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 180° by the number of teeth, ascertain the sine of the quotient and multiply it by the diameter of the wheel.
The number of teeth is 75, and the diameter 40 inches ; what is the true pitch?
180/75 = 2° 24' and tin. of 2° 24' = .04188, which X 40 = 1.6752 ins.
Multiply the number of teeth by the pitch, and divide the product by 3-1416.
The number of teeth in a wheel is 75, and the pitch 1.675 ins.; what is the diameter of it? 75 X 1.6755 / 3.1416 = 10 ins.
Divide the circumference by the pitch.
Multiply the number of teeth in the wheel by the true pitch, and again by -3184.
Take the elements of the preceding case.
75 X 1.6752 X .3184 = 40 int.
Multiply the diameter or circumference of the wheel or the number of its teeth, as the case may be, by the number of its revolutions, and divide the product by the diameter, circumference, or number of teeth in the pinion.
A pinion 10 inches in diameter is driven by a wheel 2 feet in diameter, making 46 revolutions per minute; what is the number of revolutions of the pinion?
2 X 12 X 46 / 10 = 110.4 revolutions.
Multiply the diameter in the following table for the number of teeth by the pitch, and the product will give the diameter at the pitch circle.
What is the diameter of a wheel to contain 48 teeth of 2.5 inches pitch?
15.29 X 2.5 = 38.225 inches.
Divide the diameter of the wheel by the diameter in the table for the number of teeth, and the product will give the pitch.
What is the pitch of a wheel when the diameter of it is 50-94 inches, and the number of its teeth 80?
50.94 / 25.47 = 2 inches.
Divide the diameter by the pitch, and opposite to the quotient in the table is given the number of teeth. (See p. 154.)
Change 'Wheels in Screw-cutting Lathes.
T S / t t' I = N; t t' / IT = S T representing number of teeth in traverse screw; S number in stud-wheel gearing in mandril; t number in wheel upon mandril, and t' number in gearing upon stud pinion, gearing in T; I number of threads per inch upon traverse screw; N number to be cut.
 
Continue to: