This disclosure concerns an advanced nutating positive displacement device having a high power to mass ratio and low production cost. This device in one example forms an exemplary pump as will be discussed in detail. The examples disclosed herein are of the rotary positive displacement type, but in a class by themselves. The devices are formed by a nutating rotor having a face comprising lobes and valleys, and a fixed stator also having a face with lobes and valleys. The face of the rotor opposes and cooperates with the face of the stator. The opposing faces define chambers that change volume with rotation of the rotor.