Transforming cube/octahedron geared mechanism

This is a geared mechanism that transforms shape. The twelve edges are geared together so that they all simultaneously rotate 90 degrees, transforming from a cube shape into an octahedron shape and back again. The edges extend in length as we go from the cube to the octahedron form.

To make this you will need:

• 1 cube_oct_tsfm_core part

• 6 cube_oct_orthogonal_axle parts

• 6 cube_oct_orthogonal_axle_inset parts

• 6 cube_oct_orthogonal_gear parts

• 12 cube_oct_diagonal_long_axle parts

• 12 cube_oct_edge_base parts

• 24 cube_oct_rack parts

• 6 M3 bolts, 20mm long (or longer)

• 12 M3 bolts, 35mm long (or longer)

• 18 M3 nuts

The 3D printed parts are intended to be printed with 0.2mm layer height.

There are two kinds of large bevel gears: the six "orthogonal" gears and the 12 gears on the edge base parts.

One orthogonal_axle part and one orthogonal_axle_inset part push together through the hole in an orthogonal_gear part to make the axle for the gear. (The only difference between the inset and non-inset versions is that the inset has an extra conical depression to accommodate a countersunk screw. If you do not have countersunk screws then you can use two non-inset versions of the axles.)

You may need to clean up the gear prints so that they spin freely on their axles. Once the orthogonal gears are assembled with their axles, you may be tempted to attach them onto the core. But I find it easier to "walk" around the core, adding neighbouring gears as you go. So wait until you have the edge gears assembled as well.

Slot two copies of the rack part into each edge_base part. Push the racks in as far as they will go. Then insert a diagonal_long_axle part through the hole in the edge part so that the gear on the axle meshes with the two racks.  It is important that this gear has the correct orientation - there are two small indentations in the face of the gear to indicate the orientation - these should be arranged to point perpendicular to the long direction of the edge part (see the photo of the design in the cube form). When the design is in the octahedron form, the two indentations will point in the direction of the edge.

You are now ready to assemble the whole design. There are 18 slots in the core that will each accept an M3 nut. Make sure that each nut is centered in its hole - if not, the slot may need some cleaning. Now screw the 35mm bolts through the edge parts and the 20mm bolts through the orthogonal edge parts, into the core, and through the nuts to secure them. There is a "zigzag" interface at the end of the diagonal_long_axle where it meets a complementary zigzag interface on the core. This makes sure that the gears on the diagonal_long_axle are rigidly fixed to the core and cannot rotate.

Assembling all of the bevel gears onto the core can be fiddly. You may need to loosen the bolts holding in some gears you have already added in order to be able to add a new gear.

The mechanism may need some lubrication to run smoothly. The friction is likely worst on the interface between the grooves and rails that allow the racks to slide in the edge_base parts, but it isn't a bad idea to also add grease where the gears rotate on their axles.

Thanks to the FabLab at Sorbonne University where I prototyped this model.