Carl Friedrich Gauss distinguishes between three types of curved surfaces, single curved - neutral (cylindrical), and double curved - negative (hyperboloid) and positive (spherical).

Curved surfaces are very attractive, especially negative double curved surfaces, but also very complicated to perform. What’s interesting about them in constructive terms is the increase in stiffness and load capacity as the surface is bent in one and two directions.

In a small book DIGITAL Gehry Material Resistance Digital Construction (Bruce Lindsey, Bitkhäuser 2001) writes that if flat piece cost one dollar, single curvature piece cost two dollars, double curvature piece cost ten dollars. This is true for all materials wood, metal, plastic, glass, concrete ...

It is immediately clear why some engineers are crazy about double curved surfaces and are constantly trying to find a method that can simplify and cheapen the process.

From time to time I search the Internet on that matter. One day I stumbled upon the wooden book covers that can be done on a laser cutter, with interesting technical solution of the spine; wooden board is slit in such a way that can be bend like rubber.

I immediately turned my machine on and started playing with this surface. The feeling of holding that piece of wood in my hands was incredible, something that just seconds earlier, was a stiff piece of plywood was now flexible like paper. But only in one direction, in the other was still stiff. Then I decided to cut the surface to enable it to bend in both directions, so that I could achieve double Gaussian curvature, positive and negative. After a couple of failed attempts that were based on a variety of perforations, I realized that what I was doing didn’t make any sense. I've studied the way in which the first surface was cut. In order to be bent it was turned into a series of slender elements that are easily twisted, which are interconnected on fixed points. The greater the distance between the fixed points, and the slimmer the elements, the more flexible the surfaces is. Although an element can twist for only a few degrees (before it breaks) when multiplied many times, the flexibility is incredible. I realized I should apply the same theory in both directions – so I turned the line elements into a rectangular spiral, whose segments twist in both directions, and in that way I connected the fixed point with very long slender elements. The result was even more fascinating.

When you first hold plywood cut in such a way it completely surprises you, you are not sure what exactly is in your hand, you cannot believe that it’s wood, because the lack of rigidity gives you a totally different feeling.

But, what to do with this piece of flexible plywood? I have some ideas, but I would also like to hear more suggestions ...


<p>Very cool!</p>
<p>Absolutly awesome, Thanks so much for posting this project. I just got a laser printer and this has been a real inspiration for me</p>
<p>perfect! a greek maiandros</p>
<p>This is really awesome! I had an idea to use this for a laser-cut chair, it would be nicer to sit on a surface like this than something flat and stiff!</p>
<p>Was thinking it would be more flexible. It was not. I think my setting were off because it smoked more then I wanted.</p>
Is there anyone that would sell sheets of this already done to be used for fashion design. I dont have a laser cutter but im so interested in experimenting with this material for design.
<p>Very inspiring, I made my own patterns based on this idea<br><a href="http://msraynsford.blogspot.com/2016/01/flexible-sheet-3.html" rel="nofollow">http://msraynsford.blogspot.com/2016/01/flexible-s...</a></p>
<p>Really nice, thanks for sharing! So many possibilities for floppy plywood and it's a beautiful pattern in flat sheet form too.</p>
<p>I've had a go at working this design using a hexagonal base instead of a sqaure. This way there are three axis the material can fold along. The edge isn't nearly as neat as your square design but I thought you might be interested to see it.</p>
<p>very nice, does it bend more? can you share the file?</p><p>thanks</p>
<p>This bit doesn't! Each element is a lot bigger so it's a less smooth curve. That and I made the file in a rush to have something ready to try at a maker day. The pattern isn't quite lined up so there are some weak points. It's a bit rough around the edges but it shows the idea. </p><p>I think it is worth more work. I'm going to learn how to create SVG markup programaticaly and try a more accurate version </p>
<p>Hmm, that was SVG when I uploaded it not .jpg. How do I link to a file in comments?</p>
<p><a href="https://www.instructables.com/files/orig/FP2/CXHY/IH29I3BB/FP2CXHYIH29I3BB.svg">https://www.instructables.com/files/orig/FP2/CXHY/I...</a></p>
<p>Very beautiful. I wish I had a lazer cutter. I hope they will make a consumer grade one that is affordable soon.</p>
They have, check out the glowforge http://glowforge.com/referred/?kid=mkEgpH
<p>Hmm. I'm going to wait and see if they can deliver on all those amazing promises. I hope they do though.</p>
Awesome Pattern! Is this under Creative Commons? Am I able to use this however ?
<p>Yes, you can use it how ever you like!</p>
<p>This is a fascinating cut - I had to try it as soon as I saw it.</p><p>The sample in the photo is your file, sized at 100x100mm, cut into 3mm plywood.</p><p>Now I need to come up with a use for this...</p>
<p>A simple bowl? Perhaps vac-formed over a form, impregnated with epoxy. I wonder if/how that could be done.. hmm.</p><p>Very intriguing cut indeed!</p>
<p>Well, it won't <em>vacuum</em> form, what with it being mostly holes...</p><p>Maybe soak it in glue/epoxy and then press it into another bowl with a plastic bag full of sand?</p>
<p>Should have been more specific, vacuum <em>bag forming</em> I think would work, although managing the mess of epoxy might be a real issue. </p><p>Just thinking out loud (in print?) because it's such a neat idea. Perhaps someone reading that has all the needed tools will run with it. I think that cut pattern would look amazing in a bowl shape!</p>
<p>Lets just say that with a laminating press and the right tools it works with other materials. So should also work with this. But it heavily depends on what you want to make, this pattern is quite inefficient to cut due to its very long cut distance. If you're aiming for something very specific you can usually come up with something more efficient in terms of pattern. Additionally forming these things causes a few issues you probably wouldn't think of right now, this design would not be suitable for it most likely.</p>
<p>Oh, yes, like they laminate the curved deck of skateboards, got you now!</p>
<p>should vaccuuform easily.. put it under plastic sheeting and suck the air out. the cuts will in sure that all the air comes out. </p>
<p>Sure It'll vacuum form. Just use a cover sheet/release agent like you would fiberglass or carbon fiber items.</p>
<p>Of course.</p><p>However, I don't have a vacuum former, and I am currently too busy to build one.</p>
<p>Based on the video, I think it seems to most resemble thick leather. How about one of the many leather projects like a phone case? Or you could make a bracelet(with RFID?).</p>
<p>I have had an idea, and I'm in the middle of drawing files, but I teach, and term starts today, so my output is going to be curtailed for a while...</p>
<p>Looking forward to it. Quality over quantity and quality takes time :)</p>
<p>I admire youre speed, it took me a year to publish this project, I really wish I am so quick as you are</p>
<p>it's the Immortal Kiteman we're talking about. :P i'm not suprised. </p><p>i wonder if it's possible to plan your shape in such a way that you can get a 3D object out of a single piece of such material. i LOVE the way it looks. but what can be done with it? mm.. </p>
<p>Practice, practice, practice!</p>
<br>I'm a tactile type and I bet that feels interesting to hold. I'm going to have to visit the makerspace over in MesaAZ and make one!<br><br>I chided the great MasterFounder &quot;ewilhelm&quot; on his waste in the https://www.instructables.com/id/Nautilus-Bookshelf/?comments=all#CR96PO8IBM22YOF <br><br>A simpler pattern of this would be a nice way to duplicate his shelving with lower wasted sheet count.<br><br>The pattern brings to mind the Ennis House: https://en.wikipedia.org/wiki/Ennis_House used in many movies.<br>
<p>You wouldn't need a cut this complex - the original 1-direction living hinge would work, and you can even buy flexible plywood that could be laminated in shape for strength.</p>
<p>I think I have a unique use. By carefully varying the size and/or density of the cuts, you could create a pattern that would automagically &quot;fall&quot; or drape into a desired pattern. For example, the prow of a boat. The gently curved sides would have fewer cuts. The bow would have more, and so on. It would take a lot of trial and error, or a genius, but you could make a design drape into almost any OPEN shape.</p>
<p>Super cool</p><p>I made it</p><p>!~!!</p>
<p>this looks insane! I need to find a laser cut machine =D</p>
<p>Can be used for boat building, car modeling or making any jigs you need!</p>
<p>Best wood bending laser cutting file ive cut so far!</p>
<p>Best wood bending laser cutting file ive cut so far!</p>
<p>Best wood bending laser cutting file ive cut so far!</p>
<p>That's just neat!</p>
<p>it might be a great veneer for skateboards, Longboards etc. </p>
<p>Consider the material more like a stiff fabric as to what it could be used for! Plus, the thickness of the wood can change the way it would be used, too. Seats, dashboards, bowls, screens that curve, wall coverings, shades / window covers, lampshades, ...</p>
<p>Maybe use it as a hot pan/pot pad in a kitchen. No point really I guess to be flexible for that though... except that it's so cool.</p><p>You did this on a 60W CO2 machine? I've gotta try it.</p>
<p>I could see how you could build furniture with material in this by laminating it with a layer of 1/16th thickness on the outsides and several of these layers on the inside. In building instruments that would be made of laminate like you see with the Gibson ES 335, this material could be used for that. I do think that this process wouldn't be better then traditional manufacturer techniques.</p>
<p>Not sure what the cost per square foot would be for that material, but my application would be in contoured boat building, more specifically canoes. Once it's been shaped over the skeleton, an application of fiberglass resin will fill the voids sealing it and setting it's final curved shape. Aircraft grade plywood isn't normally as durable as fiberglass, however I believe the structure you've created would remain uniquely flexible and still profoundly strong. What I'm implying is I think you could get away without layering fiberglass sheeting and still maintain all of the strength you would have had if you did. Fiberglass is $1.50 per square foot and cedar is around $2.50. If your cost is below that, you would have a truly unique product I'd be interested in.</p>
<p>Would it be better than fully plastic canoes or would you be interested just because it looks really friggin' cool?</p>
<p>this is excellent! I can't wait to incorporate this into other designs.</p>

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