The aim of this paper is to develop a mathematical model for an unconventional worm gear consisting of a globoid worm and a worm wheel where the teeth are bearings. Using rolling elements such the teeth of the worm wheel (ball bearings) transforms the sliding friction to rolling friction during the process of worm gear meshing, improving power. The geometry of the component elements of the gear is analyzed in correlation with its kinematics. After the creation of the mathematical model, it is validated both analytically (through complex graphic representations) and experimentally (by creating, for a particular case, the 3D model and the concrete physical model (prototype) of the gear through 3D printing).