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This paper analyzes interactions between the tracks and the stairs, as well as those between the tracked mobile robot and the onboard manipulator for tracked mobile manipulators (TMMs) climbing stairs. Combining a tracked mobile robot, which has the ability to climb stairs, with an onboard manipulator, a TMM extends the workspace and scope of applications of the robot dramatically. However, this combination gives rise to complex track-stair and vehicle-manipulator interactions, because the configuration of the onboard manipulator affects load distribution, which will further influence the track-stair interactive forces. Unlike the wheeled mobile robots, which are normally assumed to obey the nonholonomic constraints, slippage is unavoidable for a tracked mobile robot, especially when climbing stairs. The track-stair interactive forces are complicated, which may take the forms of grouser-tread hooking force, track-stair edge frictional force, grouser-riser clutching force, and even their compositions. In this paper, the track-stair and vehicle-manipulator interactions are analyzed systematically, which are essential for tip-over prediction and prevention, as well as for automatic control of TMMs in autonomous and semi-autonomous stair-climbing. Simulations for a TMM being developed in our laboratory have demonstrated the usefulness of the presented analysis results.