Elliptic involute gear cutting with toothed rack

thingiverse

Be sure to always download the latest version! \nI've long been intrigued by elliptical gears, fully aware that they have little practical value. Recently, I came across a gear pump online that utilized elliptical gears and actually benefited from them: http://www.ingo-laemmle.de/Imm.htm \nHaving this application in mind, I decided to delve deeper into the math behind curves and discover how to implement involute gearing efficiently on any arbitrary curve. The method I employed is a generalization of the subtractive method used in my previous gear cutting projecthttp://www.thingiverse.com/thing:636119\nIn essence, it can be applied to place involute gearing on any convex shape or object. To put it briefly: Roll a toothed rack with the correct number of teeth along the curve and let it carve out what it touches - just like a real-world gear cutting tool. \nThe outcome is: \na fascinating kinetic object or wall display \nmultiple usage examples within the code \nan easy-to-use and well-documented API \nsimply explained, neat documentation showing you how everything works \nWhat's needed: \nOpenSCAD 2015 (Toothbar utilizes a dynamic array). It renders significantly faster. \nShortCuts.scad library (I apologize for this necessity, as it greatly simplifies programming). Explanation in: http://www.thingiverse.com/thing:644830 \nHint: To also create concave curve pieces, I propose rolling along their convex inner sides and completing the result. This method works well but requires some tinkering with piecewise definitions and makes the code cumbersome. \nHave fun experimenting and share your results.