具有解析式位置正解的2T1R并联机构运动性能分析

求解具有解析式位置正解且部分运动解耦的并联机构,有利于后续的误差分析、动力学分析、运动轨迹规划与控制等。基于方位特征方程(POC)的并联机构设计理论与方法,设计了两种具有解析式位置正解且部分运动解耦的2T1R并联机构,并对这两种机构进行了方位特征、自由度及耦合度等主要拓扑性能分析;提出基于拓扑特征的运动学建模与求解方法,并据此求解了两种机构的解析式位置正解;基于导出的位置反解,分析了两种机构工作空间、奇异位形、动平台的速度与加速度变化规律。最后比较了两种机构的运动性能,选择了优选机型。为优选机型的动力学分析与样机研制提供了理论基础。

2T1R Parallel Mechanism with Analytic Positive Position Solutions and Its Kinematic Performance Based Optimization

The parallel mechanisms with analytic positive position solution and partial motion decoupling are of great benefit to subsequent research such as error analysis, workspace solution, singularity analysis and stiffness analysis, dynamic performance analysis, motion trajectory planning and control. Firstly, a class of two 2T1R parallel mechanisms with analytic positive position solutions and partial motion decoupling were proposed according to the design theory and method of parallel mechanism (PM) based on position and orientation characteristics equation (POC). The main topological performance, including position and orientation characteristics, degree of freedom and coupling degree calculation, was performed. Secondly, according to the method for kinematics modeling based on topological characteristics by the author, the analytic positive solution of one of the PMs was solved in detail. Then, based on the derived position inverse solution, the workspace, singular configuration, velocity and acceleration variation of the PM were analyzed. Finally, the difference between the two PMs in the above various performance indexes was compared and analyzed. Based on this, the preferred PM was selected. Because of its simple structure, good kinematics and dynamic performance, it had potential applications in the manufacturing, which was especially suitable for handling, grabbing, loading and unloading of workpieces with large length in the longitudinal direction. The research result laid a theoretical foundation for the dynamic analysis and prototype development of the preferred PM.