Reconstruction synthesis for the unexplained feature of the lunar subsystem of Antikythera mechanism

Antikythera mechanism, dateable around to the first century BC, is the oldest known geared mechanism treated as an astronomical computer through the decoding of modern technology. In accordance with the decoded exterior dials and their functions, the interior mechanism was confirmed to consist of five corresponding subsystems. However, some unexplained problems still exist among these subsystems, such as the lunar subsystem, in which the visible pentagonal mark is positioned on the centre of a gear, demonstrating the lunar anomaly motion. From the viewpoint of mechanical design, this strange evidence implies the existence of a shaft with a complex structure, i.e. the coaxial gears with different rates. Also, it affects strongly the identifications of links and even the positions of gears. In order to provide other possible concepts to clarify this problem, this study synthesizes all feasible reconstruction designs through a systematic procedure. Through the study of historical literature, astronomical theories and existing designs, design constraints which are indispensible for the assignments of links and joints are concluded. Then, according to the concepts of generalization and specialization of mechanism, 13 feasible designs which are consistent with the theories and techniques of the subject's time period, including the one by Freeth et al. are synthesized. Once new discoveries about the unexplained problem appear in the future, these feasible designs can be the corresponding answer.