This is the second of two columns on the Antikythera Mechanism. In each we examine one part of the mechanism that has special mathematical interest. Last month it was the Sun-Moon assembly; this month: the differential gear.
Update: Technology available to Tony Freeth and his collaborators, including computed X-ray tomography (like a high-resolution CAT-scan), has allowed a much better understanding of the structure of the mechanism and has shown that earlier work by Derek de Solla Price (upon which much of this column was based), while correctly assessing the intellectual scale of the Greek's achievement, was dead wrong on many of the details. Read about some of the discoveries made in 2009 here.
1. What is a differential gear?
First some definitions from Gear Engineering. An assembly of intermeshing gears is called a train. In a simple planetary train two coaxial gears are connected by one or more similar gears ("pinions," also called "planets" or "spider gears") mounted on intermediate shafts. Those shafts are fixed to a carrier, or "turntable".
In all the diagrams in this column, the following color scheme has been followed: the two coaxial gears are purple and green, the pinions are yellow, the turntable is blue.
If all three of the principal parts (purple, green, blue) are free to rotate, the train is called a differential. In this column we will explore the functioning of differentials, and examine in particular the differential in the Antikythera mehanism.