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Gear axial pitch $p_x$ is the axial repeat distance between corresponding flanks of successive teeth of a cylindrical helical gear. The measurement follows a line parallel to the rotation axis on a concentric cylinder. It is not the axial advance of one tooth helix through an entire revolution; that larger distance is gear lead $L$. For $N$ equally spaced teeth, $L=N{p}_x$.^[ref]

On the developed cylinder, neighboring tooth traces separated transversely by gear transverse pitch $p_t$ intersect a fixed circumferential coordinate at axial positions separated by $p_x$. Their slope givesFor $d=60\mathrm{mm}$, $N=30$ and gear helix angle $|\beta |=30{}^{\circ }$, $p_t=2\pi \mathrm{mm}$ and $p_x=2\pi \sqrt{3}\mathrm{mm}\approx 10.8828\mathrm{mm}$. The corresponding gear normal pitch is only $5.4414\mathrm{mm}$. These two distances differ by a factor of two in this example because $\sin 30{}^{\circ }=1/2$.

For an engaged gear face width $b=20\mathrm{mm}$, the ideal gear overlap ratio is $b/p_x\approx 1.8378$: successive tooth-contact traces span about1.84 axial pitches across the face. Holding $p_t$ fixed while letting $\beta$ tend to zero makes $p_x$ diverge. Straight spur gear tooth traces do not cross an axial generator successively, so a finite axial-pitch interpretation does not survive that limit. Helix hand determines orientation; the positive pitch magnitude alone does not specify hand.

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.^[ref]

If $\beta$ is reference gear helix angle, geometric projection givesFor 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 $m_n=\sqrt{3}\mathrm{mm}\approx 1.73205\mathrm{mm}$. 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.

Gear normal pitch $p_n$ is the repeat spacing of corresponding helical gear tooth flanks normal to their tooth direction on the developed reference cylinder. It equals $\pi$ times gear normal module $m_n$. It is a different geometric spacing from gear transverse pitch $p_t$, measured circumferentially, and from gear axial pitch $p_x$, measured parallel to the rotation axis.^[ref]

Unwrap the reference cylinder into a plane. The equally spaced tooth traces become parallel straight lines making gear helix angle $\beta$ with the axis. Projecting the transverse spacing onto the normal to those traces givesFor reference diameter $d=60\mathrm{mm}$, $N=30$ teeth and $\beta =30{}^{\circ }$, $p_t=\pi d/N=2\pi \mathrm{mm}$, whereas $p_n=\sqrt{3}\pi \mathrm{mm}\approx 5.4414\mathrm{mm}$. Multiplying $p_n$ by $N$ gives about $163.24\mathrm{mm}$, not the $188.50\mathrm{mm}$ circumference: normal pitch is not the circumferential step.

At $\beta =0$, normal and transverse pitches agree, as expected for a spur gear. For nonzero gear helix angle, using one in place of the other introduces a factor $\cos \beta$. Normal pitch is also distinct from gear base pitch, which refers to the base-circle geometry of an involute. Matching a pitch value without its measurement convention, pressure angle and tooth geometry is insufficient to establish a compatible mesh.