Confirmation of ring / internal gear profile

[dbb-the-bruce]

This has been bugging me for a while. When I first needed to create the tooth --profile-- for an internal / ring gear I could not find a parametric equation for the involute tooth shape. I finally came to my own conclusion that the involute shape was simply the negated or inverted shape of a spur gear with the same tooth count DP or Modulus. In other words in modeling terms use a spur gear of the same size to punch a gear shaped hole in a round disk to get your internal or ring gear.

NOTE: I am only talking about the involute tooth shape. Addendum and dedendum get flipped around and there are other interference considerations.

Today I finally found a post on an engineering board that seems to confirm my guess that the profile is just inverted. Can anyone here second that? or point me to an authoritative text that confirms this? Again, just talking about actual tooth involute profile (the curved part) not clearance, backlash etc.

I'm at the "I read it on the internet so it must be true" point.....