Joseph E. Shigley
The University of Michigan
Ann Arbor, Michigan
33.1 DEFINITIONS / 33.1
33.2 TOOTH DIMENSIONS AND STANDARDS / 33.4
33.3 FORCE ANALYSIS / 33.5
33.4 FUNDAMENTAL AGMA RATING FORMULAS / 33.6
Spur gears are used to transmit rotary motion between parallel shafts. They are
cylindrical, and the teeth are straight and parallel to the axis of rotation.
The pinion is the smaller of two mating gears; the larger is called the gear or the
The pitch circle, B in Fig. 33.1, is a theoretical circle upon which all calculations are
based. The operating pitch circles of a pair of gears in mesh are tangent to each other.
The circular pitch, p in Fig. 33.1, is the distance, measured on the theoretical pitch
circle, from a point on one tooth to a corresponding point on an adjacent tooth. The
circular pitch is measured in inches or in millimeters. Note, in Fig. 33.1, that the cir-
cular pitch is the sum of the tooth thickness t and the width of space.
The pitch diameter, d for the pinion and D for the gear, is the diameter of the pitch
circle; it is measured in inches or in millimeters.
The module m is the ratio of the theoretical pitch diameter to the number of teeth
N. The module is the metric index of tooth sizes and is always given in millimeters.
The diametral pitch Pd is the ratio of the number of teeth on a gear to the theo-
retical pitch diameter. It is the index of tooth size when U.S. customary units are used
and is expressed as teeth per inch.
The addendum a is the radial distance between the top land F and the pitch circle
B in Fig. 33.1. The dedendum b is the radial distance between the pitch circle B and
the root circle D in Fig. 33.1. The whole depth ht is the sum of the addendum and
The clearance circle C in Fig. 33.1 is tangent to the addendum circle of the mating
gear. The distance from the clearance circle to the bottom land is called the clearance c.
Backlash is the amount by which the width of a tooth space exceeds the thickn