平面平台型Stewart并联机构的奇异性分析  

Singularity Analysis of Stewart Parallel Mechanism with Planar Platform

作　　者：程世利[1] 吴洪涛[1] 王超群[1] 姚裕[1] 朱剑英[1] 

机构地区：[1]南京航空航天大学机电学院,南京210016

出　　处：《机械工程学报》2011年第9期1-7,共7页Journal of Mechanical Engineering

基　　金：国防科工委'十一五'预研基金(C4220062501);国家自然科学基金(50375071);航空科学基金(H0608-012);江苏省普通高校研究生科研创新计划(CX07B-068z)资助项目

摘　　要：提出一种研究平面平台型Stewart并联机构奇异性问题的新方法。采用四元数描述旋转矩阵,并将矢量的坐标扩展为4维形式,通过分析动平台位置与姿态变量之间的耦合关系以及四元数的性质,得到采用8个二次方程式表达的运动方程组。应用该运动方程组进一步导出平面平台型Stewart并联机构的一种新的雅可比矩阵,通过对该新雅可比矩阵求取行列式,得到了奇异性轨迹关于位置姿态变量的解析表达式。根据奇异轨迹解析表达式就可以确定奇异轨迹在空间的分布情况,无论是位置奇异还是姿态奇异都是适用的。通过一个具体的计算实例来验证新方法的正确性。提出的新方法可用于所有具有平面平台的Stewart并联机构的奇异性分析。A new method for singularity analysis of the Stewart parallel mechanisms with planar platforms is presented.The rotation matrix is described by quaternion,and both the rotation matrix and the coordinates of the vectors are expanded to four dimensions.Through analyzing the coupling relationships between position variables and orientation variables,properties of quaternion,motion equations expressed by eight quadratic equations are obtained.From the motion equations a new kind of Jacobian matrix of the Stewart parallel mechanism is derived.The analytical expression of the singularity locus,with respect to the position and the orientation variables,is obtained by calculating the determinant of the new Jacobian matrix.The analytical expression of singularity locus determines the distribution of singularity locus in space,and it is suitable for both the orientation singularity and the position singularity.Finally,the correctness of the new method is verified by a concrete calculation example.The singularity of all of the Stewart parallel mechanisms with planar platforms can be analyzed by using this method.

关 键 词：Sterwart 平台 并联机构 奇异性 四元数 雅可比矩阵 

分 类 号：TH112[机械工程—机械设计及理论] TP242[自动化与计算机技术—检测技术与自动化装置]