The photo above shows two different realizations of a working origami roller bearing;
The yellow bearing is the inner yellow triangle and the 3 inner rolled sheets of paper making the cylinders.
The Red Bearing is folded from a single 21 inch square sheet of card stock (very light poster board). The rollers are simulated using inner fins that are folded curves.
This Red one is the entry for this challenge.
The yellow bearing was my original concept before I learned that you had to use a single square.
Both will spin relatively freely on an axel. You could use any rod including a tightly rolled sheet of paper.
The yellow bearing will support considerable weight. I have used additional card stock to make arms which are strapped to the inner triangle. Arm extensions can be added by inserting additional material. I have tested the yellow bearing with three arms that were over two meters in length. The bearing still rotated freely with very minimal effort.
I also strapped 15 (1 inch) wooden blocks to test for weight. The rolled cylinders do not squash perceptibly and provide a relative smooth rotation with very minimal effort.
The red bearing depends on the strength of the paper for bearing up under weight. I believe the fins will squash inward but have not tested this bearing under substantial weight. Under moderate weight, it holds up quite well.
You can reduce the width of the red bearing by using a narrower rectangle, thus reducing the friction caused by drag. I can see using this roller on a vehicle that will roll on slight inclines. I might have to try this with either my Duesenberg or my fire truck.
For a discussion of machine design with bearing go to this link:
http://machinedesign.com/whats-differen ... bearings-1
You will notice that most bearing have many more rollers. I decided that for my “paper only” design that just 3 contact points would be most efficient.