This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
Multiply the number of teeth in the driver by its number of revolutions, and divide the product by the number of revolutions of each pinion, for each driver and pinion.
If a driver in a train of three wheels has 90 teeth, and makes 2 revolutions, and the velocities required are 2, 10, and 18, what are the number of teeth in each of the other two?
10 : 90 :: 2 : 18 = teeth in 2d wheel. 18: 90 :: 2 : 10 = teeth in 3d wheel.
Multiply the number of teeth by their pitch.
 
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