基于固有频率的运动冗余并联机构位置逆解优选方法

doi:10.3901/JME.2024.13.297

机械工程学报 ›› 2024, Vol. 60 ›› Issue (13): 297-307.doi: 10.3901/JME.2024.13.297

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基于固有频率的运动冗余并联机构位置逆解优选方法

吴震^1,2, 李秦川¹, 叶伟¹

1. 浙江理工大学机械工程学院杭州 310018;
2. 浙江交通职业技术学院杭州 311112

收稿日期:2023-10-09 修回日期:2024-01-19 出版日期:2024-07-05 发布日期:2024-08-24
作者简介:吴震,男,1991年出生,博士研究生。主要研究方向为运动冗余并联机器人设计、建模与应用。E-mail:wuzhen@zjvtit.edu.cn;李秦川,男,1975年出生,博士,教授,博士研究生导师。主要研究方向为并联机器人机构学与应用技术。E-mail:lqchuan@zstu.edu.cn;叶伟(通信作者),男,1988年出生,博士,副教授,硕士研究生导师。主要研究方向为并联机器人机构学。E-mail:wye@zstu.edu.cn
基金资助:
国家自然科学基金资助项目(52275036)。

Inverse Position Optimization Method of Kinematically Redundant Parallel Mechanisms Based on Natural Frequency

WU Zhen^1,2, LI Qinchuan¹, YE Wei¹

1. School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018;
2. Zhejiang Institute of Communications, Hangzhou 311112

Received:2023-10-09 Revised:2024-01-19 Online:2024-07-05 Published:2024-08-24

摘要/Abstract

摘要： 运动冗余并联机构在规避奇异、增大工作空间、提升机构性能等方面具有显著优势，但运动冗余并联机构位置逆解不唯一，需要考虑性能指标进行优选。提出一种运动冗余并联机构位置逆解优选新方法。首先，基于闭环矢量法和全局独立广义位移坐标法，对运动冗余并联机构进行运动学和弹性动力学建模。其次，选用机构的第一阶固有频率(基频)为弹性动力学性能指标，对于动平台某个确定的输出位姿，运用粒子群优化算法，根据基频最大得到运动冗余并联机构的最优位置逆解。然后，利用多项式拟合技术，建立最优位置逆解与动平台输出位姿参数的响应面映射模型，获得动平台在不同输出位姿下的最优位置逆解。最后，以运动冗余2PUPR-PRPU并联机构(P：移动副，U：虎克铰，R：转动副)为例应用了所提的方法，通过位置逆解优选前后机构的基频对比证明该方法的有效性。

关键词: 并联机构, 运动冗余, 位置逆解优选, 固有频率

Abstract: Kinematically redundant parallel mechanisms (KR-PMs) have significant advantages in avoiding singularity, increasing workspace, improving mechanism performance and so on, but it is difficult to obtain their optimal inverse position solutions. Thus, a new inverse position optimization method of KR-PMs is proposed. Firstly, based on the closed-loop vector method and global independent generalized displacement coordinate method, the kinematic and elastodynamic models of KR-PMs are established. Secondly, the first order natural frequency (fundamental frequency) of the KR-PM is chosen as the elastodynamic performance index. For a given output pose of the moving platform, the optimal inverse position with maximum fundamental frequency is determined based on particle swarm optimization algorithm. Then, using the polynomial fitting technology, a response surface mapping between the optimal inverse position solutions and the output pose parameters of the moving platform is established, which obtains the optimal inverse position solutions of KR-PMs under different output pose parameters. Finally, the 2PUPR-PRPU KR-PM (where P denotes a prismatic joint, U denotes a universal joint, and R denotes a revolute joint) is taken as an example to implement the proposed method. The effectiveness of the method is demonstrated by comparing the fundamental frequency of the mechanism before and after optimization.

Key words: parallel mechanism, kinematically redundant, inverse position optimization, natural frequency

中图分类号:

TH112

吴震, 李秦川, 叶伟. 基于固有频率的运动冗余并联机构位置逆解优选方法[J]. 机械工程学报, 2024, 60(13): 297-307.

WU Zhen, LI Qinchuan, YE Wei. Inverse Position Optimization Method of Kinematically Redundant Parallel Mechanisms Based on Natural Frequency[J]. Journal of Mechanical Engineering, 2024, 60(13): 297-307.

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基于固有频率的运动冗余并联机构位置逆解优选方法

Inverse Position Optimization Method of Kinematically Redundant Parallel Mechanisms Based on Natural Frequency

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