Introduction: How To: Make Curved-Fold Origami Sculptures

By
About: Hi! I'm the Donut-Man. I'm a junior studying Mechanical Engineering, and in my free time I enjoy making all types of paper art, designing projects in SolidWorks, playing soccer, driving hobby-grade R/C cars, h…

Hi there, and welcome to this instructable! Here I will be showing you how to fold simple yet elegant origami sculptures using curved creases. I was inspired to try this myself when I saw a ceramic bowl with wavy, rippled edges that I thought would be cool replicated in paper, and I soon found it could be done using concentric circular folds. Now I get to share the same technique with you!

As a disclaimer, I did not create or add to this method of folding at all; I simply found an effective way of recreating it myself. Much of my inspiration has come from a leader in curved-crease folding, Erik Demaine, whose work can be found here. Enjoy and good luck folding!

Step 1: Tools of the Trade

To create these beautiful pieces, you will need 4 tools along with your paper:

  1. A cutting board (preferably 10" x 12" or bigger)
  2. An X-Acto knife with a fresh blade
  3. A ruler with clear markings
  4. A drawing compass (preferably with 2 metal tips)

Step 2: Picking Your Paper

The paper you choose for this project can have a big impact on the look and effect your model will have and how easy it will be to fold. While this can be made with most papers, I would recommend paper with a thickness in between that of copy paper and card-stock. If you want to use materials specifically made for origami, you can search for origami-paper stores online or in your local area. I get my paper from origami-shop.us, a US-based distributor of origami-shop.com that has a fantastic selection of specialty papers in a wide range of colors, textures and thicknesses. For this instructable, I used a 27" x 27" sheet of Blue Grainy paper and a 28" x 28" sheet of Ivory Elephant Hide paper, both of which are roughly 110 gsm (relatively thick for origami paper). This thickness allows the paper to be easily scored and to hold its shape well after it has been folded and twisted into position.

Step 3: Let's Make It!

To make the basic curved-fold shape, you must first draw (or score) and cut out a thick ring from your paper. For this example I cut rings 33 centimeters in diameter (I could get 4 out of the sheets I ordered), but you can make them any size you want! I personally think bigger is better in this case, because you can fit more circular pleats into a ring without making too small a hole in the middle. The more pleats you have, the stiffer your sculpture will be and the greater the flowing effect your paper will have

You will first have to decide how large your rings will be and how many pleats you want. However tall you want your pleat will affect how many you can fit and will equal the difference in whatever radius you will be scoring. I chose a pleat height of 1 centimeter, a max. diameter of 33 centimeters and a minimum diameter of 17 centimeters. You will want an odd number of scored circles so that your outermost and innermost pleat ends will be pointing the same direction.

Once you've decided on your ring size, take your compass and angle it so that the tips match whatever your circles' radii will be. Mark the center of your paper and trace your circles, applying light pressure on the paper. If your compass is like mine (with 2 metal tips), you can score the paper directly with the compass. If your compass has a graphite end, you will need to trace your circles and then score them with a dull blade, the head of a pin or the metal tip of your compass. You can then erase your graphite marks and move to the next step!

Step 4: Forming the Shape

Use the outer and innermost circles as guides for cutting your ring out, and then begin slowly pinching your mountain and valley folds together. I found that working from the inside to the outside works best. For much of this preliminary shaping, your paper will want to revert to being flat again, but keep gently creasing until the entire ring is done. The paper should have the rough shape of a Pringle; this is because as the folded pleats become more compressed, the paper must curve in an increasingly tighter radius to follow the curved creases. Slowly compress small sections of the ring to establish the creases a bit more, and then pull one end through the hole in the middle. This essentially inverts one side of the ring and creates 2 pretty tightly looped sections that you can use to "break in" your piece and make it much more pliable. Take each tight loop and work it around the full circumference of your ring; this will make your creases more permanent while smoothing out any straight sections that don't want to follow the curved pattern.

Step 5: Almost Done!

Once you're done smoothing out your piece and un-inverting it, you should have the basic saddle shape with well-established creases ready for forming! Now for the really fun part: experiment with the paper and see what shapes you can make with it! Once you find a form you really like, display it for all to see or combine it with other pieces to create an even more impressive sculpture. Congratulations, you're finished!

Please let me know if you have any questions, and post your finished projects in the comments below! I'd love to see what new shapes you come up with.

Thanks for tagging along and good luck folding!