Elliptic involute gear cutting with toothed rack


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I was always fascinated by elliptic gears, knowing well that they are not really useful in a practical sense. Some weeks ago I found a gear pump in the internet that was indeed using elliptic gears and after all gained some advantage out of it: http://www.ingo-laemmle.de/Imm.htm

Having this application in mind I decided to go a bit deeper into the math of curves and to find out, how to do involute gearing properly on (almost) arbitrary curves in an efficient way. The method I used is a generatlization of the subtractive method I have published previously in my gear cutting project
It's in principle applicable to put involute gearing onto any convex shape or body. To describe it in a sentence: Roll a toothed rack with the right amout of theeth along the curve and let it carve out what it touches - just like a real world gear cutting tool.

What you get:

  • a nice kinetic object or wall teaser
  • lots of usage examples in the code
  • an easy and well defaulted API
  • neat documented code showing you how that all works

What you need:

  • OpenSCAD 2015 (Toothbar uses a dynamic array). It renders much faster
  • ShortCuts.scad library (sorry for that, but it simplifies programming so much). Description in: http://www.thingiverse.com/thing:644830

Hint: To also do concave curve pieces, my idea would be to roll along their convex inner sides and complement the result. This works well, but needs some fiddling around with piecewise definitions and makes the code cumbersome.

Have fun and let me know, how you put it to use.

Elliptic involute gear cutting with toothed rack by Parkinbot is licensed under the Creative Commons - Attribution - Non-Commercial license.

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