T-20
2.4 Pitch Circles
Referring to Figure 2-4, the tangent to the two base circles is the line of contact, or line-of-action
in gear vernacular. Where this line crosses the line-of-centers establishes the pitch point, P. This in
turn sets the size of the pitch circles, or as commonly called, the pitch diameters. The ratio of the
pitch diameters gives the velocity ratio:
Velocity ratio of gear 2 to gear 1 is:
d1
i = ––
(2-1)
d2
2.5 Pitch And Module
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.
Circular pitch — A naturally conceived linear measure along the pitch circle of the tooth
spacing. Referring to Figure 2-5, it is the linear distance (measured along the pitch circle arc)
between corresponding points of adjacent teeth. It is equal to the pitch-circle circumference divided
by the number of teeth:
pitch circle circumference pd
p
= circular pitch = –––––––––––––––––––––– = –––
(2-2)
number of teeth z
Module –– Metric gearing uses the quantity module (m) in place of the American inch unit,
diametral pitch. The module is the length of pitch diameter per tooth. Thus:
d
m = ––
(2-3)
z
Relation of pitches: From the geometry that defines the two pitches, it can be shown that
module and circular pitch are related by the expression:
p
–– = p
(2-4)
m
This relationship is simple to remember and permits an easy transformation from one to the
other.
d1
d2
Pitch
Point (P)
Base Circle, Gear #1
Base Circle, Gear #2
Pitch
Circles
Fig. 2-4
Definition of Pitch Circle and
Pitch Point
Line of
contact
p
Fig. 2-5
Definition of Circular Pitch
