基于四元数法求解球面七杆机构的位置  

The Position Analysis of Spherical 7-Bar Mechanism Based on Unit Quaternion

作　　者：张帅[1] 王品[2] 许东来[1] 张兆凤[3] 赵立普[4] 杜佳明[5] 

机构地区：[1]北京工业大学机电学院,北京100124 [2]鲁东大学交通学院,烟台264025 [3]浙江大学机械工程学系,杭州310027 [4]河北工业大学机械工程学院,天津300130 [5]上海大学机电工程与自动化学院,上海200072

出　　处：《上海第二工业大学学报》2011年第2期144-153,共10页Journal of Shanghai Polytechnic University

摘　　要：对国内外球面机构特点、理论及性能研究的进展等内容进行了简要综述,并且使用四元数对球面七杆机构进行数学建模,求出各个转动副在球面上的位置,根据角度关系,列出3个约束方程。在消元过程中,使用Sylvester结式分两次求出一元32次方程。然后借助Mathematica软件求解其位置参数,完成其位置分析。The academic achievements about characteristics of spherical bodies,the progress of theory and performance studies,which are studied at home and abroad,are introduced in the paper.And with using quaternion to construct mathematical model for spherical 7-bar Mechanismk,every position of revolute joint on the surface of unit sphere can be obtained.Three constraint equations are obtained according to the angles constraint.Using Sylvester resultant elimination by two steps,a 32 degree univariate polynomial equation can be obtained.And with the help of Mathematica software,the location parameters have been solved.Then,their position analysis is completed.

关 键 词：球面七杆机构 位置分析 四元数法 

分 类 号：TH112[机械工程—机械设计及理论] TH123.1