Origami and Kirigami

I enjoy doing Origami and Kirigami for quite some time now, even if I very rarely find the time to do something about it. Here are some examples, an easy dragon and a hard camera as a gift from a sturdy 50€ bill. So I decided to do something with these skills this week.

Dragon

Camera

Research about it - get inspired

I started off with some research about origami in science and research about it. It is actually amazing what applications origami has, one example is unfolding a solar array in space, which needs to be cylindric to fit into the rocket.

The latest work of art by Robert Lang

A nice source is Robert Lang, who is an origami designer and also works on the mathematical backgrounds of origami. He lists several papers on his site on the topic of origami with thick materials, deployable structures and deployable mechanisms. As well as a lot of design tools for computational origami. One example is the origami simulator which is a nice tool to see how a crease pattern folds, and also with quite some examples to play around.

Origami simulator

I also looked into the MIT Lecture on Geometric Folding Algorithms, which has also a part on architectural origami.

Kirigami

As a first experiment how good I can work with paper I decided to recreate a popup card from Peter Dahmen. Therefore I created the template for the cutting in inkscape, redrawing the pdf Peter Dahmen has available to download.

The finished svg

I decided to use a laser cutter for cutting, to be more precise and faster. I used thick paper (200g/m²) so I needed to cut halfway through the paper for creasing the paper.

The cut paper with the lasercutter

Pre-creased with the cutter

Then I folded the creases and stuck the lower parts together, so it can hold the form. It's still a bit round and can be glued to a piece of paper, then it looks even better.

The finished model

Could be glued down to look better

Origami

Christian showed me the Maze generator by Erik Demaine and immediately I wanted to create a maze displaying FabLab Aachen, but this turned out to be a bit too hard, looking at the crease pattern. The crease pattern is linked below if anybody wants to try to fold it.

Rendering

Crease pattern

But something more realistic is using the Miura Ori fold to create a pattern. This pattern is just a geometric pattern, but the nice thing is that it can hold some weight. So it is great for supporting structural weight with a very small structure. It is also able to fold to a very small flat strip. My first test was just printing the crease pattern and doing it by hand:

Crease pattern for Miura Ori pattern

What I realized then was that the most time is needed to pre-crease all the folds that need to be done, because otherwise the flat sheet of paper won't fold into this sheet. I only had a small sample, but this will increase with bigger sheets and more patterns.

The folded Miura Ori pattern

Designing

To design the pattern with different angles and sizes I wrote an Inkscape plugin that lets you input the desired characteristics and will create the pattern for you. To install it you need to look where your User extensions folder is by going to Edit -> Preferences -> System in Inkscape and copy the miura.inx and miura.py file there. When you restart Inkscape you should find the plugin in the Extensions menu.

The Inkscape plugin

In the plugin you can set how many cells the crease pattern should have horizontally and vertically, at which angle the zig-zag lines should be and how wide and high each cell should be. The plugin then adds the pattern to your current layer.

The Inkscape plugin working

The plugin is written in python, but the documentation on how to write plugins is wuite bad. My starting point was this general plugin development page. Then I read this tutorial on how to write an effect plugin for Inkscape with python. But this example only helps for this specific case, I needed to add paths with my plugin. Luckily I found this example template plugin, which somebody published. It isn't explained, but does a lot of stuff and I could figure out which functions it uses to add paths. Then I just needed to write a function to add lines and use this to draw the miura pattern.

Just a few notes to the code of the plugin. I found that to add paths with a plugin you need to generate the corresponding svg code by yourself and append it to to the file. This is done in the following function:

def points_to_svgd(p, close=True):
    """ convert list of points (x,y) pairs
        into a closed SVG path list """
    f = p[0]
    p = p[1:]
    svgd = 'M%.4f,%.4f' % f
    for x in p:
        svgd += 'L%.4f,%.4f' % x
    if close:
        svgd += 'z'
    return svgd

To get this svg code into your file you then need to generate a style for the path, put it together with the path into attributes for the path node and add them to a group:

def create_path(points, color, group):
    # Create path
    path = points_to_svgd( points )
    # define style using basic dictionary
    style = { 'stroke': color, 'fill': 'none', 'stroke-width': 1.0 }
    # convert style into svg form (see import at top of file)
    mypath_attribs = { 'style': formatStyle(style), 'd': path }
    # add path to scene (Create SVG Path under group)
    inkex.etree.SubElement(group, inkex.addNS('path','svg'), mypath_attribs )

Cutting

So when you want to create a really big sized version of this pattern it would be really nice to have something to pre-crease everything automatically, so I tried to do pre-creasing with the lasercutter. I used 200g/m² paper, because it is more sturdy and therefore will hold more weight and will also hold it's own structure better. A Vinylcutter would be an alternative, but our is temporarily out of work. It would remove the burn marks from the paper, but if you don't mind them the lasercutter work also fine.

At first I tested which laser cutter settings I would need to burn away so much material that the crease would be easily foldable but still strongly connected. I did lines and dotted lines each with different power of the lasercutter. It turned out that for this paper and a 30W lasercutter (Epilog Zing 6030) for creasing I used a power of 9%, speed of 100% and frequency of 500. For cutting I used a power of 20%, speed of 80%, frequency of 500.

The test creases

With those settings I cut the small Miura Ori pattern again. With the pre-creasing already done it was really fast to fold this pattern.

The cut Miura Ori pattern

The folded Miura Ori pattern

Then I went to create a complete A4 page of this pattern.

The lasercutter while cutting

The cut pattern

Folding this was a bit harder, because of the sheer size of it. But it turned out really great:

The finished pattern

The advantage of this pattern is that it is a big sheet that can be stored in a much smaller room:

The squeezed pattern

At last, I couldn't resist to make a weight test and tried to stand upon the pattern. I would say I could shift half my weight on it, but when fully standing on it, it broke down. But I guess the problem here was that I put too much weight on the back of my feet, because it only broke down there. And when you restrict the spreading of the pattern it should work even better.

Standing on it

The broken pattern

Files

Here you can download the files created during this week:
The maze crease pattern
The Inkscape plugin for the Miura Ori crease pattern
The Miura Ori crease pattern
The Miura Ori crease pattern for a full A4 page of paper
The kirigami cut template