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.
Divide the diameter, circumference, or number of teeth in the driver, as the case may be, by the diameter, etc., of the pinion.
Divide the continued product of the diameter, circumference, or number of teeth in the wheels by the continued product of the diameter, etc., of the pinions.
If a wheel of 32 teeth drive a pinion of 10, upon the axis of which there is one of 30 teeth, driving a pinion of 8, what are the revolutions of the last!
32/10 X 30/8 = 960/80 = 12 revolutions.
The diameters of a train of wheels are 6, 9, 9, 10, and 12 inches; of the pinions, 6, 6, 6, 6, and 6 inches; and the number of revolutions of the driving shaft or prime mover is 10; what are the revolutions of the last pinion ?
6X9X9X10X12X10 / 6X6X6X6X6 = 583200 / 7776 = 75 revolutions.
Subtract the less velocity from the greater, and divide the remainder by one less than the number of wheels in the train; the quotient is the number, rising in arithmetical progression from the less to the greater velocity.
What should be the velocities of 3 wheels to produce 18 revolutions, the driver making 3?
18 - 38 / 3 - 1 = 15 / 2 = 7. 5 number to be added to velocity of the driver = 7.5 + 3 = 10.5, and 10.5 + 7.5 = 18 revolutions. Hence 3, 10.6, and 18 are the velocities of the three wheels.
 
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