This diagram shows five different versions of a bending curve.
1. Elastica curve, curvature varies with Sine (0-180°)
2. Clothoid curve, linear increase / linear decrease of curvature
3. The original traced saw blade (it was difficult to meassure the curvature of the scanned line)
4. Curve from Daniel Pikers Kangaroo (see previous post)
5. A curve with curvature made up of two different Sine curves.
The last curve is based on a diagram by Maarten Kuijvenhoven, see image below from his thesis. The curve is a combination of two sine waves, the first one with aplitude 1 (0-180°) and the other one with amplitude -0.1 (0-540°). The amplitude relation was something I had to experiment with, but the one used above seemed to work quite well. In the illustration below, both sine waves have amplitude 1.