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A novel redundantly actuated parallel mechanism with three translational motion was proposed. It had four kinematic limbs that connected the moving platform to the fixed base. The output degrees of freedom of the mechanism was analyzed by using Lie Group theory and the modified Grübler-Kutzbach criterion. The parallel mechanism had three translational degrees of freedom, four actuated prismatic joints, and thus was redundantly actuated. Position model of the parallel mechanism was established. Inverse position solutions and direct position solutions with analytical expressions were derived. The partially decoupled motion feature of the mechanism was studied. Singularity analysis was conducted based on the derived Jacobian matrix. Workspace of the mechanism was analyzed. Velocity and acceleration of each joint and each part of the parallel mechanism were derived through screw theory. Dynamic model was established by using virtual work approach, through which the optimal joint torques were obtained. A numerical simulation based on the ADAMS software was carried out. The maximum deviation between the theoretical and simulation results was 0.6%, which verified the correctness of the theoretical model. Dexterity index and dynamic manipulability ellipsoid index were used to evaluate the kinematic and dynamic performances of the mechanism. Mapping relationship between the performance and dimensions were investigated. Dimensional optimization was conducted based on the performance atlas, which improved the performance of the mechanism. The proposed parallel mechanism can be used to construct a five axis grinding machine.