Rationale for non-inverted orientation of gear z in the Lunar Phases sphere gearing

Establish the mechanical rationale for why the Antikythera Mechanism’s ancient craftsman did not invert the orientation of gear z in the Lunar Phases sphere gearing to avoid constructing two additional gears and a shaft, given the evidence that gear z could not be adapted in inverted position.

Background

Fragment C preserves half of gear z and its axis in the Lunar Cylinder area, showing gear teeth oriented toward the perimeter of the Lunar Cylinder. The authors argue this position is original and not invertible based on CT scans and mechanical fit.

Inverting gear z would reduce the number of required gears for the lunar phase display, yet the craftsman did not do so. The authors raise this as an explicit unresolved question, noting the lack of explanation for the design choice.