3D finger tenon joint and hammer joint laser cut from birch plywood

Supplies

Fusion, laser cutter, birch plywood

Step 1: 3D Finger Tenon

Make some parameters in Fusion. The width of the component needs to be 5 times the material thickness. Start with an extruded rectangle and cut material thickness size notches in the end, side and middle as shown. Each of the notches are material thickness in width. Notice there are two unit of cutout on the sides and that the middle cut is four units in from the end.

Step 2: Pattern

Use lines from the midpoints of the edges to find the midpoint of the component. Use this midpoint for the center of a circle. Make a circular pattern with the circle as the axis. Set the number to 2 and the pattern will duplicate to the other side. This step is only necessary if you want to keep expanding your joint with more pieces. A single joint only needs one end to be notched.

Step 3: Second Shape

This shape was a copy of the first with some additional cuts as shown

Step 4: Assemble Joint

I won't spoil the joy of figuring out how the pieces fit together. These pictures should make it fairly clear. I have yet to get a chance to experiment with adding more joints to this first one, so I'm not really sure if it's possible given the way this joint snaps together.

Step 5: Hammer Joint

This joint is a mortise and tenon joint that results in smooth joints at 90 degrees. The shoulder height is the material thickness with the wedge sticking up an addition material thickness above that. The width of the wide part of the wedge should be at least 3/4 of the overall width of the mortise. The length of the gap below the wedge should be the material thickness. Be sure to clear enough material below the wedge for the wedge to easily drive into that space. Small tabs of material can be left of the sides of the wedge to keep it in place until it is hammered down. I ran out of time working on this joint and hope to iterate on it some more.