Calculating the curves of bending

These saw blade curves (seen in two previous posts: here and here) are arranged to have identical midpoint and when viewed like this, the endpoints of the curves all lie on two circles. The radius of each circle is 2/5 of the curve length, and the two circles are 1/5 of the curve length apart.
Based on this fact, I could use the Pythagorean theorem to formulate a mathematical relationship between the original length L, distance d between end points and curve height h:


  1. I don't necessarily understand the algorithms behind bending, but I do know that to able to bend thing is crazy. When normal things would brake, this would not break at all.

    Jim Tracy | http://www.hygradelaser.com.au/bending_services.html

  2. Hi Marten, thanks for this great post. I am applying this to my research on bending and I wanted to ask you how did you keep the length of the bent curve constant? In my tests, when the height of the middle point change, the overall length of the curve is not constant to 100 (length starting value).

  3. Hi Fabio and thanks! These curves were not generated in the computer but scanned from a bent saw blade (check the links to inside the post). That's why they all have the same length. /Best regards

    1. Thanks for your reply Marten. as you guessed, I am trying to simulate the bending digitally and I am still figuring out how to control the elasticity of the bent curve.

  4. Sorry Fabio, I meant this post: