Fig. 17. Scheme of an adder mechanism.
Fig. 18. Example of an adding mechanism
(differential gear assembly).
A type of differential gear assembly that will add is shown in [Fig. 18]. This is a set of 5 gears A to E. The 2 gears A and B are input gears. The amount of their turning is a and b, respectively. They both mesh with a third gear, C, free to turn, but the axis of C is fastened to the inside rim of a fourth, larger gear, D. Thus D is driven, and the amount of its turning is (a + b)/2. This gear meshes with a gear E with half the number of teeth, and so the amount of turning of E is a + b.
We can subtract the turning of one shaft from the turning of another simply by turning one of the input shafts in the opposite direction.
Integrators
Another mechanism in a differential analyzer, and the one that makes it worth while to build the machine, is called an integrator. This mechanism carries out the process of integrating, of adding up a very large number of small changing quantities. [Figure 19] shows what an integrator is. It has three chief parts: a disc, a little wheel, and a screw. The round disc turns horizontally on its vertical shaft. The wheel rests on the disc and turns vertically on its horizontal shaft. The screw goes through the support of the disc; when the screw turns, it changes the distance between the edge of the wheel and the center of the disc.
Fig. 19. Mechanism of integrator.
Now let us watch this mechanism move. If the disc turns a little bit, the wheel pressing on it must turn a little bit. If the screw turns a small amount, the distance between the edge of the wheel and the center of the disc changes. The amount that the wheel turns is doubled if its distance from the center of the disc is doubled, and halved if that distance is halved. So we see that: