含间隙冗余混联机构高精度刚度建模方法

doi:10.3901/JME.2025.11.072

机械工程学报 ›› 2025, Vol. 61 ›› Issue (11): 72-85.doi: 10.3901/JME.2025.11.072

• 机器人及机构学 • 上一篇

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含间隙冗余混联机构高精度刚度建模方法

王森^1,2, 宋敬伟^1,2, 李浩然^1,2, 李仕华^1,2

1. 燕山大学河北省并联机器人与机电系统重点实验室秦皇岛 066004;
2. 燕山大学机械工程学院秦皇岛 066004

收稿日期:2024-01-30 修回日期:2025-02-12 发布日期:2025-07-12
作者简介:王森，男，1995年出生，博士后。主要研究方向为并联机器人技术及理论。E-mail：senwang@hit.edu.cn;李仕华(通信作者)，男，1966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技术及理论。E-mail：shli@ysu.edu.cn
基金资助:
国家自然科学基金(52275032)、河北省自然科学基金(E2022203077)、河北省重点研发项目(22371801D)和中央政府引导地方科技发展基金(246Z1818G)资助项目。

High Accuracy Stiffness Modeling Method for Hybrid Mechanism with Clearance and Redundant Drive

WANG Sen^1,2, SONG Jingwei^1,2, LI Haoran^1,2, LI Shihua^1,2

1. Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004;
2. College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004

Received:2024-01-30 Revised:2025-02-12 Published:2025-07-12

摘要/Abstract

摘要： 针对现有混联机构刚度模型考虑因素不全面，缺乏统一的刚度模型，提出了考虑驱动刚度、杆件变形、冗余驱动和铰链间隙的混联机构静刚度建模方法，建立了全局静刚度模型。首先，提出了具有高刚度的混联机构新构型，并推导出了机构各支链约束力。考虑驱动刚度和杆件变形，基于柔度矩阵叠加法，得到理想铰链时混联机构的整体刚度矩阵。然后，提出含铰链间隙支链偏移量判别准则，根据各支链所受约束力分析含铰链间隙的支链偏移情况，基于虚功原理，建立铰链间隙与机构末端变形的映射关系。通过蒙特卡洛法解决由支链约束力耦合引起的间隙铰链偏移值建模误差问题，得到了机构末端刚度分布图。最后，以4CPR-PPP/2UPR-RR-2RPU+R含间隙混联机构为例，通过有限元对该机构进行刚度仿真，研究结果表明，提出的高精度刚度建模方法是正确的，对应用于重载领域的含间隙混联机构的刚度预测具有重要意义。

关键词: 混联机构, 刚度, 铰链间隙, 柔度矩阵, 概率统计模拟

Abstract: In response to the incomplete consideration of factors and the lack of a unified stiffness model in the existing stiffness models of hybrid mechanisms, this paper proposes a static stiffness modeling method for hybrid mechanisms that considers driving stiffness, rod deformation, redundant driving, and hinge clearance, and establishes a global static stiffness model. Firstly, a new configuration of a hybrid mechanism with high stiffness was proposed, and the constraint forces of each branch chain of the mechanism were derived. Considering the driving stiffness and rod deformation, based on the flexibility matrix superposition method, the overall stiffness matrix of the hybrid mechanism with ideal hinges is obtained. Then, a criterion for determining the offset of branch chains with hinge gaps is proposed. Based on the constraint force on each branch chain, the offset of branch chains with hinge clearances is analyzed. Based on the principle of virtual work, a mapping relationship between hinge clearances and the end deformation of the mechanism is established. The Monte Carlo method was used to solve the modeling error problem of hinge clearance offset caused by the coupling of branch chain constraints, and the stiffness distribution map of the mechanism's end effector was obtained. Finally, taking the 4CPR-PPP/2UPR-RR-2RPU+R hybrid mechanism with clearances as an example, the stiffness simulation of the mechanism was carried out through finite element analysis. The research results show that the high-precision stiffness modeling method proposed in this paper is correct, and it is of great significance for predicting the stiffness of the hybrid mechanism with clearances used in the heavy-duty field.

Key words: hybrid mechanism, stiffness, hinge clearance, compliance matrix, probabilistic statistical simulation

中图分类号:

TH112

王森, 宋敬伟, 李浩然, 李仕华. 含间隙冗余混联机构高精度刚度建模方法[J]. 机械工程学报, 2025, 61(11): 72-85.

WANG Sen, SONG Jingwei, LI Haoran, LI Shihua. High Accuracy Stiffness Modeling Method for Hybrid Mechanism with Clearance and Redundant Drive[J]. Journal of Mechanical Engineering, 2025, 61(11): 72-85.

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含间隙冗余混联机构高精度刚度建模方法

High Accuracy Stiffness Modeling Method for Hybrid Mechanism with Clearance and Redundant Drive

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