3-PRR柔性微动平台的运动建模与工作空间分析

Motion Modeling and Workspace Analysis of a 3-PRR Flexible Micro Motion Platform

基于3-PRR型柔性并联微动平台较3-RRR型更适合直线驱动,提出了一种含不同类型柔铰的3-PRR柔性微动平台最简型式,整体结构形式由3组呈120°对称均布的柔性运动支链构成。针对伪刚体模型法的不足,运用卡氏第二定理,根据不同柔铰的刚度模型和力传递关系建立柔性支链的刚度模型,基于刚度叠加原理得到以柔铰刚度为自变量的系统刚度模型,建立了微动平台封闭型整体运动模型。通过分析结构参数对雅克比矩阵的影响,选取了最佳结构参数。通过建立约束条件,将原平台的工作空间与最佳结构参数时的工作空间进行对比,验证了最佳结构参数选取的正确性。通过有限元法与理论模型计算结果之间的分析比较,模型的运动误差在可控范围之内,说明了该模型的正确性。

Based on the 3-PRR compliant parallel micro motion platform than the 3-RRR type is more suit- able for linear drive, and a 3-PRR compliant micro displacement platform with different types of flexure hin- ges is proposed. The structure form of the micro motion platform is composed of 3 groups of flexible motion branched chains with 120 degree symmetrical uniform distribution, aiming at the deficiency of the method of pseudo rigid body model at present , using the castigliano＇s second theorem . Combining the compliance e- quations of flexure hinge with the force transmission relations of mechanisms , the stiffness model of each sub-chain was obtained and the stiffness of the entire system which took the hinge flexibility as the independ- ent variables was obtained. The closed form of the micro motion platform was established. Through the a- nalysis of the influence of structure parameters on the Jacobian matrix, the optimum structural parameters were selected. By establishing the constraint conditions and comparing the working space between the origi- nal platform and the optimal structure parameters, which verifies the correctness of the selection of the opti- mal structural parameters. By comparing the kinematic model between theoretical analysis and FEA, the re- sults show that the model motion error within the controllable range, which illustrates that the model is cor- rect.