This paper presents a deep research on 2-DOF planar parallel mechanism during developing a new type of hybrid machine tool. The composition of this planar parallel mechanism is introduced, its direct and inverse kinematics solution equations as well as the solution equations for the speed and the acceleration are deduced, meanwhile, the jacobian matrix is obtained. The statics problems of the parallel mechanism are modeled and analyzed based on principle of virtual work, and the balancing driving force solution equation of the driving part is given. Through the solving process we can see that the direct and inverse solution equations of this mechanism have explicit expressions and convenient to realize real-time control. It forms a solid basis for the design and development of this mechanism.