Fascinating, but has anybody got a use for this?

Rapid prototyping has been used to make Gömböcs, which are solid shapes that have only one stable and one unstable position of equilibrium.

This means that whichever way you put them down, they tip themselves into a single standing position.

In 1995, the Russian mathematician Vladimir Arnold suggested that it should be possible to devise such a "Mono-monostatic" object. The final shape that meets the criteria was developed by Gábor Domokos, head of mechanics, materials and structures at the Budapest University of Technology and Economics in Hungary, and a former student of his, Péter Várkonyi, at Princeton University.

The main problem in making a real world Gömböc is its size tolerance: a Gömböc of diameter 10 cm has to be made to a tolerance of less than 0.1 mm. The first operational Gömböc was manufactured in the summer of 2006, using 3D rapid prototyping technology, but its accuracy was not quite up to the requirements.

A series of properly working Gömböcs have since been made using 'PolyJet Technology' machines made by Objet Geometries. Taking advantage of the technology, the Gömböc logo and serial numbers may be printed inside the object in 3D as narrow 3D tubes, filled with a transparent material that has the same density as the basic printing material.

Some turtles, it turns out, have evolved their shells into the same basic shape in order to be turned upright should they fall and land upside down, but so far, to our knowledge, nobody in engineering has yet managed to make practical use of the shape. Should they do so, we would be most interested to hear about it.

Tom Shelley

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