@Involutius contributed an article on the equations that describe the root profile of gears which are cut by a trapezoidal-profiled hobbing tool. From that article, I was able to do a slightly different derivation to get accurate curves for the involute as well as the trochoidal root curve, for both normal and profile-shifted gears. Thanks so much, Involutius!
But I have another question regarding gear tooth profiles. The entire discussion of the root curve profile is based on a conventional (and, for that matter, a flat trapezoidal) hobbing gear cutter. I'm interested in somewhat more exotic gear applications, and I wonder if the newer power skiving machines can cut, say, negatively profile-shifted spur pinion without the severe impact to tooth strength.
Simply put, my question is, "Does power skiving have a dramatically different result for root gear profiles than conventional hobbing?"