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The new mechanism of drum-shaped gear with ring-involute teeth is presented to implement dimensional transmission for the stairlift. The structure of the gear and rack in this actuating mechanism is designed,and then its inherent radius of turn and modulus selection have been studied. In order to make the mechanism move steadily, the drive guide is proposed. After using the dynamics simulation software ADAMS to analyze the 3D model, this kind of mechanism is confirmed to be able to implement dimensional track. The useful method and basis would be provided for the optimization design of the mechanism.