Curved Folding

foldable=makable

Big Project (for me)

I am certainly new to curved folding, but not new to sheet metal forming. I have a project that is currently over my head. What I want to do is provide a basic 2D geometric shape of an open obround slot projected perpendicular to its plane to define the curve in 3D space for a curved fold. For clarification, see the pictures I have attached. Based on the pictures I have seen posted by others on this site, it appears to be a relatively simple task to do just one of these folds from a defined curve, (a task which I have yet to tackle successfully) but I'm not certain how to define a curve for a developable surface from a pre-constraining set of geometry. The only secondary constraint other than the given geometry is that the developable surface at the apex of the curve in Z must be at 45 degrees. The attached images are best-guesses of the curve, and surfaces from Autodesk Inventor, but the result is made from two pieces and definitely not a developable surface.

I am new to Rhino, Grasshopper and Kangaroo so am still in the early stages of learning how to get what I want out of them, but am amazed at their flexibility over the cookie-cutter 3D modelling programs I am used to in industry. I am also familiar with Calculus from school almost 20 years ago but I am finding much of the terminology such as osculating planes, TNB frames, curvature and torsion outside of the scope of my experience. Until now, I've relied on the software to figure this kind of thing out for me. Now that I am having to define them for the software, it's a completely different story.

Any direction, assistance and Grasshopper sample files in this bent that I can learn from are more than greatly appreciated!

Tags: constraints, curved, developable, fold, geomerty, grasshopper, metal, sheet, surface

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Permalink Reply by Gregory Epps on June 22, 2010 at 16:35
Hi Shawn - this geometry is typically used in industry to translate sheet packaging material to cylindrical products... biscuits basically! I would recommend you model this in Tomohiro Tachi's free software to model this ; if you look at some of the previous work in this area on the website, you can see how it could be used to ensure you have a viable geometry to develop to 2D.
Permalink Reply by Shawn Fernandez on June 22, 2010 at 18:33
Translating sheet material to cylindrical product is exactly what I am doing. What I have works well now, but I know that it is not "correct." It has been developed through trial and error and I want to be able to develop a system for generating these for a very wide range of shapes.

Tomohiro's software seems great for folding up a pattern that you already have. I can't seem to figure out how to get it to do a curved fold since it wants a target angle for the crease line. The target angle is constantly changing as it progresses along the curve.
Permalink Reply by Gregory Epps on June 23, 2010 at 8:51
I would recommend you refer to Helmut Pottmans book on Differential Geometry, where he shows this problem, and the development (I think). But the best approach for now is to use trial and error with card the same shape as your sheet - then add rulings by placing a ruler on the surface until it touches along the length and draw straight lines - these will be the folds for Tomohiro's software. You can modify this quickly in 2D - but you will have to re-run it in TT's software until you output the desired mesh. If you are looking for a parametric 3D model then Kristoff Joesffson might be able to help you with a single crease method in Grasshopper.
Permalink Reply by Shawn Fernandez on June 30, 2010 at 14:59
Thanks will do. =)
Permalink Reply by Max Angeli on July 14, 2011 at 8:57

Hello! I've noticed your post and wondered if you have been able to follow through. I'm an independent consultant and a member of a small university research team. Our objective is to study specific processes used in the packaging industry and in particular those related to forming shoulders.

I don't know if you want or can share further details about the geometries you posted, but have you been able to model those parts in Rhino and other plugins so that you can easily modify them later?

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