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Research on Kinematics for Planetary Bevel-Gear Trains

A kinematics model of planetary bevel-gear trains, which included two sun gears, four planet gears and two carriers, was established. With analyzing of the gear trains, non-oriented graph representation of the mechanism was developed. Then, the kinematic structure of the gear trains was represented. With coordinate conversion, the successive transformation matrices were derived. And then, the oriented graph representation of gear pair was obtained by analyzing rotation vectors. Lastly, the inverse kinematics equation was obtained. To given the orientation of the moving platform variables, the equations have the identify solutions.