This paper proposes a new type of curve, an elliptical roulette, which it initially applies to rotary lobe pumps. Once the new rotor profile has been mathematically modeled using the principle of gearing, equations can be derived to assess the presence or absence of undercutting in the tooth profile. The effect of the new profile properties on pumping performance is evaluated using a specially developed three-dimensional fluid analysis model. The proposed curve is tested using six novel rotor profiles based on the elliptical axial ratio parameter lambda (a shorter axis divided by a larger axis). These six new cases and a traditional case are analyzed under the same volume and clearance conditions and their differences compared. The results show that a smaller elliptical axial ratio design produces better flow characteristics. In particular, an elliptical axial ratio smaller than 0.6 not only achieves high discharge efficiency but allows vibration and noise to be controlled by the flow rate fluctuation coefficient, which approximates the traditional indicator. The proposed curve can thus serve as a useful reference for pump or rotary fluid machine design. (C) 2015 Elsevier Ltd. All rights reserved.