3-RRS 并联机构的奇异性质研究

doi:10.3901/JME.2023.23.033

机械工程学报 ›› 2023, Vol. 59 ›› Issue (23): 33-45.doi: 10.3901/JME.2023.23.033

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3-RRS 并联机构的奇异性质研究

罗子茂^1,2, 李艳文^1,2, 彭宏鑫^1,2, 霍伟豪^1,2, 陈子明^1,2

1. 燕山大学河北省并联机器人与机电系统实验室秦皇岛 066004;
2. 燕山大学先进锻压成形技术与科学教育部重点实验室秦皇岛 066004

收稿日期:2023-05-29 修回日期:2023-09-15 发布日期:2024-02-20
通讯作者: 李艳文(通信作者)，女，1966年出生，博士，教授。主要研究方向为机器人技术及应用。E-mail：ywl@ysu.edu.cn
作者简介:罗子茂，男，1997年出生。主要研究方向为并联机器人。E-mail：1593838831@qq.com
基金资助:
国家自然科学基金资助项目(52275035)。

Singular Properties Research on 3-RRS Parallel Mechanisms

LUO Zimao^1,2, LI Yanwen^1,2, PENG Hongxin^1,2, HUO Weihao^1,2, CHEN Ziming^1,2

1. Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004;
2. Key Laboratory of Advanced Forging & Stamping Technology and Science, Ministry of Education, Yanshan University, Qinhuangdao 066004

Received:2023-05-29 Revised:2023-09-15 Published:2024-02-20

摘要/Abstract

摘要： 并联机构的奇异是多数并联机构的固有特性，为了防止机构在应用的过程中接近奇异位形，掌握机构的奇异变化规律特别重要。对于3-RRS并联机构，通过建立对应的数学模型，对求得的奇异曲面进行识别，得到了一部分抛物面、锥面和波浪面，然后采用单一变量法研究了机构参数对该机构奇异曲面的影响：当定平台半径R和驱动杆的杆长l1变大时，对应机构空间奇异点的z值会相应增加；动平台的半径r和从动杆的杆长l2增大时则会使奇异点的高度下降；还与3-RPS并联机构进行对比，探究机构本身的变化对奇异曲面的影响。除此之外，基于改进后的G-K方法计算其自由度，基于运动学反解方程遍历其工作空间，在运动分支平面内建立约束关系，从而给出对应机构的运动学反解方程。然后根据螺旋理论，建立分支的运动螺旋系和约束螺旋以及驱动螺旋，构建机构的全雅可比矩阵，利用机构位于奇异位形时的性质得到奇异判别式，给出奇异分布曲面。最后通过搭建该机构的样机模型，采集动平台的位姿数据进行实验，验证理论研究的正确性。

关键词: 3-RRS并联机构, 奇异曲面, 性质识别, 奇异空间

Abstract: The singularity of parallel mechanisms is an inherent characteristic of most parallel mechanisms. In order to prevent the mechanism from approaching singular configurations during application, it is particularly important to grasp the singularity variation laws of the mechanism. For the 3-RRS parallel mechanism, a corresponding mathematical model was established to identify the obtained singular surfaces, obtaining a portion of parabolic, conical, and wavy surfaces. Then, the single variable method was used to study the influence of mechanism parameters on the singular surfaces of the mechanism. When the radius R of the fixed platform and the length l1 of the driving rod increase, the z value of the corresponding spatial singular point of the mechanism will correspondingly increase; When the radius r of the moving platform and the length l2 of the driven rod increase, the height of the singular point will decrease; The research also compared it with the 3-RPS parallel mechanism to explore the impact of changes in the mechanism itself on singular surfaces. In addition, this research calculates its degree of freedom based on the improved G-K method, traverses its workspace based on the inverse kinematics equation, establishes the constraint relationship in the motion branch plane, and gives the inverse kinematics equation of the corresponding mechanism. Then, according to the screw theory, the branch motion screw system, constraint screw and drive screw are established, and the full Jacobian matrix of the mechanism is constructed. The singularity discriminant is obtained by using the properties of the mechanism in the singular configuration, and the singular distribution surface is given. Finally, by building a prototype model of the mechanism and collecting pose data of the moving platform for experiments, the correctness of the theoretical research was verified.

Key words: 3-RRS parallel mechanism, singular surface, property identification, singular space

中图分类号:

TH112

罗子茂, 李艳文, 彭宏鑫, 霍伟豪, 陈子明. 3-RRS 并联机构的奇异性质研究[J]. 机械工程学报, 2023, 59(23): 33-45.

LUO Zimao, LI Yanwen, PENG Hongxin, HUO Weihao, CHEN Ziming. Singular Properties Research on 3-RRS Parallel Mechanisms[J]. Journal of Mechanical Engineering, 2023, 59(23): 33-45.

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3-RRS 并联机构的奇异性质研究

Singular Properties Research on 3-RRS Parallel Mechanisms

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