关键词: 角位移, 静刚度, 球面并联机构, 线位移, 正交变换

Abstract: The spherical parallel mechanism 3-RRR with 3-DOF rotations is one of the most important less-mobility mechanisms and it is very complicated and difficult to calculate the stiffness of 3-RRR mechanism where the bars in each branch are arc-shaped. Based on this，the angle displacement of mobile platform and line displacement of spherical center of the mechanism are derived by means of calculating deformation and superposition principle at small strain—the relationship between the displacements and forces acted on the members in each branch. And then the relationship between outer loads and the line displacement, the angle displacement of (spherical center) vertex of mobile platform is set up based on the result of static analysis—the relationship between external wrenches and forces acted on the members in each branch. Finally the flexibility, stiffness matrix are obtained. The 6 principal stiffness and directions of the mechanism are achieved by orthogonal transformation. The results show that the principal stiffness and directions are varied with the pose-position of the mechanism in which the principal stiffness is gradually enlarged away from the origin where 3 principal stiffness (torsional stiffness) are much greater and the others(line deformation stiffness) are smaller, the difference between the two parts are giant. This research is the important theoretical foundation and support for engineering design and application of 3-RRR mechanism in practice.

Key words: Angle displacement, Line displacement, Orthogonal transformation, Spherical parallel mechanism, Static stiffness