Cause of sinusoidal systematic tooth-position errors in Antikythera gears

Determine whether the sinusoidal systematic error observed in the angular positions of teeth in Antikythera Mechanism gears is caused exclusively by rotational-axis eccentricity or also by errors introduced during the marking of tooth positions on the bronze discs.

Background

The study incorporates Edmunds’ model of manufacturing errors, which includes random tooth-position errors and a sinusoidal systematic error. A key unresolved issue is the physical origin of the systematic component: potential causes include axis eccentricity and layout/marking errors on the gear blank.

Because the authors’ simulations need to partition the systematic error between these causes, they adopt a 50-50 split as a modeling hypothesis, explicitly noting that Edmunds could not conclude that eccentricity alone explains the effect, leaving the causal attribution unresolved.

References

One possible cause is the eccentricity of the actual center of the gear (i.e., the center around which the gear rotates) relative to the geometric center (i.e., the center of the circle that best fits the tips or valleys of all the teeth). However, in his 2011 study, Edmunds could not conclude that this was exclusively due to this phenomenon. He also attributed it to the shift generated when marking the tooth positions on a bronze disc.

— The Impact of Triangular-Toothed Gears on the Functionality of the Antikythera Mechanism  (2504.00327 - Arenas, 1 Apr 2025) in Section 4 - Introducing manufacturing errors in the gears