= Gear normal module
{title2=$m_n$}
<Gear normal module> $m_n$ is the <gear normal pitch> divided by $\pi$, measured normal to the tooth direction of a <helical gear>. It describes a different section from <gear transverse module> $m_t$, which uses the circumferential spacing in a plane perpendicular to the rotation axis.<KHK Gear Nomenclature>[Basic Guide B §2, printed p.19, normal versus transverse systems and equations(2.13)–(2.14)]{ref}
If $\beta$ is reference <gear helix angle>, geometric projection gives
$$
m_n=m_t\cos\beta=\frac dN\cos\beta,\qquad p_n=\pi m_n.
$$
For an original inference example, reference diameter $d=60\,\mathrm{mm}$, tooth count $N=30$ and $\beta=30\,{}^{\circ}$ imply $m_t=2\,\mathrm{mm}$ but $m_n=\sqrt3\,\mathrm{mm}\approx1.73205\,\mathrm{mm}$. The normal pitch is approximately $5.4414\,\mathrm{mm}$, compared with transverse pitch $6.2832\,\mathrm{mm}$. This is a geometric example, not a claim that the inferred normal module belongs to a particular manufacturer's preferred series.
Conversely, specifying $m_n=2\,\mathrm{mm}$ for the same30 teeth and30degree helix angle gives reference diameter $69.282\,\mathrm{mm}$. Thus two drawings both labeled “module2” can describe different gears when one means normal module and the other transverse module.
Pressure angles need the same care: for reference tooth geometry, $\tan\alpha_t=\tan\alpha_n/\cos\beta$. Matching only a module number, without its plane, pressure-angle convention and helix geometry, does not establish a compatible pair. In a conventional parallel-axis external mesh, the two <helical gears> also require appropriate opposite hands; the normal-module definition alone does not specify that connection.
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