关键词: Sterwart平台, 并联机构, 奇异性, 四元数, 雅可比矩阵

Abstract: A new method for singularity analysis of the Stewart parallel mechanisms with planar platforms is presented. The rotation matrix is described by quaternion, and both the rotation matrix and the coordinates of the vectors are expanded to four dimensions. Through analyzing the coupling relationships between position variables and orientation variables, properties of quaternion, motion equations expressed by eight quadratic equations are obtained. From the motion equations a new kind of Jacobian matrix of the Stewart parallel mechanism is derived. The analytical expression of the singularity locus, with respect to the position and the orientation variables, is obtained by calculating the determinant of the new Jacobian matrix. The analytical expression of singularity locus determines the distribution of singularity locus in space, and it is suitable for both the orientation singularity and the position singularity. Finally, the correctness of the new method is verified by a concrete calculation example. The singularity of all of the Stewart parallel mechanisms with planar platforms can be analyzed by using this method.

Key words: Jacobian matrix, Parallel mechanism, Quaternion, Singularity, Sterwart platform