具有连续转轴的3-RSR并联机构及其运动学分析

3-RSR parallel mechanism with continuous rotational axes and its kinematic analysis

对一种新结构3-RSR并联机构的连续转轴问题进行了深入研究;根据螺旋理论对机构进行了自由度分析,说明该机构具有2个转动自由度和1个移动自由度;采用单叶双曲面的数学理论简单、直观地推导了定动平台的对称关系,证明了该机构具有以对称平面内任意直线为转轴进行连续转动,并沿对称平面法线方向进行连续移动的特性,便于对机构进行运动学标定和轨迹规划;根据机构的几何特性,利用对称平面的法向量来描述该机构的姿态矩阵,使其位置反解过程变得简单、新颖。基于该机构,提出了一种空间二维指向机构的新构型,可应用于雷达姿态调整机构等。

This article conducts an in-depth study on the continuous axe of a new 3-RSR parallel mechanism.Based on the screw theory,degree of freedom(DOFs)is analyzed,which indicates that the mechanism has two rotational DOFs and one translational DOFs.The symmetric relationship between the fixed platform and the moving platform is identified briefly with the aid of the mathematical theory of uniparted hyperboloid;it proves that the mechanism can rotate continuously with any axis located in the symmetric plane and move continuously along the normal direction of the symmetric plane,which is convenient for kinematic demarcating and trajectory planning.According to the mechanism’s geometric characteristics,the attitude matrix is described by means of the normal vector of the symmetric plane,which makes the inverse solution simple and novel.Based on this mechanism,a new configuration of the spatial two-dimension directing mechanism is proposed,which can be applied in many mechanisms,for instance,radar-attitude adjusting mechanism.