This paper uses the theory of gearing to derive the mathematical model of an internal cycloidal gear with tooth difference. Whereas the outer rotor profile is based on a curve equidistant to a hypotrochoidal (or extended hypocycloid) curve, the inner rotor design generally depends upon type of use—e.g., when used as a speed reducer, it is a pin wheel. Therefore, this analysis proposes designs for both a gerotor and a speed reducer. Specifically, for an inner rotor used as a gerotor pump, it outlines a mathematical model to improve pump efficiency and derives a dimensionless equation of nonundercutting. For the speed reducer, it develops and demonstrates with numerical examples, a feasible design region without undercutting on the tooth profile or interference between the adjacent pins.
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Hwang et al. (2006) studied this question.