一种运动部分解耦的2R2T并联机构运动学与性能分析

Kinematics and Performance Analysis of 2R2T Parallel Manipulator with Partially Decoupled Motion

摘要:

提出了一种新型四分支并联机构。采用李群理论对机构进行了自由度分析，该机构能输出两转动两移动运动，可由与机架相邻的移动副驱动。研究了机构的位置模型，推导得到了位置反解和正解的表达式，分析了机构的运动部分解耦特性。求解了机构的雅可比矩阵，基于雅可比矩阵行列式讨论了其奇异位形。绘制了机构的工作空间及内部奇异分布，机构的奇异分布在工作空间边缘，具有很大的转动能力。机构在中间位置两个方向的转角范围分别可达-44°~60°和-35°~52°。对机构进行了运动/力传递性能分析，得到了工作空间内的性能分布情况，以全域传递指标为目标对机构进行了尺度优化。

Abstract:

A novel parallel manipulator with two rotations and two translations was proposed. The moving platform of the parallel manipulator was connected to the fixed base through four kinematic limbs. Four prismatic joints can be used as actuations to fully control the motion of manipulator. The mobility and motion characteristic of the manipulator were analyzed by using Lie Group theory. Position model of the parallel manipulator was established. Inverse and forward position solutions were analyzed. It was demonstrated that the analytical expressions can be obtained for the inverse and forward position solutions. Partially decoupled motion characteristic of the manipulator was analyzed. Position of the moving platform can be determined by two limbs. Singularity analysis was conducted based on Jacobian matrix. Singular configurations, including inverse kinematic singularity, forward kinematic singularity and combined singularity were analyzed. Workspace and singularity curves were determined. It was found that the singularities located near the boundary of the workspace and the parallel manipulator had relatively high rotational capability. The rotational ranges in two directions were -44°~60° and -35°~52°, respectively. Performance analysis was carried out by using the method of motion/force transmission. Performance distribution over the orientation workspace was sketched. Global performance index was used in optimal design of the manipulator. The proposed parallel manipulator can be used in many fields such as five axis machine and motion simulator.