Just like the ancient Romans (with lasers)¶
In this process, I created a 4 different 2D shapes that could be press fit together: a square, a triange, a pentagon and a small angle joiner (for dodecahedron goodness).
Design¶
Square¶
Started by designing the sqaure piece in Autodesk Fusion. Drew a 4cm x 4cm piece with small rectangular pieces for joining divots.
Started adding constraints and variables: cornerRoundness, sideLength, materialThickness, kerf, indentDepth, indentWidth. All these variables were defined at the beginning of the workflow, so that I could add variables to measurements when creating the objects, and I would not need to edit multiple already created object after the pieces were already finished.
I constrained indents’ outer edges midpoint to midpoint of each side of the main square. I defined all variables to the upper side and indent, and constrained other similar edges to the upper edge.
Pentagon¶
Drew a pentagon with polygon tool. I had trouble changing the default hexagon of polygon tool to pentagon, until I noticed that Fusion asked the number of edges in the same place where it normally asks for dimensions.
Drew a rectangular indent in the bottom the same way that in the square.
Drew four new reactangles for the other indents. Added constraints to it so that it follows the dimensions set by the bottom indent.
Had trouble figuring out how to rotate the indents around the pentagon. Either the indents were not rectangular, or the pentagon warped to too large a size.
Solved it by fixing the center or the pentagon to position and constraining the upper and lower edges of the rectangle to be parallel. Then constrained each indents shorter edge’s midpoint to the midpoint of each edge of the pentagon, and made a contraint that forced those edges to be parallel.
The Triangle¶
Nothing fancy here. A triangle is just a pentagon with fewer edges.
Trouble with indent depth¶
When working with the triangle, I noticed that the indent depth calculation I had used for the square did not work with the triangle. With square it is easy to calculate that indent 1/4 of the side length creates a case where interlocking pieces do not interfere with each other, but with square those dimensions do not suffice. The calculation per piece should actually be distance(edgeMidPoint, polygonCenter) / 2. But as that measurement changes from polygon to polygon, it becomes quite hard to solve if these polygons need to be intercompatible.
I solved the problem by using the smallest possible measurement, which in this case was the triangle. In that case the formula would be ( sqrt(3) / 2 * sideLength ) / 6.
(sqrt(3)/2 * sideLength is the height of the triangle with equal sides, 1/6 is the halfway point towards the center from the edge.) From here.
The corner joiner¶
If I want to make a dodecahedron from these pieces, they need to be able to be joined together in a nonperpendicular angles. The angle between the faces of dodecahedron is about 116,5 degrees. So I needed a piece that could join other pieces together in that angle.
Created the indent rectangles as before. This time I wanted the joint piece to be circular, so the indents needed to be connected to the circle in a different way than to the polygons. They no longer could use the center of an edge as an anchor point.
To accomplish this, I drew two construction lines, that were connected to each other with a 116,6 degree angle, and used their ends as midpoint constraints for the indents. The length of these construction lines was set to indentDepth * 2 + 5mm. Then I drew arcs (with normal lines) connecting the corners of the indents to each other.
Cutting¶
For cutting I used Epilog Fusion M2 40 Laser with the Fablabs predefined settings for 3mm HDF, which were:
| speed | power | focus |
|---|---|---|
| 80% | 12% | 20% |
I jogged the laser pointer to the top left position of an area that was large enough to cut, and locked to jog in place by pressing the control stick. After that I focused the laser. Wit the cutter, the focus needs to be set manually with a small triangular pronger as a measuring device. Once the tip of the triangle hits the cuttable surface, the focus should be right. I moved the bed up by small increments while at the same time watched the triange that swayed a bit with the internal airflow. Once the tip had stopped swaying, I knew that it had hit the surface. After that I made small adjustments to make sure that I had not gone too far.
I cut my pieces. Noticed two problems with my prints:
- The indents were too loose for press fit.
- The joiner piece was way too big, and created gaping holes when joining
I noticed that the problem with fits was that my calculation for indentWidth incorrectly added the kerf to the materialThickness instead of substracting it. Before the formula was indentWidth = materialThickness + kerf*2 and I changed it to indentWidth = materialThickness - kerf*2
The joiner piece was easy to fix, because I had used a formula to calculate the distance between the indents, so I just reduced the distance from 5mm to 0.5mm.
Cutting was easy. In my file, the indents were separate rectangles from the outline, so I was worried that the cutter would cut the outlines first, and the indents later. To fix it, I used colors to determine the order the pieces should be cut. This way the indents were cut last. (Except for the square, in which the indents were trimmed to be part of the outline.) In the final file, there are blue lines (#0000ff), red lines (#ff0000) and black lines (#000000) that are intended to be cut in that order (i.e. blue, red, black). (Please note, the final file may seem blank, as the linewidth is set to 0.02.)
In the laser settings, I made sure that each color had the same power, speed and frequency as the material (3mm HDF) required for successful cut. Then in the settings, I dragged the colors in the correct order that I wanted the cutter to cut them in.
smkds
Assembling the dodecahedron was easier than I anticipated. I expected to have trouble assembling it, as the fit was quite tight, and I had not added any chamfers to the design. In the end, there were hardly any problems, even the last piece needed just a bit of additional leverage from a nearby screwdriver.
