A novel method for singularity analysis of the 6-SPS parallel mechanisms
A novel method for singularity analysis of the 6-SPS parallel mechanisms作者机构：College of Mechanical & Electrical Engineering Nanjing University of Aeronautics & Astronautics Nanjing 210016 China College of Engineering Nanjing Agricultural University Nanjing 210031 China College of Aerospace Engineering Nanjing University of Aeronautics & Astronautics Nanjing 210016 China
出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)
年 卷 期：2011年第54卷第5期
页 面：1220-1227页
核心收录：
学科分类：08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程]
基 金：supported by the National Natural Science Foundation of China (Grant No. 50375071) the Aviation Science Foundation of China (Grant No. H0608-012) Jiangsu Province Graduate Research and Innovation Program of China (Grant No. CX07B-068z)
主 题：parallel mechanism singularity analysis quaternion Jacobian matrix
摘 要：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.
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