Problem features in synthesizing the non-circular gearwheels for a planetary train with the floating pinion

The idea of using a planetary train with the non-circular central gearwheels and floating pinions in a hydraulic machine is circulating for more than a hundred years. However, until now any exact solution to the problem of profiling the central wheel of a non-circular gearwheel is missing. Unlike most flat gearwheels used in practice, their synthesis could not be carried out based on the Willis theorem. It requires introduction of the Arongold-Kennedy theorem. The paper proposes an adjusted method in designing mechanisms under consideration. It includes the following stages: computing trajectories of the generating pinion center in the coordinate systems associated with each of the central wheels; computing the pinion angular positions; graphical construction of the non-circular wheels’ profiles enveloping the generating pinion. The proposed method ensures favorable conditions for transferring motion and absence of the teeth interference in any position of the mechanism. The method is fairly simple and could be used by a wide range of the design engineers.
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