MN-Curvature analysis2

The drawing is related to this one and they are both based on this scanned drawing (that you see in the background). They are part of a little project of mine called "The Geometry of Bending" that aims to understand the shape of elastically bent materials.
So, those three drop-like shapes are attempting to describe this geometry. The underlying scan are curves drawn along a bent sawblade. The rhino-curve to the right is just a trace of one of those drawn curves. The middle one is something I created in Grasshopper and its geometry is related to the Cornu spiral (the curvature increases linearly until it reaches the midpoint). The curve to the left is an elastica curve, also created in Grasshopper, it's commonly believed that this is the shape of a bent material.
I put those 3 curves back into GH to plot their curvature as a graph and the image above is from that process. So the red curves are Curvature circles from the Elastica curve and the points are centre points of those circles.
I think it is clear that the traced saw-blade has more in common with the Cornu-spiral curve than with the elastica curve...

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Comment by Mårten Nettelbladt on June 25, 2013 at 3:06pm: Hi Kartik, I've collected some of my bending investigations in this little book: http://martennettelbladt.se/bending-book/

Comment by Kartik on May 20, 2013 at 8:29pm: hi was am closely following this discussion and i'd like to know more about the bending logics.

Comment by Stan Carroll on June 23, 2010 at 7:50am: Thanks for taking the time to describe. Fascinating subject!!! Your blog was very helpful as well. I start to think about the effects of thickness variation (geometric stiffness) on elastic bending. Your ideal curves seem to be based upon a uniform thickness material. Is there a way to predict the curvature variation as a result of a modulating the thickness of the bent element? I was wondering if subtle thickness variations in the actual saw blade might be responsible for the inconsistencies in the saw blade curvature (in addition to measuring accuracy as you suggested). Conversely, you should be able to determine the micro thickness variations of the saw blade by comparing the actual graphed curvature with the theoretical ideal.

Interesting to think about.
Thanks again,
Stan

Stan

Stan

Comment by Mårten Nettelbladt on June 19, 2010 at 2:53pm: Thanks Stan! I added some details above.

Comment by Stan Carroll on June 19, 2010 at 8:54am: I love this drawing purely as a work of art. I would love to hear the back-story of what this drawing is about.

Stan