Abstract: The research subject is spherical 2-DOF parallel manipulator with actuation redundancy. Considering the elasticity of the bar, via the traditional dismantle-bar method, the static equilibrium equations of the mechanism are established, calculating the deformation of the bar by integral method, and then utilizing the micro-deformation and superposition principle, the deformation equations of compatibility are derived, 42 equations are obtained, but there are 43 unknown parameters in all because of redundant mechanism. So static full-solutions of the manipulator are obtained via input forces optimization method. By numerical example, under the action of external load, drawing the output P-shaft’s force diagram which is along the given trajectory. The research provides the theoretical basis of statics for structure design and application of the manipulator in engineering.

Key words: Deformation equation of compatibility, Force optimization, Spherical manipulator, Statics, Two degrees of freedom (2-DOF)