Optimal teeth design of the lost mechanisms demonstrating interior planets in antikythera astronomical device

Antikythera Astronomical Device, the oldest calculator with multiple-functions, is driven by gear trains with five subsystems. The authors synthesized four feasible 1-DOF designs of the lost mechanisms for interior planetary motions by a systematic design procedure. The optimal teeth design corresponding to the simplest structure is presented. To compare the ancient astronomical theory, the peak errors respectively for Mercury and Venus are about 0.227 and 0.365 days. It is proved strongly that the reconstruction designs generated by systematic synthesis procedure are feasible.