Stewart并联机构位置奇异研究  

Position-singularity Analysis of the Stewart Parallel Mechanism

作　　者：李保坤[1,2] 曹毅[1,3] 张秋菊 黄真[4] 

机构地区：[1]江南大学机械工程学院,无锡214122 [2]安徽理工大学机械工程学院,淮南232001 [3]浙江大学流体动力与机电系统国家重点实验室,杭州310027 [4]燕山大学机器人研究中心,秦皇岛066004

出　　处：《机械工程学报》2012年第9期33-42,共10页Journal of Mechanical Engineering

基　　金：国家自然科学基金(50905075);安徽省高等学校优秀青年人才基金重点(2010SQRL047ZD);江苏省数字化制造技术重点实验室开放基金(HGDML-0910);浙江大学流体动力与机电系统国家重点实验室开放基金(GZKF-201105);江苏省普通高校研究生创新计划(CXZZ11_0482);江南大学博士研究生科学基金(JUDCF11014)资助项目

摘　　要：对动定平台为两个非相似的半规则正六边形的Stewart并联机构位于给定姿态时的位置奇迹进行了系统地研究。基于建立该并联机构的力雅可比矩阵,推导出机构位于给定姿态时的三维位置奇异轨迹的三次符号表达式。进一步分析发现,该机构的对于给定姿态参数的三维位置奇异轨迹相当复杂,其在一般倾斜截面上的投影曲线的几何特征也很难识别。定义动平台所在平面为特征平面,研究表明在特征平面上的位置奇异轨迹曲线均是一条二次曲线,包括无数对双曲线、四对相交直线以及一条抛物线。对于个别特殊姿态,特征平面上的位置奇异轨迹二次曲线退化为平行于脊线的一对或一条直线。提出并证明关于特征平面上的位置奇异轨迹曲线几何特征的两个定理。此外,基于Grassmann线几何以及螺旋理论简要分析了位置奇异轨迹的运动学特性。For a special class of the Stewart parallel mechanism whose moving platform and base platform are two dissimilar semi-regular hexagons,the position-singularity of the mechanism for a constant-orientation is analyzed systematically.Based on constructing the force Jacobian matrix,a cubic symbolic expression that represents the 3-dimensional position-singularity locus for a constant orientation is derived.The concept of the characteristic plane is proposed.Further analysis shows that the 3-dimensional position-singularity locus of the mechanism for a given position is very complicated,and the geometric characteristics of the position-singularity locus lying in a general oblique plane are difficult to be identified.The plane where the moving platform lies is defined as the characteristic plane.Research shows that the position-singularity curves in the characteristic planes are all quadratic curves,including infinity many sets of hyperbolas,four pairs of intersecting lines and a parabola.For some special orientations,the quadratic position-singularity curves in the characteristic planes degenerate into two parallel lines or even one line which are all parallel to the ridge line.Two theorems concerning the geometric characteristics of the position-singularity curves in the characteristic planes are advanced and proved.Moreover,the kinematic property of the position-singularity locus is briefly analyzed based on the Grassmann line geometry and the screw theory.

关 键 词：并联机构 位置奇异 几何特征 运动学特性 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]