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

In the mechanical world or in speaking of machines, the expression "geared to 75" is often heard. This means that one turn of the driving wheel will cause the circumference of the drive to pass over 75 in.

To illustrate: A bicycle sprocket with a circumference of 30 in. and a rear wheel of 80 in. would give this ratio of speed: - 80/30 = 8/3 = 2 2/3; i.e., one turn of the pedal would turn the rear wheel 2 2/3 times. The gear of the wheel is found by multiplying this number by the diameter of the wheel, say 27 in.; 27 X 8/3 = 72 in.

The proportion between the speeds and the diameters of gears is just the same as the proportion between the speeds and the number of teeth. This means that we can find the ratio of the speeds of two gears just as well if we know their diameters as if we know the number of their teeth. Suppose the diameters of two gears are 12 in. and 24 in. respectively. Then the ratio of their speeds would be as 2 is to 1, if the 12 in. gear is the driver. If the 24 in. gear is the driver the ratio would be as 1 is to 2; i.e., if the 24 in. gear is driving and turns once, the 12 in. gear would turn twice.

Sometimes it is easier to figure the ratio of the speeds of gears from their diameters, but as the diameter used is the diameter of the pitch circle and not the diameter outside of the teeth, it is often hard to measure it exactly. For this reason gears are usually classified according to the number of teeth. As we can count the teeth we can get a more exact answer when figuring their speeds than if we figured from pitch circles.

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