Antikythera mechanism is known as the oldest astronomical calculator in ancient Greece. With the development of modern science and technology, the inscriptions, functions and exterior appearance are decoded from the surviving fragments. The corresponding reconstruction designs of interior structure and physical models are continuously presented. This work introduces an assembly process of physical model that is one of 48 feasible reconstruction designs presented by Yan and Lin. Firstly, the geometric constraints of interior subsystems are concluded so as to generate the reconstruction designs with complete interior structure. Then, a detail design procedure of reconstruction model is presented. Through this systematic procedure, teeth calculations are resolved based on the concluded teeth relations. Gear sizes and gear models of lost structures are reconstructed, and space arrangements can be finished by graphical method. Finally, the simulation model and its corresponding physical model re built to confirm the operation of reconstruction design.