(2PRR)~2+R平面并联机构的刚度与固有频率  

Stiffness and natural frequency of a(2PRR)~2+R planar parallel mechanism

作　　者：张东胜[1] 许允斗[1,2] 姚建涛[1,2] 赵永生[1,2] ZHANG Dong-sheng;XU Yun-dou;YAO Jian-tao;ZHAO Yong-sheng(Parallel Robot and Mechatronic System Laboratory of Hebei Province,Yanshan University, Qinhuangdao 066004, China;Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education,Yanshan University, Qinhuangdao 066004, China)

机构地区：[1]燕山大学河北省并联机器人与机电系统实验室,河北秦皇岛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,河北秦皇岛066004

出　　处：《光学精密工程》2017年第11期2904-2913,共10页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.51405425);河北省重点基础研究资助项目(No.15961805D);河北省研究生创新资助项目(No.2016SJBS001);河北省自然科学基金资助项目(No.E2017203387)

摘　　要：基于两移动一转动三自由度平面并联机构构造了一种新型五自由度串并混联机器人并对其并联部分,一具有运动冗余和驱动冗余两种不同模式的平面并联机构(2PRR)~2+R进行了运动学分析。首先,建立了三自由度平面并联机构的运动学模型,基于机构的运动学模型推导得到了冗余和非冗余驱动并联机构的刚度矩阵,并且通过求取并联机构各组成构件的等效质量,得到并联机构的质量矩阵;然后,借助系统刚度矩阵和质量矩阵建立的并联机构动力学方程,求得了机构的固有频率方程;最后,通过数值仿真对冗余和非冗余驱动并联机构的刚度及固有频率进行对比分析。结果显示:冗余驱动分支对机构绕Z轴方向角刚度和系统的一阶固有频率均值影响最大,其增幅分别为88.46%和31.50%;对X轴方向的线刚度和系统的二阶固有频率均值影响最小,其增幅分别为52.34%和1.90%。因此,冗余驱动分支有助于提高并联机构的整体刚度,改善机构的动态性能。A novel5-degree-of-freedom(DOF)hybrid serial-parallel manipulator was proposed.The kinematics of Parallel Mechanism(PM)of the5-DOF hybrid manipulator was analyzed.The PM is a3-DOF(one translational DOF and two rotational DOFs)metamorphic planar PM(2PRR)2+R with two different types of configurations:actuation redundancy and kinematic redundancy.Firstly,the kinematics model of the3-DOF planar PM was established.Then,the stiffness matrix of the planar PM was obtained on the basis of kinematics analysis and the mass matrix was obtained by solving each equivalent component mass of the planar PM.Furthermore,the system dynamic equation was established through combining the stiffness matrix and mass matrix,and the natural frequency equation was obtained incidentally based on the dynamic equation.Finally,the stiffnesses and natural frequencies for the redundant and non redundant planar PMs were analyzed and compared by numerical simulation.The results show that the maximum extend ranges of the stiffness around Z-axis and the first order natural frequency reach88.46%and31.50%,respectively;and the minimum extend ranges of the stiffness along X-axis and the second order natural frequency reach52.34%and1.90%,respectively.Thus,the stiffness and natural frequency of the planar PM have been obviously improved by adding actuation redundancy.

关 键 词：平面并联机构 运动冗余 驱动冗余 刚度 固有频率 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]