3-PUU并联机构的运动学分析与验证  

Kinematics analysis and validation of 3-PUU parallel mechanism

作　　者：陈明方[1] 黄良恩 张永霞 姚国一 CHEN Mingfang;HUANG Liangen;ZHANG Yongxia;YAO Guoyi(Faculty of Mechanical and Electrical Engineering,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学机电工程学院,云南昆明650500

出　　处：《工程设计学报》2023年第6期763-778,共16页Chinese Journal of Engineering Design

基　　金：国家自然科学基金资助项目(51965029);国家重点研发计划项目(2018YFB1306103)。

摘　　要：为提升少自由度并联机构设计的效率和准确性,针对自主设计的3-PUU并联机构进行了理论分析和实验研究。首先,利用螺旋理论和修正的Kutzbach-Grubler公式分析了并联机构的自由度;同时,解算了并联机构的运动学正反解和雅可比矩阵,并基于雅可比矩阵分析了其约束奇异和运动奇异。然后,利用极限边界搜索法分析了并联机构的工作空间,并以雅可比矩阵条件数的倒数作为局部灵巧度来构造全局灵巧度,分析了并联机构的运动性能。接着,搭建了并联机构的ADAMS/Simulink联合仿真模型,基于给定的动平台运动方程,通过仿真得到了动平台位置的仿真曲线及误差曲线。最后,利用并联机构样机、PC(personal computer,个人计算机)、STM32单片机、伺服电机及激光跟踪仪搭建了实验平台,并测定了并联机构动平台的位置曲线。结果表明,该并联机构具有较大的可达工作空间且其运动性能较好;通过对比理论结果与仿真结果可知,所构建的并联机构运动学模型正确;动平台位置的实测值与理论值之间存在一定误差,主要原因是并联机构存在机械误差以及控制系统精度不足,但实测曲线与理论曲线的变化趋势基本一致,进一步验证了并联机构运动学模型的正确性。研究结果可为少自由度并联机构的设计提供参考。In order to improve the efficiency and accuracy of the design of parallel mechanisms with few degrees of freedom,the theoretical analysis and experimental research were conducted on a selfdesigned 3-PUU parallel mechanism.Firstly,the degree of freedom of the parallel mechanism was analyzed by using the screw theory and the modified Kutzbach-Grubler formula.At the same time,the forward and inverse kinematics solutions and Jacobian matrix of the parallel mechanism were solved,and its constraint singularity and kinematic singularity were analyzed based on the Jacobian matrix.Then,the workspace of the parallel mechanism was analyzed by using the limit boundary search method,and the global dexterity was constructed by taking the reciprocal of Jacobian matrix condition number as the local dexterity,so as to analyze the kinematic performance of the parallel mechanism.Next,an ADAMS/Simulink co-simulation model of the parallel mechanism was built.Based on the given motion equation of the moving platform,the simulation curves and error curves of the moving platform position were obtained through simulation.Finally,the experimental platform was built by using the parallel mechanism prototype,PC(personal computer),STM32 microcontroller,servo motor and laser tracker,and the position curves of the moving platform were measured.The results showed that the parallel mechanism had a large reachable workspace and good kinematic performance.By comparing theoretical results with simulation results,it could be concluded that the constructed kinematics model of the parallel mechanism was correct.There were some errors between the measured and theoretical values of the moving platform position,mainly due to the mechanical errors of the parallel mechanism and the insufficient precision of the control system.However,the variation trends of the measured curve and the theoretical curve were basically consistent,which further verified the correctness of the kinematics model of the parallel mechanism.The research results can provide reference

关 键 词：3-PUU并联机构 运动学分析 奇异性 工作空间 灵巧度 ADAMS/Simulink仿真 

分 类 号：TH122[机械工程—机械设计及理论] TP242.2[自动化与计算机技术—检测技术与自动化装置]