The paper introduces the novel Modular Pipe Climber III with a Three-Output Open Differential (3-OOD) mechanism to eliminate slipping of the tracks due to the changing cross-sections of the pipe. This will be achieved in any orientation of the robot. Previous pipe climbers use three-wheel/track modules, each with an individual driving mechanism to achieve stable traversing. Slipping of tracks is prevalent in such robots when it encounters the pipe turns. Thus, active control of each module's speed is employed to mitigate the slip, thereby requiring substantial control effort. The proposed pipe climber implements the 3-OOD to address this issue by allowing the robot to mechanically modulate the track speeds as it encounters a turn. The proposed 3-OOD is the first three-output differential to realize the functional abilities of a traditional two-output differential.