Abstract:By taking the linear conjugate internal gear pump gear pair as the researching object, through designing the external gear, and then using the fundamental law of gearing and tooth profile conjugate designing method, the mathematic models of meshing line of internal and external gears were deduced, as well as for the models of tooth shape line of internal gear. At the same time, by aiming at the design structure of external gear, the limited radius of the tooth top round of the external gear and the feasible range of the half angle of the tooth shape were confirmed. It provides a theoretical basis for the designing of the linear conjugated internal gear pump.