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This paper presents a novel 3-DOF translational parallel robot mechanism 3-RRRP(4R). Firstly, the position analysis of parallel robot is done in order to find out in real time the desired angular displacements of robot mechanism active joints in terms of the movement requirement for the mechanism's moving platform. Secondly, the control scheme is proposed and the system model is developed. Then, a practical chattering-free sliding mode controller is designed. Finally, the motion control system of the parallel mechanism is implemented. The experimental results verify the effectiveness of the sliding mode control method on parallel robot mechanism control. The designed sliding mode controller has no chattering problem of traditional variable structure sliding mode controller, has good performance in motion control and is easy to implement. Because of adopting the closed-loop controls of stepping motors and the sliding mode control method, the developed control system for the parallel robot mechanism has the higher performance-price ratio.