This paper presents the design of an in-pipe climbing robot that operates using a novel `Three-output open differential'(3-OOD) mechanism to traverse complex networks of pipes. Conventional wheeled/tracked in-pipe climbing robots are prone to slip and drag while traversing in pipe bends. The 3-OOD mechanism helps in achieving the novel result of eliminating slip and drag in the robot tracks during motion. The proposed differential realizes the functional abilities of the traditional two-output differential, which is achieved the first time for a differential with three outputs. The 3-OOD mechanism mechanically modulates the track speeds of the robot based on the forces exerted on each track inside the pipe network, by eliminating the need for any active control. The simulation of the robot traversing in the pipe network in different orientations and in pipe-bends without slip shows the proposed design's effectiveness.