低耦合度3T1R并联操作手设计与运动学分析

Design and Kinematics Analysis of a Novel 3T1R Parallel Manipulator with Lower Coupling Degree

基于方位特征(POC)方程的并联机构拓扑结构设计理论和机构结构降耦原理,设计了一种低耦合度能实现三平移一转动(3T1R)的SCRAR并联操作手机构。首先,阐述了该机构的组成,计算了该机构的耦合度k=1;然后,根据该机构的几何特点和运动约束,通过建立输入参数与动平台输出位姿参数间的约束方程,运用运动学序单开链法原理求解了位置正解的数值解,导出了其位置反解的解析解,用实例验证了位置正、反解的准确性;最后,基于位置反解得到了机构位置工作空间的形状与大小及Z向各截面形状,并基于Jacobian矩阵对机构奇异位形进行了分析。结果表明:该机构比H_4、I4结构简单,在一组相同等效尺寸参数下其工作空间大、转动能力强。

Comparing with the 3-DOF Delta mechanism, the 4-DOF parallel mechanisms which can achieve SCARA motion （i. e. , three translations and one rotation） have their own complex topological structures with coupling degree k = 2, which results in the higher complexity level of solutions for forward kinematics and dynamics. According to the design theory for parallel mechanisms （PMs） based on position and orientation characteristic （POC） equation and the principle for the coupling degree reducing, a novel 4-DOF SCARA type parallel manipulator with lower coupling degree of k = 1 was proposed. Firstly, the structure of the 4-DOF SCARA PM was introduced and the coupling degree of the mechanisms was calculated as being k = 1. Secondly, 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. Meanwhile, rotation ability of the PM was analyzed. Finally, the singularity analysis of the mechanism was also performed based on Jacobian matrix, from which three kinds of singular conditions were obtained. The results showed that the manipulator had a simpler mechanical structure and larger workspace and rotation ability than H4 or Cross-IV under the same set of structural parameters. The research provided a theoretical base for its kinematics and dynamics and optimal design of this manipulator.