含S副间隙6-SPS机构奇异性分析

Singularity Analysis of 6-SPS Parallel Mechanism with Clearance in S Pair

采用四元数法描述6—SPS机构位姿矩阵,并把该矩阵和矢量坐标扩展为4维形式,通过推导无间隙机构的运动方程,得到了机构运动的新型雅克比矩阵JA和JB;在此基础上,利用连续接触模型得到了含间隙6—SPS机构的运动系数矩阵J_(AS)和J_(BS)。分别把J_(AS)和J_(BS)的行列式展开,得到含间隙机构第一类奇异和第二类奇异的轨迹方程,利用MATLAB得到了机构在给定位置时的第一类位姿奇异轨迹和第二类位姿奇异三维轨迹曲面。通过把两类含间隙机构奇异轨迹曲面的比较,发现机构间隙对第二类奇异的影响大于对第一类奇异的影响;以无间隙机构奇异轨迹曲面上奇异点作为参考点,通过含间隙机构奇异轨迹曲面上与参考点相对应奇异点的相互比较,发现在参考点附近存在一个关于参考点的奇异域。

The matrix of the 6-SPS parallel mechanism was described by quaternion,and both the rotation matrix and the coordinates of the vectors are expanded to 4—dimensions. And the kinematical equations was obtained in it. The variable quantities of the equations was derivatived so that the novel Jacobian matrix JAand JBwas derived. On this basis,the JASand the JBSof the 6-SPS parallel mechanism with clearance was got through continuous contact model. Determinants of the JASand the JBSwas carried out,so that both the trajectory of the first singularity and the trajectory of the second singularity was obtained.when the location of the mechanism was given,their curved surfaces was obtained by the program of MATLAB. A comparison of the trajectory of the first singularity and the trajectory of the second singularity indicates that the effects of the parallel mechanism＇s clearance in the second singularity was more than in the first singularity;And when the point in the trajectory of the singularity of parallel mechanism without clearance was regarded as the reference point,a comparison of the corresponding points about the reference point of the trajectory of the parallel mechanism with clearance indicates that there is a singularity region near the reference point.