The Antikythera mechanism is one of the most extraordinary examples of the degree of sophistication reached by the Hellenistic culture in the field of mechanism design. This calendar mechanism not only witness the degree of astronomic knowledge of the greeks, but also their capability to conceive and build marvelous mechanical devices. The mechanism is the first documented example of differential gear arrangement in western culture. The paper gives first a description of the kinematic structure of the mechanism in terms by means of a graph, then a full kinematic analysis of this complex gear train is performed. The results of our kinematic analysis, only partially coincident with those obtained by De Solla Price, match very closely the discoveries made by the Greek astronomer Hipparcus about the duration of the lunar months. There is also a conjecture on the kinematic structure and gear dimensions of some of the missing parts. In the Appendix is reported the listing of the Maple program developed for the kinematic analysis.

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