Abstract: By the traditional dismantle-bar method, the static equilibrium equations of the mechanism are set up, considering the elasticity of member and then utilizing the micro-deformation and superposition principle, the deformation equations of compatibility are derived and then the static analysis of the spherical parallel mechanism with 3-DOF is fulfilled. All torques and forces acting on each member are obtained, including the relationship between input torques and output load. As a numerical example, some figures which show the relationship between input torque, each force on each member and the position and posture of the mechanism are drawn under three kinds of external loads, respectively. The results show that, when the external force (only) F acting on the mechanism overpasses the spherical center, the input torque of the mechanism is identically vanishing and the variation of forces acting on members with the position and orientation of the mechanism in whole space is gentler slope, meanwhile, the mechanism has been equivalent to a common frame-structure and the forces are not related to the properties of the mechanism, Under the external torque M only, the variations of the input torques and the forces with the position and orientation of the mechanism. are associated with the characteristic (coincided with singularity of the Jacobian matrix) of the mechanism. The two portions of force jointly produced by F and M are independent and detachable. The research provides the theoretical basis of statics for structure design and application of the mechanism in engineering.

Key words: Deformation equation of compatibility, Linear displacement, Spherical parallel mechanism, Statics