# Origami Electronics Enclosure

## Custom Design Modula Origami Box

In an effort to make a minimalist digital clock, I was looking for an easy to construct enclosure for all the small electronics modules, such as AAA battery, display modules, and MCU boards etc.

Yes, 3D printing is still outside of my skill set.

Interestingly, I’ve seen origami paper boxes, as introduced in this youtube video (link), which can be traced back to Tomoko Fuse’s earlier books (Amazon link). In her recent 2018 book, she used the term “modular origami”, which roughly speaking is a technique of stacking cleverly multiple identical origami pieces, called modules, to form a complex 3D structure. A 3D box is the simplest one of these structures.

This works well for electronics enclosures.

Because individual module, folded with a piece of paper, can have slots, holes cut into them with ease.

It then joins with other pieces to form a 3D box. To emphasis, this is origami, no glue or stapler. Everything is easy to assemble/disassemble, but hold together strongly. Another advantage for prototyping electronics.

In that youtube video, four modules assemble into a square box, and a different four modules form into a lid for the square box. Each module is folded from a square piece of paper.

However the paper doesn’t have to be square. In fact you can customize the width and height of the final box by using a rectangle shaped paper, following the formula below. This assumes the same folding method, as described in the video.

To design a 3D origami box with a wall height of `B`, and a width of `A` , you can start with four pieces of paper with

`width = 2 A and length = 2 B + A`

For example to divide 8.5" x 11" US Letter paper into four pieces, that amounts to

`4A = 8.5" and 2(2B+A) = 11"` resulting in

`A= ( 2 + 4/32)" and B = (1 + 9/32)"`

That is a box size that can fit a lot of electronics inside, and along its sides.

The lid, per the video, has to come from a square sheet of paper `2A by 2A`. After folding, the lid has its width `C` and depth `D`. The following formula has its relationship to the box dimension `A` :

`width C = 3 √2/4 A and depth D = √2/4 A`

As you can calculate, `C` is about 6% larger than `A`, which fits well for a small box.

In our case of `A = ( 2 + 4/32)"` , that amounts to

`C = ( 2 + 8/32)" and D= 24/32"`

That’s an extra width of 4/32" on all four sides. It doesn’t feel like a tight fit lid anymore.

But there is an easy fix with some math to the help.

Let’s say, instead of folding the bottom-left corner to the center, we can move along the diagonal line further inward. That shortens 2C, which can make the lid fit tighter around the box.

In the case of US Letter paper, if we make `2C’ == 2A`exactly, where is the folding point (big black dot) on the diagonal line. Here are the two equations

`2C' = 2A = (4 + 8/32)" = x + y and x + 2y = 2√2 A = 6"`

to solve for x, y. The results are

`x = 2.5" and y = 56/32"`

It means that pick the corner folding point to be 2.5" from the upper right corner on the diagonal line, as for the lid depth F, since `y = 2F = 56/32"; F = 28/32"`

Comparing with the earlier `D = 24/32",` now F is `4/32"` deeper, which is the same size shortened from the lid width.

You can move the dot along the diagonal line to size for different lid tightness.

Final note: Here all the dimensions stems from the original US Letter paper size in imperial units. They are kept in fractional numbers, so that it is easier to measure with an imperial ruler (nothing to do Palpatine, if you urge to ask).

(to discuss my minimal digital clock soon)