24] Su Haijun, Liao Qizheng, Liang Chonggao. Direct positional analysis for a kind of 5-5 platform in-parallel robotic mechanism[J]. Mechanism and Machine Theory, 1999(34): 285-301.
[25] Han Lin, Liao Qizheng, Liang Chonggao. Forward displacement analysis of one kind of general 5-5 parallel manipulators[J]. Mechanism and Machine Theory, 2000(35): 271-289.
[26] 王品, 廖启征, 魏世民, 等. 基于Dixon结式的一种9杆巴氏桁架位置分析[J]. 北京航空航天大学学报, 2006, 32(7): 852-855. Wang Pin, Liao Qizheng, Wei Shimin, et al. Direct position analysis of nine-link Barranov truss based on Dixon resultants[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(7): 852-855.
[27] 王品, 廖启征, 魏世民, 等. 一种9杆巴氏桁架位置分析[J]. 北京邮电大学学报, 2006, 29(3): 12-16. Wang Pin, Liao Qizheng, Wei Shimin, et al. Research on displacement analysis of a kind of nine-link Barranov truss[J]. Journal of Beijing University of Posts and Telecommunications, 2006, 29 (3):12-16.
[28] 王品, 廖启征, 魏世民, 等. 一种9杆巴氏桁架的位置正解[J]. 清华大学学报:自然科学版, 2006, 46(8): 1373-1376. Wang Pin, Liao Qizheng, Wei Shimin, et al. Direct position analysis of a nine-link Barranov truss[J]. Journal of Tsinghua University: Science and Technology, 2006, 46 (8): 1373-1376.
[29] 庄育锋, 王品, 廖启征. 一种非平面9杆巴氏桁架位移分析的研究[J]. 北京邮电大学学报, 2006, 29(6): 13-16. Zhuang Yufeng, Wang Pin, Liao Qizheng. Research on displacement analysis of a kind of non-planar nine-link Barranov truss[J]. Journal of Beijing University of Posts and Telecommunications, 2006, 29(6): 13-16.
[30] McCarthy J M. Geometric design of linkages[M]. : Springer, 2000.
[31] Liao Qizheng, McCarthy J M. On the seven position synthesis of a 5-SS platform linkage[J]. Transaction of the ASME, 2001, 123: 74-79.
[32] Wempler C W, Morgan A P, Sommess A J. Complete solution of the nine-point path synthesis problem for four-bar linkages[J]. ASME J Mech Design, 1992, 114: 153-159.
[33] 李洪波. 共形几何代数与运动和形状的刻画[J]. 计算机辅助设计与图形学学报, 2006, 18(7): 895-901. Li Hongbo. Conformal geometric algebra and algebraic manipulations of geometric invariants[J]. Journal of Computer Aided Design and Computer Graphics, 2006, 18 ( 7): 895-901.
[34] Duffy J. Analysis of mechanisms and robot manipulators[M]. : Edward Arnold (Publisher) Ltd. 1980.
[35] Yang A T. Displacement analysis of spatial five-link mechanisms using (3×3) matrices with dual-number elements[J]. Journal of Engineering for Industry Transactions of the ASME, 1969, 91(13): 152-157.
[36] Veldkamp G R. 论对偶数、对偶矢量和对偶矩阵在瞬间时空运动学中的应用//机构学译文集. 北京: 机械工业出版社, 1982: 58. Veldkamp G R. On the use of dual numbers, dual vectors and matrixs in instantaneous,spatial kinematics//Translations of Mechanisms. Beijing:China Machine Press, 1982: 58.
[37] McCarthy J M, Etzel K. Spatial motion polation in an image space of SO(4)//Proceedings of the 1996 ASME Design Technical Conference. California: , 1996: 18-22.
[38] Ge Q J,Varshney A, Menon J P, et al. Double quaternions for motion interpolation//CD-ROM Proceedings of the ASME DETC’98. Atlanta: , 1998: 13-16.
[39] 李洪波. 共形几何代数与几何不变量的代数运算[J]. 计算机辅助设计与图形学报, 2006, 18(7): 902-911. Li Hongbo. Conformal geometric algebra and algebraic manipulations of geometric invariants[J]. Journal of Computer Aided Design and Computer Graphics, 2006,18(7): 902-911.
[40] 关霭文. 吴文俊消元法讲义[M]. 北京: 北京理工大学出版社, 1994. Guan Aiwen. Wu Wenjun elimination method notes[M]. Beijing: Beijing Institute of Technology, 1994.
[41] 韩林, 张昱, 梁崇高. 吴方法在平面二簧系统静力逆分析中的应用[J]. 北京邮电大学学报, 1997, 20(1): 1-7. Han Lin, Zhang Yu, Liang Chonggao. Wus method in the plane Erhuang system static inverse analysis[J]. Journal of Beijing University of Posts and Telecommunications, 1997, 20(1): 1-7.
[42] 韩林, 张昱, 梁崇高. 吴方法在平面并联机构位移正解中的应用[J]. 北京航空航天大学学报, 1998, 24(1): 116-119. Han Lin, Zhang Yu, Liang Chonggao. Wus method in the plane parallel mechanism displacement of positive solutions[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(1): 116-119.
[43] 何青. 计算代数[M]. 北京: 北京师范大学出版社, 1997. He Qing. Computational algebra[M]. Beijing: Beijing Normal University Press, 1997.
[44] Donald B R, Kapur D, Mundy J L. Symbolic and numerical computation for artificial intelligence[J]. Harcourt Brace Jovanovich, 1992: 52-55.
[45] Gan D M, Dai J S, Liao Q Z. Mobility analysis of two types of metamorphic parallel mechanisms//ASME Journal Mechanisms and Robotics. 2008.
[46] 廖启征, 李端玲. 平面图形放缩机构[J]. 机械工程学报, 2005, 41(8): 100-105. Liao Qizheng, Li Duanling. Mechanisms for scaling planar graphs[J]. Journal of Mechanical Engineering, 2005, 41(8): 140-143.
[47] 廖启征, 李端玲. 单层及多层平面图形放缩机构[J]. 机械工程学报, 2008, 44(6): 72-77. Liao Qizheng, Li Duanling. Construction method of monolayer and multilayer mechianisms for scaling planar graphs[J]. Journal of Mechanical Engineering, 2008, 44(6): 72-77.
[49] Su H J, McCarthy J M. Inverse static analysis for a planar compliant platform mechanism//ASME International Design Engineering Technical Conferences. Salt Lake City: , 2004. 量子密码技术研究研究单位: 北京邮电大学网络技术研究院课题负责人: 温巧燕课题组成员: 温巧燕郭奋卓高飞秦素娟林崧张劼莫骄朱萍丁金扣刘吉佑黄铮刘太琳杨宇光杜建忠陈秀波李玉英孙莹王天银验收时间: 2009年12月4日本课题为国家"863计划"信息技术领域信息安全技术专题项目(课题编号:2006AA01Z419). 课题组系统研究了量子密码协议的设计和分析理论,利用不同的量子力学性质设计了多种量子密码协议,包括量子密钥分发、量子认证、量子秘密共享、量子安全直接通信及量子隐形传态等,并对其安全性和有效性进行了较深入地分析. 利用密码分析理论对平时跟踪的量子密码协议进行了深入地安全性分析,发现了一些协议的安全性漏洞,给出了具体的攻击方法,如参与者攻击、相关提取攻击、隐形传态攻击、蛮力攻击等,同时提出了有针对性的改进方案. 用信息论方法分析协议安全性,收集了多种窃听检测模式下的安全性分析方法,并对其进行了分类和总结;发现了量子双向通信协议中的信息泄露问题,纠正了此前关于此类协议效率的错误认识;建立了量子秘密共享的通用分析模型,对量子密码协议的安全性评估具有重要的指导意义. 在量子密码模拟方面取得了突破性进展. 首先对量子密码中最杰出的协议进行了模拟实现. 该模拟器能够完整地演示BB84协议,建立共享的密钥,而且考虑到实际环境中噪声(相位反转、比特反转信道等)及其窃听者的影响,能够在噪声比率小于15%的信道中建立共享的密钥. 此外,为了方便量子计算,利用量子线路理论,设计了5粒子的量子线路模拟软件. 该软件可以模拟5个粒子的基本幺正运算 H门、X门、Y门、Z门和CNOT门. 利用这些基本的量子操作,可以实现复杂的量子计算. 课题组出版专著1部,发表论文76篇,其中被SCI检索42篇,国际期刊论文18篇.

连杆机构运动学几何代数求解综述

Geometry Algebra Method for Solving the Kinematics of Linkage Mechanisms

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	张英, 邵英奇, 魏世民, 廖启征. 基于共形几何代数的一种9杆巴氏桁架位移分析[J]. 北京邮电大学学报, 2023, 46(3): 91-96.
[2]	倪振松廖启征魏世民李瑞华. 基于共形几何代数的一种平面并联机构位置正解[J]. 北京邮电大学学报, 2010, 33(2): 7-10.
[3]	倪振松廖启征魏世民乔曙光李瑞华. 空间一般6R机械手位置反解的新方法[J]. 北京邮电大学学报, 2009, 32(2): 29-33.