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.^[ref]

Let the gear centers be separated by $a$, with tooth counts $N_1,N_2$. Their operating radii locate the pitch point atFor 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 ${\omega }_1=50rad/s$ and ${\omega }_2=-25rad/s$, both surface velocities at that location have magnitude $1m/s$ 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.