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2.5 Pitch

Essential to prescribing gear geometry is the size, or spacing of the teeth along the pitch circle. This is termed pitch and there are two basic forms.
       2.5.1 Circular pitch — A naturally conceived linear measure along the pitch circle of the tooth  spacing. Referring to Figure 1.5 it is the linear distance (measured along the pitch circle ar between corresponding points of adjacent teeth. it is equal to the pitch-circle circumference divided by the number of teeth:
p_c = circular pitch = pitch circle circumference = Dp                                         (2)
                                   number of teeth           N         
        2.5.2 Diametral pitch — A more popularly used pitch measure, although geometrically much less evident, is one that is a measure of the number of teeth per inch of pitch diameter. This is simply: expressed as:
             P_d = diametral pitch = N                                                                       (3)
                                              D
Diametral pitch is so commonly used with fine pitch gears that it is usually contracted simply to "pitch" and that it is diametral is implied.
      2.5.3 Relation of pitches: From the geometry that defines the two pitches it can be shown that they are related by the product expression:

              P_d x P_e   =   p                                                                                     (4)
This relationship is simple to remember and permits an easy transformation from one to the other.

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