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Unification of epitrochoid origin profile design approaches for external lobed star member used in hydrostatic and gear units

We propose unification of various geometric design approaches, available in the open literatures and published research papers, for profile of star rotor used in rotary piston machines type hydrostatic units, namely pumps and motors. The star rotor profile has cycloidal root. We consider three basic approaches. These approaches are otherwise self-sufficient for profile selection purpose although the end formulae are different in relation to the common parametric terms. A closer scrutiny reveals that the initial selection of co-ordinate systems, profile generating centrode pairs and the location of the generating point lead to such differences. Our unification provides infusion and integration of three different paradigms that we have considered. This investigation is aimed at helping researchers develop a better understanding design approaches of such machines.