Details on Involute Gear Profiles
On an involute profile gear tooth, the contact point starts closer to one gear, and as the gear spins, the contact point moves away from that gear and toward the other. If you were to follow the contact point, it would describe a straight line that starts near one gear and ends up near the other. This means that the radius of the contact point gets larger as the teeth engage.
The pitch diameter is the effective contact diameter. Since the contact diameter is not constant, the pitch diameter is really the average contact distance. As the teeth first start to engage, the top gear tooth contacts the bottom gear tooth inside the pitch diameter. But notice that the part of the top gear tooth that contacts the bottom gear tooth is very skinny at this point. As the gears turn, the contact point slides up onto the thicker part of the top gear tooth. This pushes the top gear ahead, so it compensates for the slightly smaller contact diameter. As the teeth continue to rotate, the contact point moves even further away, going outside the pitch diameter -- but the profile of the bottom tooth compensates for this movement. The contact point starts to slide onto the skinny part of the bottom tooth, subtracting a little bit of velocity from the top gear to compensate for the increased diameter of contact. The end result is that even though the contact point diameter changes continually, the speed remains the same. So an involute profile gear tooth produces a constant ratio of rotational speed.