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214 Making Things Move

NOTE Gears with an even number of teeth are easiest to measure, since
each tooth has another tooth directly across the gear. On a gear with an odd
number of teeth, if you draw a line from the center of one tooth straight
through the center across the gear, the line will fall between two teeth. So,
just be careful using outside diameter in your calculations if you estimated it
from a gear with an odd number of teeth.

• Center distance (C) Half the pitch diameter of the first gear plus half the
pitch diameter of the second gear will equal the correct center distance. This
spacing is critical for creating smooth-running gears.
• Pressure angle The angle between the line of action (how the contact point
between gear teeth travels as they rotate) and the line tangent to the pitch
circle. Standard pressure angles are, for some reason, 14.5° and 20°. A
pressure angle of 20° is better for small gears, but it doesn’t make much
difference. It’s not important to understand this parameter, just to know that
the pressure angle of all meshing gears must be the same.

All of these gear parameters relate to each other with simple equations. The
equations in Table 7-1 come from the excellent (and free) design guide published by
Boston Gear (www.bostongear.com/pdf/gear_theory.pdf).

TABLE 7-1 Gear Equations

TO GET IF YOU HAVE USE THIS EQUATION
Diametral pitch (P) Circular pitch (p) P = π/p
Number of teeth (N) and pitch diameter (D) P = N/D
Number of teeth (N) and outside diameter (D ) P = (N+2)/D (approx.)
0 0
Circular pitch (p) Diametral pitch (P) p = π/P
Pitch diameter (D) Number of teeth (N) and diametral pitch (P) D=N/P
Outside diameter (D ) and diametral pitch (P) D = D – 2/P
0 0
Number of teeth (N) Diametral pitch (P) and pitch diameter (D) N = P × D
Center distance (CD) Pitch diameter (D) CD = (D + D )/2
1 2
Number of teeth (N) and diametral pitch (P) CD = (N + N )/2P
1 2