A novel method for singularity analysis of the 6-SPS parallel mechanisms
A novel method for singularity analysis of the 6-SPS parallel mechanisms
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DOI：
10.1007/s11431-011-4323-2
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
Shili Cheng;Hongtao Wu;Chaoqun Wang;Yu Yao;Jianying Zhu
中科院分区：
文献类型：
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作者：
Shili Cheng;Hongtao Wu;Chaoqun Wang;Yu Yao;Jianying Zhu
奇异性分析是并联机构的一个基本问题，无论是在工作空间还是在运动规划中都无法回避。如何用解析形式表示奇点轨迹，一直是许多研究者的研究重点。提出了一种6-SPS并联机构奇异性分析的新方法。采用四元数描述旋转矩阵，并将旋转矩阵和坐标矢量展开为四维形式。通过分析位置变量和姿态变量之间的耦合关系，利用四元数的性质，得到了八个等效方程。由这些方程导出了一种新的雅可比矩阵，并通过计算新雅可比矩阵的行列式得到了奇异轨迹的解析表达式。利用该解析表达式，可求解动平台由6个杆件驱动，且动平台和基座的顶点均位于一圆上的并联机构的奇异性分析。
Singularity analysis is a basic problem of parallel mechanism, and this problem cannot be avoided in both workspace and motion planning. How to express the singularity locus in an analytical form is the research emphasis for many researchers for a long time. This paper presents a new method for the singularity analysis of the 6-SPS parallel mechanism. The rotation matrix is described by quaternion, and both the rotation matrix and the coordinate vectors have been expanded to four-dimensional forms. Through analyzing the coupling relationship between the position variables and the orientation variables, utilizing properties of the quaternion, eight equivalent equations can be obtained. A new kind of Jacobian matrix is derived from those equations, and the analytical expression of the singularity locus is obtained by calculating the determinant of the new Jacobian matrix. The singularity analysis of parallel mechanisms, whose moving platform actuated by 6 links and the vertices of both the base and the moving platforms has been placed on a circle respectively, can be solved by this analytical expression.