Manufacturing of gears can be achieved with various methods, including the cutting of gears in a hobbing machine. The function of such a machine tool is based on a combination of timing gears which synchronize all moving components accurately. Variations in the synchronization, which alter the geometric features of the gear being cut, are achieved via external gearboxes with interchangeable gears. Thus, precise knowledge of the change gears that correspond to the desired gear geometry is essential in order to operate the machine tool properly. The hobbing machine examined in this paper had remained unused for years, without a manual to indicate the correct use of the external gearboxes. The task was to render the machine tool functional by devising an experimental procedure for the calculation of the internal gear ratios and the correct combination of change gears, making use only of simple tools. The project was carried out successfully and proved to be an excellent case study to delve into the manufacturing as well as the use of gears. The documentation of the whole procedure and a short explanatory video are integrated within the educational aids of a relative course in the School of Mechanical Engineering 1. The nature of gear drivetrains themselves, in particular the fact that all gear ratios are ratios of integer numbers; this is not true, for example, for belt drives.