具有耦合分支的两转动两移动并联机构分析与优化

Analysis and Optimization of 2R2T Parallel Mechanism with Coupling Kinematic Chain

摘要:

提出了具有耦合分支的两转动两移动并联机构。基于李群理论分析了机构自由度，该机构动平台能输出两个转动运动和两个移动运动；采用闭环矢量法对机构进行了位置分析，求得位置反解；通过速度分析得到机构的雅可比矩阵，在雅可比矩阵基础上对机构的奇异位形进行了分析；采用虚功原理建立了机构的刚度模型，并进行了刚度性能分析；为消除内部奇异产生的刚度退化，在机构上增加了冗余驱动分支，并对添加冗余驱动分支前后机构的刚度、工作空间等性能进行了对比分析。以工作空间内刚度平均值为目标对冗余驱动机构进行了尺度优化设计，结果表明，优化后的冗余驱动机构的刚度性能得到明显提升。

Abstract:

A parallel mechanism with coupling kinematic chain was proposed. The moving platform of the parallel manipulator with two rotations and two translations was connected to the fixed base through three kinematic limbs. Mobility of the parallel mechanism was analyzed based on Lie group theory. The moving platform of the mechanism can output two rotations and two translations. Position analysis was conducted through closed-loop vector approach, and inverse position solutions were obtained. The mechanism had two positive singular cases. Singularity analysis was conducted based on Jacobian matrix. Jacobian matrix of the mechanism was derived based on velocity analysis. Singularity analysis was carried out according to the rank reduction conditions of the Jacobian matrix. Workspace and singularity curves were analyzed. The principle of virtual work was used to establish stiffness model for the mechanism, and stiffness performance evaluation was conducted. To avoid stiffness degeneration caused by internal singularities, a redundant limb was added to the mechanism. Performance comparison in terms of stiffness and workspace between the mechanisms with and without redundant limb was carried out. Optimal design of the redundantly actuated mechanism was conducted to improve the average stiffness throughout its workspace. The variation law of the optimized target with the scale parameters can be obtained through numerical calculation. The results show that the stiffness performance of the optimized redundantly actuated mechanism is significantly improved.