含R副间隙6-RPS机构奇异性分析  

Singularity analysis on the 6-RPS mechanism with R pair clearance

作　　者：赵德胜 ZHAO De-sheng(School of Automation,Xi＇an University of Posts ＆ Telecommunications,Xi＇an 710121)

机构地区：[1]西安邮电大学自动化学院,陕西西安710121

出　　处：《机械设计》2018年第8期86-92,共7页Journal of Machine Design

基　　金：陕西省教育厅2016科学研究计划基金资助项目(16JK1692)

摘　　要：采用四元数法描述了4维形式的6-RPS机构位姿矩阵,由此推导出理想机构的运动方程,得到了理想机构的新型雅克比矩阵JA和JB。在此基础上,利用连续接触模型得到了含间隙6-RPS机构的位姿矩阵J_(AR)和J_(BR)。根据四元数的性质,把矩阵JA和J_(AR)转化为8维方阵,使之适用于分析奇异位形。分别把J_(AR)和J_(BR)的行列式展开,得到含间隙机构的奇异轨迹方程,利用MATLAB得到了机构在给定位置时的第1类位姿奇异轨迹和第2类位姿奇异三维轨迹曲面。结果表明,机构间隙对奇异位形轨迹有影响;以理想机构奇异轨迹曲面上的奇异点作为参考点,通过与含间隙机构奇异轨迹曲面上与参考点相对应的奇异点的相互对比,发现在参考点附近存在奇异域。In this paper, by means of the quaternion method, the 4-dimensional position matrix of the 6-RPS mechanism is illustrated. Then, the motion equation of the ideal mechanism is deduced, and a new Jacobian matrix JAand JBis obtained.Based on this, a continuous contact model is utilized to obtain the position matrix JAR and JBR of the 6-RPS mechanism with clearance. According to the quaternion nature, the matrix JAand JAR is transformed into the 8-dimensional square matrix, which is suitable for the analysis on the singular configuration. After the determinants of JAR and JBR are expanded respectively, the equation of locus on the singular mechanism with clearance is obtained, and then MATLAB is adopted to obtain the I-class position singular locus and the 3-dimensional locus curve of the II-class position singularity at the given place. The result shows that the mechanism clearance exerts certain influence on the singularity of the parallel mechanism. With the singular points on the singular locus curve of the ideal mechanism as reference points, a comparison is conducted between the reference points and their corresponding singular points on the singular locus curve of the mechanism with clearance, and then a singular field is found near the reference points.

关 键 词：四元数 奇异位形 含间隙并联机构 雅克比矩阵 奇异域 

分 类 号：TH112[机械工程—机械设计及理论]