Piecewise gear function with 2D plot and CAD wireframe
Christopher Clayton
09/04/2017
Plotted three lines in Mathematica for gear tooth slope and half of the tooth face, as well as half of the transition curve for a neighboring tooth.
This was created with bicycles in mind. So the transition between teeth is meant to mesh with a chain, not another gear tooth.
The intended conversion is dimensionless units to millimeters.
Used an image of the Mathematica plot to create the wireframe of one gear tooth. Then created copies and rotated each copy by 11.25 degrees successively to achieve a 32-tooth design.
Proportionally adjusted the diameter of the full gear to match real-world proportions after completing the entire wireframe in ViaCAD.