Reconstruction synthesis of the lost subsystem for the planetary motions of antikythera mechanism

The mechanism for the planetary motions contained in the lost subsystem of Antikythera mechanism is a strict challenge of the reconstruction design. This work presents a systematic procedure of the reconstruction design to synthesize all feasible designs which agree with the science and technology standards of the subjects time period. Based on the kinematic analysis of ancient planetary theories, the anomaly planetary motions could be formulated. By the mechanism analysis, two types of feasible topological structures with the minimum numbers of members are obtained, and the relationships of teeth for the inferior and superior planets are derived. Through the study of the historical literature, the astronomical theories and the existing designs, the required design constraints are concluded. For the two reconstruction designs, one, the design by Edmunds and Morgan, and three feasible design concepts are, respectively, synthesized in accordance with the concepts of generalization and specialization. Focusing on each feasible design concepts, this work derives the relationships of teeth. Furthermore, one feasible combination of these feasible designs for different planets is adopted for detail design. And, it could be the original structure for the planetary motions of the lost subsystem of Antikythera mechanism.