Expanding 3-4-5 triangle

This is an expanding mechanism: it goes from small to big, and it has one degree of freedom. In the first photograph, the two triangles are identical copies of this mechanism. The green triangle is fully expanded, while the white triangle is fully collapsed.

Assembly

I have uploaded the same print files in both stl and step formats. The parts are designed to be printed with 0.2mm layer heights and support. It's probably a good idea to print just a few of the parts at first, to make sure that they can be cleaned up nicely and slide together smoothly. I have printed these parts in both PLA and PETG. I found the PLA could be a little “sticky”. PETG seems to have lower friction. Putting a lubricant (e.g. Vaseline) on the rails and grooves before sliding the parts together will reduce friction.

Along with the 3D printed parts, you will need M3 nuts, and bolts with lengths at least: 14mm (nine bolts), 18mm (one bolt), 25mm (one bolt), and 30mm (one bolt).

The 3D printed parts are labelled on the pdf “expanding_345_triangle_parts.pdf” and “expanding_345_triangle_assembled.pdf”. Note that there are many identical parts, and a few special parts near the corners.

Each double rack is made from two printed parts, bolted together through a gear. (There is some extra space between the two parts where they meet to accommodate roughness from removing the support material.)

I find it easiest to assemble the three sides of the triangle first, and then bolt the three sides together at the corners. 

Slide the racks of each side together and collapse them down as far as they will go before inserting the gears (parts G) and caps (parts C) and bolting through. This should ensure that the gears are aligned with the correct teeth of the racks. 

Similarly, make sure that the sides of the triangles are all fully collapsed before you connect them together through the corner gears. 

More mechanisms

The parts in this design can be repurposed to make expanding square grids. Use parts 

• U1 and U2 to make double-racks on the upper layer, 
• L1 and L2 to make double-racks on the lower layer, 
• G1 as the gear where the upper and lower layers cross, and 
• G and C where they do not cross. 

Use parts U1e, U2e, L1e, and L2e for the ends of a line of double-racks. (You might complain that there is no part L1e in the files. However, L1e is the mirror image of U1e, so you can just reflect U1e to make L1e. The same is true for the other pairs of parts with “L” and “U” in their labels.)