= Gear reference circle
{title2=$d=mN$}
A <gear reference circle> is the imaginary <circle> used to specify an individual <gear>'s tooth geometry. For a <spur gear>, its diameter $d$ is defined by <gear module> $m$ and tooth count $N$ through $d=mN$. It supplies a common datum for tooth spacing and other dimensions, whether or not that <gear> is currently meshing with another one. The <operating pitch circle>, in contrast, describes the mounted pair's motion.<KHK Gear Nomenclature>[The ABC's of Gears, Basic Guide B, §2, printed pp. 14–17, equation (2.8), Figure 2.6 and Table 2.1]{ref}
For a 30-tooth <spur gear> with <gear module> $2\,\mathrm{mm}$, the reference diameter is $60\,\mathrm{mm}$. Thus successive teeth repeat at an angular interval of $2\pi/30$ and a <gear circular pitch> of $2\pi\,\mathrm{mm}$ on that <circle>. In the standard full-depth, unshifted geometry specified by KHK, the tooth-tip diameter is $d_a=d+2m$, giving $64\,\mathrm{mm}$ in this example. Measuring the outside diameter and calling it the reference diameter would therefore produce the wrong <gear module>.<KHK Gear Nomenclature>[The ABC's of Gears, Basic Guide B, §2, printed p. 15, equations (2.8)–(2.10): reference, tip and root diameters]{ref}
The <gear base circle> is another distinct geometric datum. For a tooth profile constructed as the <involute> of a <circle>, the <gear base circle> generates the curved tooth flank, whereas the <gear reference circle> fixes its nominal sizing. Their diameters obey $d_b=d\cos\alpha$, with reference <gear pressure angle> $\alpha$. With $d=60\,\mathrm{mm}$ and $\alpha=20\,{}^{\circ}$, the base diameter is approximately $56.382\,\mathrm{mm}$. These three diameters—base, reference and tip—answer different questions about the same physical <gear>.<KHK Gear Nomenclature>[The ABC's of Gears, Basic Guide B, §3, printed pp. 20–21, base-circle construction and equation (3.1)]{ref}
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