This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.

Suppose we have two shafts, Dand F, as shown in Fig. 153 and that we want to connect these shafts by gears so that shaft D will make one revolution while shaft F makes two.

In order to do this we must place a gear on shaft D having twice the number of teeth of the gear on shaft F. If we put a gear on D with 24 teeth, the gear on F will then have 12 teeth, or half as many, and each time the gear on D turns around once the gear on F will turn twice; that is, the 24 teeth on gear D will have to turn gear F twice in order to mesh with 12 teeth on F.

The relation of the speed of F to the speed of D is 2 to 1. This is called the ratio of the gearing. We can now write the ratios between the speeds and the number of teeth in the form of a proportion thus: 24 :12 =2:1, that is, the number of teeth on gear D is to the number of teeth on gear F as the speed of F is to the speed of D.

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