Dear sir
I am a student in mechanical engineering and because of my internship I have seen the the CMM output diagrams for gears and I am interested in this case.I want to know how can we calculate the crown of gears according to the cmm output diagrams and what is the engineering or mathematical base for that?
As far as I know and according to the standards,gear crowns are usually like the parabolic curve.So to calculate this curve we could use the least square method but in my opinion this method is not precise because if the parabolic curve is rotated in the XY plane it is a mistake to use least square method and also there is another problem,by using least square method we could minimize the error in one direction(for example Y direction)but because of systematic errors we should find the best curve.
I wonder if you could help me in this case.
I look forward to hearing from you.
Yours faithfully

Bostandoust