空间4R球面机构作为转动副的3RPS并联机构运动学分析

Kinematics Analysis of 3RPS Parallel Mechanism with Spatial 4R Spherical Mechanisms as Rotating Pairs

目的设计一种新型3RsPS并联机构,使得机构可以输出3个转动自由度与3个移动自由度耦合的运动。方法根据机构的几何关系,在4R空间机构连杆运动学分析的基础上,建立该机构的运动学方程,使用消元法对其运动学正、逆解进行了求解。使用空间4R机构替换3RPS并联机构的转动副,使得该机构在初始位形下的结构,与3RPS并联机构等效。结果使用Matlab计算得到了运动学方程消元后方程的最高次数,从而得到了运动学正解最多的个数。该机构具有3个自由度,3个移动输出和3个转动输出耦合,机构的运动学正解最多有16个,这与3RPS最多拥有的正解数目一致。结论得到了一种新型的3RsPS机构,该机构的特征为RS副的转动轴线是在空间变化的,该机构的输出为三维移动伴随三维转动,具有此类运动模式的并联机构在不规则形状的产品分拣筛选时,具有一定应用前景。

The work aims to design a new type of 3RsPS parallel mechanism that can output the motion of three rotation freedom degrees coupled with three movement freedom degrees.Based on the geometric relationship of the mechanism and kinematics analysis of the connecting rod of 4R spatial mechanism,the kinematics equation of the mechanism was established.The forward and inverse kinematics solutions of the mechanism were solved by elimination method.The rotating pair of 3RPS parallel mechanism was replaced by 4R spatial mechanism,so that the structure of 3RPS parallel mechanism under the initial configuration was equivalent to that of 3RPS parallel mechanism.The highest number of equations after elimination of kinematics equation was obtained by calculation through MATLAB,and the maximum number of the forward kinematics solution was obtained.The mechanism had three freedom degrees and three movement outputs coupled with three rotation outputs.The maximum forward kinematics solutions of the mechanism were 16,consistent with the number of positive kinematics solutions of 3RPS.A new type of 3RsPS mechanism is obtained.The feature of the mechanism is that the rotation axis of Rs pair changes in space,and the output of the mechanism is three-dimensional movement accompanied by three-dimensional rotation.The motion characteristics of the mechanism have certain application value in the field of efficient packaging sorting and screening.