Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Feature Column

antikythera2-3
The Antikythera Mechanism II

With Java animations by Bill Casselman


3. Elementary rotary differential

In this family of diagrams, meshing gears are represented by tangent circles. In this case the upper and lower gears and the pinion must be bevel gears, with teeth at a 45-degree angle to the face. Notice that since the three discs are stacked, the blue axle must be threaded through one of the outer ones. Such a device, usually incorporating several pinions, is called a Simple bevel-gear differential; the blue axle is the "spider shaft take-off."

This mechanism is a rotary form of the straight-line differential: imagine folding the purple and green racks back and bending them into equal circular gears. The slider folds over to a disc of the same radius; now the pinion is attached to its circumference.

Let us count counter-clockwise rotation as positive, since it correponds, in this interpretation, to the racks moving to the right. Since the three wheels have the same radius, their rotational speeds a (top), b (bottom) and c (central blue disc) must still satisfy c=(a+b)/2.


Welcome to the
Feature Column!

These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
Read more . . .

Search Feature Column

Feature Column at a glance


Show Archive

Browse subjects