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CHAPTER XXIII 
TOOTHED GEARING 
318. Definitions Relating to Toothed Wheels.—The jitch surfaces 
of two toothed wheels which gear with one another are the surfaces of 
two imaginary friction wheels which have the same axes, and which 
would have the same relative angular velocities as the toothed wheels if 
one was to drive the other by rolling contact. 
A section of a pitch surface by a plane at right angles to its axis is 
called a pitch line, or a pitch circle, if the section should be a circle, which 
it is in most cases. 
The pitch of the teeth is the distance from a point on one tooth to the 
corresponding point on the next, measured along the pitch line. In the 
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J 
ROOT CIRCLE 
Fig. 575. 
ease of a circular wiieel whose pitch circle has a diameter d, and which 
has n teeth of pitch p, it is obvious that mp=ad. The pitch just defined 
is the circumferential or circular pitch, and is equal to the circumference 
of the pitch circle divided by the number of teeth. If the diameter of 
the pitch circle be divided by the number of teeth, the result is called the 
diametral pitch. If p’ denote the diametral pitch, then np’=d and 
p=tp’. In the designing of machine-cut toothed wheels it is usual to - 
arrange that p’ is a simple fraction of the form =; where m is a whole 
number, then m is the number of teeth in the wheel per inch of diameter, 
and the number m is frequently called the diametral pitch. 
When the term pitch is used without qualification, circular pitch is to 
be understood. 
The part of a tooth beyond the pitch surface is called the point or 
addendum, and the part within the pitch surface is called the root. The 
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