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In this paper, a study of an all-terrain wheeled mobile robot which is a complex multi-body mechanism is presented. An effective approach for kinematics modeling of the robot traversing uneven terrain has been proposed. Denavit-Hartenberg algorithms and differential kinematics are derived for the individual wheel motions in contact with the terrain. The resulting equations of the individual wheel motions are then combined to form the composite equation for the rover motion. The motion study of the rover for step climbing is also presented. Simulation and experimental results have been employed to verify the rover mobility.