2UPR-RPS型并联机构精度设计

Accuracy Design of 2UPR-RPS Parallel Mechanism

摘要:

几何误差对并联机构末端位姿精度产生重要影响。为揭示几何误差对并联机构末端位姿精度的影响规律，并据此确定其最优区间，以2UPR-RPS型并联机构为例，进行过约束并联机构的精度设计。采用一阶摄动法建立该并联机构的几何误差模型，获得对末端位姿误差有影响的几何误差源。利用区间分析理论建立末端位姿精度关于几何误差源的灵敏度指标，通过灵敏度分析揭示几何误差源对末端位姿精度的影响程度。以灵敏度指标作为权重建立精度综合模型，采用均匀设计法确定在任务空间内精度综合的位姿点，推导各几何误差源的最优区间，并据此制定关键零部件的精度等级及配合公差。采用Sobol序列的拟蒙特卡洛法预估该并联机构的末端位姿精度，仿真结果表明，经过精度综合得到的几何误差区间数满足预设的末端位姿精度要求，从而验证了该精度设计方法的可行性。

关键词:并联机构;误差模型;灵敏度分析;精度设计

Abstract:

Geometric errors have an important effect on the pose accuracy of the parallel mechanism (PM). In order to reveal the influences of geometric error sources on the pose accuracy of the parallel mechanism and determine its optimal intervals, a 2UPR-RPS parallel mechanism was taken as an example to demonstrate the accuracy design of overconstrained PMs. An error mapping model of the parallel mechanism was established by using the firstorder perturbation method, based on which the geometric error sources that affected pose accuracy of the endeffector were obtained. The set of sensitivity index of the geometric error sources was formulated with the interval analysis theory and the sensitivity analysis was carried out to reveal the influence of the geometric error sources on the pose accuracy of the endeffector. Based upon the proposed sensitivity index, a accuracy synthesis model of the geometric error sources was established, in which the uniform design method was used to provide appropriate pose points within the workspace of the parallel mechanism. The optimal intervals of the geometric error sources of the parallel mechanism were derived and the accuracy class and the fitting tolerances of key components of the parallel mechanism were determined. The Pseudo Monte Carlo method of Sobol sequence was used to estimate the pose accuracy of the endeffector of the parallel mechanism. The simulation results showed that the optimal intervals of the geometric error sources obtained by accuracy synthesis met the accuracy requirements of the endeffector, confirming the feasibility of the accuracy design and providing a reference for the development of physical prototype.

Key words:parallel mechanism;error model;sensitivity analysis;accuracy design