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I'd like to a plot spur gear in python (using matplotlib, but that is not important..). I've already worked out the involute curves, which can by parametrized easily and which define the main part of the tooth. I have a problem with the base of the tooth, where a phenomenon called undercut is going on. It is created by "rolling" a rack (its pitch) along the gear (its pitch circle), as described in this video: Involute gear undercut. Unfortunatelly for me, the description there is not complete and I think it only works for one half of the undercut gap. I'd like to get some parametrization of the whole undercut gap from one tooth to another, which can be then transfered to code. enter image description here

Thank you for your help. If you could provide a python code for this, would be great, but not neccessary. It is partially for a class and partially for a hobby, any advise is welcome.

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