3PRRR并联机构性能评估与尺度综合

doi:10.3901/JME.260409

摘要/Abstract

摘要： 为了解决并联机构多闭环多约束特征带来的动力学和刚度建模困难，提出了一种同时适用于预设计阶段与样机设计阶段的并联机构弹性动力学与刚度建模一体化方法。该模型首先基于矩阵结构分析方法建立每一个离散体的单元刚度和质量矩阵，然后结合多点约束理论与机构约束方程提取机构全局坐标系下的全局独立广义位移坐标，结合拉格朗日方程建立机构的弹性动力学方程，结合静态缩聚技术建立反应出口节点的静刚度模型。基于拉格朗日方程和整体刚度矩阵建立反映机构刚度极值与各向同性的椭球指标，采用多目标遗传算法建立多目标优化问题的Pareto前沿，进一步结合合作平衡点方法确定最优解，在此基础上开展并联机构样机设计，借助有限元软件提取涉及非规则横截面的零部件的刚度和质量矩阵，并替换预设计阶段梁单元刚度和质量矩阵，实现3PRRR并联机构三维模型性能的快速评估。提出的弹性动力学与刚度一体化模型与有限元仿真软件的最大误差在1.48%之内，优化前后机构的基频、线刚度与角刚度各向同性指标分别提升了2.3%、19.05%与43.75%，最后基于螺旋理论开展的连杆横截面的合理设计进一步提高了机构的性能指标，验证了本文模型的正确性与有效性。

关键词: 并联机构, 弹性动力学, 刚度建模, 性能评价, 尺度综合

Abstract: To solve the dynamics and stiffness modeling difficulties caused by the multi-closed loop and multi-constraint characteristics of parallel mechanisms (PMs), an integrated method of elastodynamic and stiffness modeling for PMs that is applicable to both the pre-design and the prototype design stages is proposed. The model first establishes the element stiffness and mass matrices of each free body based on the matrix structure analysis method, and then extracts the global independent generalized displacement coordinates of the mechanism in the global coordinate system by combining multi-point constraint theory and kinematic constraint equations. The elastodynamic equation of the mechanism is established through Lagrange equation, and the elastostatic stiffness model corresponding to the exit node is established through static condensation technology. Based on the Lagrange equation and overall stiffness matrix, an ellipsoid index for the extreme stiffness and isotropy of the mechanism is established. A multi-objective genetic algorithm is used to establish the Pareto front of the multi-objective optimization problem. Further, the cooperative equilibrium point method is combined to determine a set of optimal solutions on the Pareto front. On this basis, the prototype of the 3PRRR PM is designed. The stiffness and mass matrices of components involving irregular cross-sections are extracted using finite element software to replace those of beam elements in the pre-design stage to achieve rapid performance evaluation of the three-dimensional model of the 3PRRR PM. The maximum error between the proposed theoretical model and the finite element model is within 1.48%. The performance comparison of the mechanism before and after optimization shows that the fundamental frequency, isotropic of the linear stiffness and angular stiffness have been improved by 2.3%, 19.05%, and 43.75%, respectively. The reasonable cross-section design of the links based on the screw theory further improves the performance indices of the mechanism, verifying the correctness and effectiveness of the model proposed in this work.

Key words: parallel manipulator, elastodynamic, stiffness modeling, performance evaluation, dimensional synthesis

中图分类号:

TG156

祝高永, 鹿业波, 张玲玲, 叶伟, 杨超. 3PRRR并联机构性能评估与尺度综合[J]. 机械工程学报, 2026, 62(9): 88-103.

ZHU Gaoyong, LU Yebo, ZHANG Lingling, YE Wei, YANG Chao. Performance Evaluation and Dimensional Synthesis of a 3PRRR Parallel Manipulator[J]. Journal of Mechanical Engineering, 2026, 62(9): 88-103.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I9/88

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