Abstract

This work investigates the stiffness characteristics of a planar parallel manipulator with variable platforms. The stiffness model is established with shape variables of the base and mobile platforms based on the Jacobian matrix. By virtue of a nondimensionalization of the inhomogeneous stiffness matrix, two homogeneous submatrices are obtained. Upon which, two kinds of performance indices are derived to evaluate the manipulator’s stiffness behaviors, one for translation and the other for rotation. Stiffness performance of the considered manipulator with three types of platforms, namely variable base platform, variable mobile platform and both variable base and mobile platforms, is analyzed. To validate the stiffness models, the established analytical models are compared with the FEA based evaluations. In order to find the configurations with the best global stiffness performance, stiffness optimization with consideration of shape variables is conducted with the particle swarm optimization algorithm. Finally, a case study of platforms’ shape changing in stiffness adjustment is presented.

摘要

这项工作研究了具有可变平台的平面并联机械手的刚度特性。基于雅可比矩阵，利用基础平台和移动平台的形状变量建立刚度模型。通过非齐次刚度矩阵的无量纲化，获得了两个齐次子矩阵。在此基础上，推导出两种性能指标来评估机械手的刚度行为，一种用于平移，另一种用于旋转。分析了所考虑的具有三种类型平台的机械手的刚度性能，即可变底座平台、可变移动平台和可变底座和移动平台。为了验证刚度模型，将已建立的分析模型与基于 FEA 的评估进行比较。为了找到具有最佳全局刚度性能的配置，使用粒子群优化算法进行考虑形状变量的刚度优化。最后，给出了刚度调整中平台形状变化的案例研究。