Wide and narrow crimp bends

Most of the origami I’ve done for the past several years has been based on shaping tubes of paper in various ways, whether that’s by adding curves or intersecting the tubes with vertical or diagonal planes. One thing I’ve wanted to figure out for a while is how to create bends and curves in the paper tubes. I’ve explored some simpler approaches to that problem before, but this is the first approach I think I can realistically use as a part of a more complex model.

The concept here was inspired in part by my diagonal shift design. The top and bottom edges of the bend are both sine waves, which get folded such that they touch each other along the bend line. Inside, each gore has a small crimp to create a partial flat plane visible inside the model. The crimps all have slightly different angles, but the mathematical to find those angles is the same that I used for the diagonal shift.

Here’s the inside view for a simple tube of paper:

Inside view of the wide crimp bend

Things get a bit more complicated when there is already overlap of the paper along the outside of the tube, but the concept is the same. It’s harder to see, but there’s a similar partial plane of paper inside this one, too:

Inside view of the narrow crimp bend

It’s a decent bit of work to measure and score all the appropriate lines for these, especially for the narrower tube, but the folding went more smoothly than I expected. Especially with a bit of wet-folding, all the crimps seem to form fairly easily. I have quite a few ideas of how I’d like to incorporate these into a variety of more complicated designs.