The small actuator torque range brings advantages for the high-accuracy control of a manipulator. By taking the minimum actuator torque range into account, this paper proposes a novel torque optimization method of a 3-DOF redundantly actuated parallel manipulator for friction stir welding. The dynamic model of the 3-DOF redundant parallel manipulator with four kinematic chains is derived by using the principle of virtual work. The solution of the dynamics is not unique, and the range of four actuator torques constitutes a 4D generalized rectangle. A torque optimization method that minimizes the actuator torque range is presented by determining the generalized 4D rectangle with minimum side length. The proposed optimization method is a global solution corresponding to one trajectory of the moving platform, and it is compared with the least square method which is a local solution corresponding to one pose of the moving platform.