Gear pitch point
= Gear pitch point
The <gear pitch point> is where the <gear line of action> meets the line joining the gear centers. For a fixed-axis external <involute> pair, it is the tangency point of the <operating pitch circles>. The point is a geometric location in the mesh, rather than a material mark permanently attached to one tooth.<Elements of Metric Gear Technology by SDP-SI>[§3.1, pressure-angle, line-of-centers and base-circle tangent geometry]{ref}
Let the gear centers be separated by $a$, with tooth counts $N_1,N_2$. Their operating radii locate the pitch point at
$$
r_{w1}=\frac{aN_1}{N_1+N_2},\qquad
r_{w2}=\frac{aN_2}{N_1+N_2}.
$$
For external signed <angular velocities>, $r_{w1}\omega_1+r_{w2}\omega_2=0$. The two hypothetical material points occupying the pitch point therefore have the same instantaneous <velocity>. This is the local <rolling without slipping> property used to construct the operating pitch circles.
For an original example, use20 and40 teeth separated by $60\,\mathrm{mm}$. The pitch point is20mm from the first center and40mm from the second. With $\omega_1=50\,\mathrm{rad/s}$ and $\omega_2=-25\,\mathrm{rad/s}$, both surface velocities at that location have magnitude $1\,\mathrm{m/s}$ and the same direction. Ideal relative <gear sliding velocity> is zero there.
Elsewhere on the <gear path of contact>, the two tooth surfaces can slide even while maintaining the required normal contact condition. The pitch point remains fixed in this fixed-axis geometry, while successive tooth-contact points advance through the mesh. Whether the pitch point itself belongs to a particular usable contact interval depends on the available flanks; the geometric definition does not assert that every modified tooth profile physically contacts at that point.