In order to improve the machining accuracy of the precision surface grinding machine, a 3-DOF micropositioning table is used as an auxiliary table to form the dual infeed system with nanometer level positioning accuracy. This paper mainly deals with the static characteristics of the micropositioning table. The direct and inverse kinematic models are obtained under different orientation descriptions, and the inherent relationship between different orientation descriptions is investigated. By use of Eular angle description, the reachable orientation space of the micro-positioning table is obtained. The theoretical static stiffness on the top surface of the table is also given, and the experimental tests are carried out to verify the established models.