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This paper presents a new type of 4-degree-of-freedom (DOF) robotic surgical instrument for a minimally invasive surgical robot system. The forceps wrist mechanism was designed here on the basis of the 3-DOF parallel structure with three prismatic-spherical-revolute kinematic chains. The pitch and yaw motions of the moving platform generated the wrist rotational motions of the forceps. The axial translation of the parallel mechanism was converted into the forceps grasp motion by an inversion of the slider-crank mechanism. Furthermore, for a more dexterous movement of the forceps, a full revolution of the forceps for the axial rotation is also possible with the instrument. While the proposed instrument realized all the required DOFs of a forceps, the parallel structure of the wrist and the driving mechanism that was designed using only rod elements made the proposed instrument more reliable and rigid than other wire-driven instruments. The kinematic constraints and inverse kinematics of the proposed instrument were derived. Furthermore, the screw-based Jacobian was formulated geometrically, and the static force relation and the linear constraints on a twist were derived. Finally, a prototype of the proposed instrument with a diameter of 8 mm was introduced, and the performance of the prototype was verified through several experiments.