一种低耦合度半对称球面并联机构的设计、拓扑分析与运动学

Design, Topology Analysis and Kinematics of A Semi-symmetric Spherical Parallel Mechanism With Low Coupling Degree

根据基于方位特征(POC)方程的并联机构拓扑结构设计理论,设计了一种低耦合度半对称的三转动(3R)球面并联机构,分析计算了该机构输出运动的方位特征集(POC)、自由度以及耦合度(κ=1)三个主要拓扑特性;其次,运用序单开链法运动学原理求解了位置正解的数值解。再次,基于导出的机构位置反解公式,分析了动平台的工作空间,并基于Jacobian矩阵对机构奇异位形进行了分析;最后,利用Matlab给出工作空间中的奇异轨迹。

According to the design theory for parallel mechanisms (PMs) based on position and orientation characteristic(POC) equation,a novel 3-DOF Semi-symmetric spherical parallel Mechanism with lower coupling degree of κ= 1 was proposed. The orientation characteristic (POC) of the output motion ,degree of freedom and coupling degree(κ= 1) of the mechanism are analyzed and calculated. Next ,the direct position and the inverse kinematics problem of the mechanism was solved by using the modeling methods based on the ordered SOC unit ,and the positive and inverse solutions were verified by numerical methods using Matlab. Furthermore ,the workspace of the mechanism was analyzed based on inverse solutions formula ,then ,the singularity analysis of the mechanism was also performed based on Jacobian matrix ,from which three kinds of singular conditions were obtained. Finally ,the singular locus in workspace can be solved by Matlab.