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@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?"

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Tooth bending strength is more dependent on tooth geometry than actual manufacturing processes. You can get customs tools for either hobbing or skiving to achieve whatever root geometry you want although they will be more expensive than off the shelf tools.

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