6—SPS机构位姿矩阵采用四元数法描述，并把该矩阵和矢量坐标扩展为4维形式，推导出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 和 ；在此基础上，利用连续接触模型得到了两个含间隙S副共连杆和异杆时机构的运动系数矩阵。分别把各个运动系数的行列式展开，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；在两类奇异轨迹中，当S副异杆时，机构间隙的影响均大于S副共连杆时的影响。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，发现存在一个关于参考点的奇异域。
Abstract
The pose matrix of 6-SPS mechanism is described by quaternion method, where the matrix and vector coordinates are expanded to the 4-dimensional form to derive the motion equations of mechanism without clearance. Then, the novel kinematic Jacobi matrixes JA and JB of the mechanism are achieved. On this basis, the movement coefficient matrixes of two S-pairs co-linkage and different-linkage mechanism are derived through continuous contact model. Each determinant of movement coefficients is expanded respectively. Subsequently, the trajectory equations containing the first category of singular and the second category of singular of clearance mechanism are derived separately. Using MATLAB software, the three-dimensional track surface of the first category of and the second category of pose-attitude singular trajectories at a given location of the mechanism is obtained. The comparison between two types of singularity trajectory surfaces containing the clearance mechanism highlights that the influence of mechanism clearance on the second category of singular is greater than the first category. Among the two types of singularity tracks, the influence of mechanism clearance in different-linkage S pairs is greater than that in co-linkage S pairs. The singular points on the trajectory surface of mechanism without clearance are considered as reference points. Comparing the singular points with each other on the singularity trajectory surface containing clearance mechanism corresponding to the reference points, a singular area about the reference point can be found.
关键词
四元数 /
奇异位形 /
含间隙并联机构 /
雅克比矩阵 /
奇异域
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Key words
quaternion ;singularity /
parallel mechanism with clearance /
Jacobi matrix /
singular area
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