In this paper I develop a theoretical analysis of a two gear eccentric system in the Antikythera Mechanism, the oldest known analog computer. One gear carries a pin and as it rotates it transmits the motion to the other gear, which has an aperture. The angular velocity of the second gear depends from the shape of the aperture. Until now it was believed that the aperture was an orthogonal parallelogram. Prof. Xenophon Moussas expressed the idea that its shape could also be an ellipse or ellipse like. In this work the shapes Slot, Ellipse and Parabola are examined. The resulting motion of the gears is determined by a model in the framework of Lagrangian Mechanics. The theoretical results of the three shapes are compared with ephemeris data in order to specify which of them fits better with the data
