(2PRR)~2+R平面并联机构的刚度与固有频率

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。

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

A novel 5-degree-of-freedom (DOF) hybrid serial-parallel manipulator was proposed .The kinematics of Parallel Mechanism (PM ) of the 5-DOF hybrid manipulator was analyzed .The PM is a 3-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 the 3-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 reach 88 .46% and 31 .50% ,respectively ;and the minimum extend ranges of the stiffness along X-axis and the second-order natural frequency reach 52 .34% and 1 .90% ,respectively .Thus ,the stiffness and natural frequency of the planar PM have been obviously improved by adding actuation redundancy .