The Impact of Triangular-Toothed Gears on the Functionality of the Antikythera Mechanism (2504.00327v1)

Abstract: The Antikythera Mechanism is based on a complex system of interconnected gears. Recent analyses have highlighted the influence of triangular tooth profiles and manufacturing inaccuracies on its performance. This study combines Alan Thorndike's analytical solution for the non-uniform motion caused by triangular teeth with Mike Edmunds' error model accounting for manufacturing imprecisions. We developed a computational program to simulate the behavior of the mechanism's pointers, integrating variables from both models. Since the impact of these variables is speculative, our results must be interpreted with caution. Our findings indicate that while the triangular shape of the teeth alone produces negligible errors, manufacturing inaccuracies significantly increase the likelihood of gear jamming or disengagement. Under our assumptions, the errors identified by Edmunds exceed the tolerable limits required to prevent failures. Consequently, either the mechanism never functioned or its actual errors were smaller than those reported by Edmunds. Although it seems unlikely that someone would build such a complex yet non-functional device, there are strong reasons to question whether Edmunds' values accurately reflect the mechanism's original errors.