3d expanding racks (NbO)

This is a building system for making mechanisms which can change size. The parts can be built out to make expanding mechanisms of varying sizes and shapes.

The simplest version of this mechanism is a "right-angled hexagon" - six of the edges of a cube. To make it, you will need:

• 6 left handed racks

• 6 right handed racks (the racks file contains one rack of each handedness)

• 6 gears

• 12 half-cap-half-hexes

• 12 half-axles

• 6 M3 nuts

• 6 M3 bolts (12 mm long)

The parts are intended to be printed with 0.2mm layer height. Only the half-axles require support (be sure to clean off all of the support so that the parts fit together properly). To assemble it, first make 12 "half-junctions", each one made from a half-axle, a rack, and a half-cap-half-hex. The rack and the half-cap-half-hex push into the bottom of the half-axle.

Next, each junction is made from two half-junctions, pushed together with a gear in between them. However, you want to have the racks of the neighbouring junctions meshing with the gear of this junction. Slot the rack of a neighbouring (half-) junction into this one so that when you put the gear in, it locks that rack into place. When you slot two half-junctions into each other, their racks need to have the same handedness.

Once you have the racks from both neighbouring junctions correctly positioned in your junction (they should be the same distance away from your junction - you can count the teeth on the racks to see how far from the gear in your junction they are), insert a bolt through your junction and screw it into a nut on the other side. This holds the junction together.

A couple of tips:

• Don't over-tighten the bolt: the nut is held in a hexagonal cup in its half-cap-half-hex (or cap). If you overtighten, the nut will start slipping in its cup, and then it will be difficult to loosen the nut.

• I like to keep track of the handedness of the half-junctions by always inserting the bolt through the side of the junction so that, seen from that side, the gear rotates anti-clockwise as you collapse the mechanism. (Unless you're really getting into the symmetry stuff, don't worry about this!)

This video shows the design process and many example mechanisms, and looks in (probably excessive) detail at the symmetries of this design. It also describes the NbO network, which is the crystal structure this design is based on. I show how to assemble half-junctions at 11:26 and 12:09, and how to slot two junctions together at 12:46.

Instead of building a half-junction using a rack and a half-cap-half-hex, you can use two racks (of the same handedness) and a cap. This gives you an extra rack, and so an extra direction to connect a neighbouring junction to your one. By putting these together, you can build larger shapes: expanding cubes, tetris pieces, and so on. Have fun exploring!