Ochs und Junior Moon Phase Complication

3D Model

The Ochs und Junior moon phase calculates the lunation as 1447/49 = 29.5306122449 days. As a result, it can correctly predict the phase of the moon for around 3478 years before being off by one day.

Ludwig Oechslin explains the implementation of the moon phase function as follows:

An epicyclic gear train driven by a central finger bonded directly to the hour pipe turns the lunar disk beneath the dial counter-clockwise. The central finger engages with a wheel bearing 12 teeth, whose pinion with 14 teeth meshes with a wheel bearing 18 teeth, whose pinion with 14 teeth meshes with the fixed recessed ring gear with its 109 teeth machined into the underside of the dial.

How can this be, since 1447 is a prime number?

The solution lies in the panetary gearset. The trick can be set as follows:

(2×1447+49)/49 = 2943/49 =  (3³×109)/7² = (12/14)×(18/14)×(109/2)