This paper discusses the gear coupling mechanics of the ancient Antikythera mechanism, among whose distinctive characteristics was the triangular shaping of the teeth. The engagement of the tooth pairs is analyzed in detail, estimating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the theoretical contact points is carefully checked, and the magnitude of the successive tooth collisions is calculated together with the energy losses arising from the particular nature of the coupling. Some interesting results are that only one tooth pair turns out to be active at each time instant and the real path may belong only to the approach or to the recess region entirely, or may split into separate subphases, in approach and in recess, or may even straddle both regions. The occurrence of each of these conditions depends on the average speed ratio (tooth ratio) and the assigned clearance between the 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 rather rudimentary technology used in the construction of the tooth profiles.

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