A Note on the Mechanics of Ancient Gear Systems

This paper deals with the mechanical behavior of the gearwheels of the antiquity, which were generally characterized by triangular shaping of the teeth. The engagement of the conjugate profiles is analyzed in detail, calculating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the points of the theoretical contact path is carefully checked, estimating also the magnitude of the successive tooth collisions and ascertaining the energy losses arising from the particular nature of the coupling. Some very interesting results are that only one couple of teeth turns out to be active at each time instant and that the real path may belong to the only approach region or to the only recess region entirely or may be split into two separate sub-phases, the one in approach and the other in recess, or may even straddle both regions. The occurrence of each of these conditions depends on the average speed ratio (tooth ratio) and on the assigned clearance between the two wheels. It is also found that the speed oscillation is roughly contained in a ±10% range and the efficiency may reach rather high values, despite the presumable crude finishing of the ancient gearwheels due to the rudimentary technology used in the construction of the tooth profiles.