Hello MathHeads:

I am a mechanical engineer. Over the years I have allowed my paltry calculus skills get all corroded out in the rain... If they could ever have been referred to as "skills", they are certainly dis-integrated at this point. I shamefully admit that I have happily allowed my CAD software to do my math for me. Now that habit is returning to haunt me. And, I need some help...

I have a real world geometric problem that I am sure has a math function associated with it.

Starting with a flat strip connecting an array of leaves with a given thickness that are touching one another and perpendicular to the strip, roll the strip into a circle with the leaves projecting out. This results in a tube with the leaves protruding outward radially, with their roots touching one another. Bend the leaves over to one side until there is no more space in between the leaves. Generate the profile of a leaf of a given thickness as it lies on its neighbor.

I am ideally looking for the ability to input ID, leaf length, and leaf thickness and generate a neutral axis curve that will somewhat satisfy the requirements.

Hopefully the images I have will upload to make this problem easier to visualize.

Any ideas?

Thanks a lot!


Archimedes Spiral? A real life application...-flat.png

Archimedes Spiral? A real life application...-radial.png

Archimedes Spiral? A real life application...-rolled1.png

Archimedes Spiral? A real life application...-rolled2.png