This paper presents a complete description of a specific geometry applicable to internal rotary pump. A particular design is considered, characterized by superior flow-rate performance and a different contact mechanism in respect with the common trochoidal pumps. All the necessary aspects regarding the kinematics and operation of the machine are taken into account, by means of a mathematical formulation. In particular, the kinematic analysis considers the possible presence of transmission errors and assures the absence of interference by a tooth contact analysis. The achieved mathematical model allows the designer to obtain the complete definition of the rotor profiles in parametric form.