Laser-cut Hinges (a.k.a. kerf hinge, living hinge)
Designing a pattern to allow flexibility in a rigid material can take a lot of trial and error. However, with a bit of persistence, as well as an understanding of a few rules, you can turn a solid sheet of plywood into a flexible work of art.
There are a number of constraints that will affect whether or not your design will work. After a lot of attempts, I have tried to codify the rules that seem to govern how to make a strong, functional hinge in plywood. I used 3 mm thick birch plywood - thicker material will need more material removed, and thinner stock should be fine with less taken out.
Step 1: Make the Long Axis of the Repeat Unit Perpendicular to the Axis of Bending
When you pick a 'repeat unit', you need to orient it correctly. The long axis of that unit (green) needs to be perpendicular to the way that you want the hinge to bend (red).
Step 2: My First Attempt
This was one of my first attempts, using a leaf shape for a ‘fall themed’ project. Although the shape is somewhat elongated, there is too much material between the repeating units, especially in a diagonal direction. This results in a piece that is actually very rigid. As you can see, it failed at multiple points when it was flexed.
Step 3: Figure Out Your 'Repeat Unit' Spacing
You need to have enough space between your repeats. Too close in either the horizontal or vertical direction will result in a design that will fail as soon as it is flexed, or even fall apart as you try to remove it from your laser.
The spacing is a function of both the material and the laser - you will need to do some test cuts to find the right combination of speed, power, and pattern spacing to get something that works for you.
Step 4: My Revised Spacing
This is about my third attempt. While more flexible, the near-contact points at the leaf tips and at some of the leaf petioles resulted in a very brittle hinge, that failed very easily.
Step 5: Yet Another Revision
This is approaching a workable design - it fixes the horizontal and vertical spacing somewhat, and addresses some thoughts that I developed later (see the next steps).
Additionally, I found that leaving more material at the outside edges, the top and bottom of the hinge, made for a stronger piece. When the hinge flexes, the inside edge can touch along the sections that remain, and seems to act like an arch, more effectively distributing the bending forces.
Step 6: Final Version
This is a close up shot of the final spacing tests. Notice that the space between the tips is slightly larger, as well as between the leaf petioles.
Step 7: So You Have Something That Flexes - Now What?
The amount of curvature is a function of both the amount of material removed and the number of repeats ‘wide’.
The more material that is removed, the more gaps there are available for flexing.
This version, with a bit more material removed, will flex more.
Step 8: Hinge 'width'
The more 'repeats' that you have, the greater the length available to spread out the bend, and the more robust the hinge will be. The wider example here will be able to flex farther, and also survive more cycling than the narrower one.
Step 9: How Tall Should It Be?
It also turns out that you need enough height to distribute the bending load as well. A very short hinge seems to fail more easily than a longer one.