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This paper reports an enhanced mechanical design and stability analysis of a new stair-climbing robotic wheelchair for the disable and elderly. The mechanism is based on a pair of rotational multi-limbed structures pivotally mounted on the opposite sides of the base. The corresponding short arm, long arm and support triangle comprising each rotational multi-limbed structure are actuated to rotate through epicyclic gear trains so that the robotic wheelchair can ascend and descend stairs in a statically stable way. Experimental results with carrying a person validate the feasibility of the proposed mechanism design and show the simplification of the associated operation process.