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Half-lap intersecting slices

· Fox Bright

Two flat profiles, a slot in each, and they slide together into a 3D form. The fastest way to get a solid-looking object out of sheet material.

A rendered flame made of two intersecting laser-cut profiles slotted together at right angles.

This is how flat-pack furniture, stage props and a lot of laser-cut decor get made. Take a 2D shape, cut it twice, slot one piece from the top and the other from the bottom, and push them together. The slot is exactly the material thickness. Everything else is up to you.

The sketch

Start with your outline. Symmetrical shapes along a centre axis are easiest, but anything works if you can find its middle. I traced a flame from a canvas image.

  1. Set a user parameter for material thickness (3 mm for our plywood after kerf).
  2. Draw a centre rectangle whose centre point sits at the centre of your shape, and whose width equals the material thickness. Its height should run the full height of the shape.
  3. Draw a line across the middle of that rectangle so it splits into an upper half and a lower half. You now have closed profiles: the shape with a slot from the bottom (piece A), and the shape with a slot from the top (piece B).
Fusion sketch of a flame shape with a thin vertical rectangle through the centre
The flame outline with a centre rectangle the width of the material, split at the middle.

For splines you will be estimating the centre. Get it close, extrude, and look. If it is off, drag the rectangle in the sketch and everything downstream updates.

Extrude and align

  1. Extrude the profile with the lower slot by the material thickness. New body.
  2. Hide it, then extrude the profile with the upper slot by the same amount. Second body.
  3. Move one body out of the way so you can see both.
  4. Align the two: click the middle of the slot face on one piece, then the middle of the matching face on the other. The pieces snap together but flat; set the angle to 90° so they cross.
Two extruded flame bodies being aligned at right angles in Fusion
Align puts the two pieces together; the angle setting turns one perpendicular to the other.

Hide one body, then the other, and check that each piece alone makes sense as a flat part with a slot. That is what the laser will cut.

A phone holder from the same joint

The laser-cut phone stand is this joint turned sideways: a side profile with a slot, and a cross piece with a matching slot, pushed together at right angles. The side piece is the shape, the cross piece is the foot, and the slots are the material thickness. Draw the side profile with the lean you want, put the slot where the foot should land, and extrude both by the thickness. If it rocks, the slot is loose; if it will not go together, the slot is tight, and 0.05 mm either way on the parameter fixes it. Two slots in the side piece give a stand that holds a tablet as well.

From here

Make the bodies into components if you want to arrange them on a sheet, or add a third slice at 60° for a rounder form. The same idea scales to a whole shelf built from intersecting slices, or a lampshade with a dozen. For the kerf side of this, read Kerf, explained.