# Can the pitch circle of a gear be farther out than the intersection point of the involutes on opposite sides of a tooth?

I'm trying to make an involute spur gear generator but can't seem to get it right. I know that the diameter of the base circle of the involutes is equal to the pitch diameter * cos(pressure angle). But this means that as I increase the number of teeth and the pitch circle gets larger, its scale relative the base circle also increases. And at a certain point, the pitch circle passes the the intersection point of the two involute curves that will make up the sides of a tooth! (My tooth sides are made of an involute in standard position, and one that is mirrored and rotated by an appropriate angle)

## 1 Answer

That is impossible. The whole point of the pitch diameter is that the thickness of the tooth $X$ equals the gap $Y$ at that radial distance.

Take one profile and rotate it half the tooth separation angle and where it intersects the other profile is where the pitch diameter is.