3T1R并联机构降耦设计与分析

Design and Analysis of Structure Coupling Reduction on Novel 3T1R Parallel Mechanism

根据基于方位特征集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的3T1R运动解耦并联机构。首先,对一种耦合度κ为2的3T1R并联机构进行了结构降耦设计,得到了耦合度较低(κ1=1,κ2=0),但自由度和末端执行件输出运动类型均保持不变的新机型;又对其进行了运动解耦性分析,表明机构具有部分运动解耦;然后,导出了机构位置正、逆解方程和雅可比矩阵;最后,基于雅可比矩阵分析了机构奇异性,并进一步对该并联机构可达工作空间和转动能力进行了分析,得到了机构无奇异工作空间区域。结果表明,降耦机构具有结构简单、无奇异工作空间形状规则、体积大,且全工作空间所有位置的转动能力一致等特点,克服了一般并联机构耦合性强、控制复杂的弱点,具有较好的工业应用前景。

According to the design theory for parallel mechanisms (PMs) based on position and orientation characteristic (POC) equation and the principle for coupling degree reduction, a novel 3T1R PM with lower coupling degree was proposed. Firstly, the structure coupling-reducing optimization design for a kind of 3T1R PM was performed, whose POC and degree of freedom were unchanged with lower coupling degree (κ 1 =1 and κ 2 =0).Moreover, the topological structure and the decoupling characteristic were analyzed and the results showed the motion of the mechanism was partially decoupled. Secondly, the positive and inverse analytic solutions were analyzed, and the singularity analysis was also performed based on Jacobian matrix, from which two singularity-free workspace regions were obtained. Finally, the workspace and rotation capability were also analyzed, which showed that workspace and rotation capability of the coupling reduction PM were enhanced compared with that of the original PM under the same structural parameters. The results showed that the coupling reduction mechanism had good motion-decoupling property, simple mechanical structure, large workspace and remarkable consistent rotational capacity in full workspace, and avoided the shortcomings of bad rotational capacity and strong coupling, which made it a promising prospect in the application of industry.