GEOMETRY: Gömböc a self-perpetual machine


The Gömböc is an amazing self-perpetual machine. If you place it upside-down on a table it slowly rocks from side to side building up momentum, until eventually, it flips itself upright as if by magic. Similar to a child’s punching bag or toy but with one important exception: the Gömböc has no internal counterweight to help it flip over.

Instead, its precisely determined geometric shape is solely responsible for it being able to self-right. The Gömböc is the result of a long-standing mathematical quest. In 1995 the great Russian mathematician Vladimir Arnold mused that it would possible to create a ‘mono-monostatic’ object, or in really easy English – a homogenous three-dimensional entity with only one stable and one unstable equilibrium point.

The quest was taken up by Gabor Domokos and Peter Varkonyi, both of the Budapest University of Technology and Economics. Rigorous research spanning numerous years then followed before the professors could confirm that such a mono-monostatic object could exist.

Presenting it as a physical demonstration was another thing however. It soon became clear that any technology used to build the Gömböc required high precision. Such an object with a radius of approximately 10cm required a tolerance of less than 0.1mm. Furthermore, both mathematicians shared the belief that the Gömböc should be manufactured from transparent material; otherwise, the homogeneity of the object would be hard to demonstrate.

The final model was printed on an Objet 3D printer, chosen for it’s combination of high accuracy, reliability, trasparent and translucent homogenous materials and ability to print 3D shapes with highly smooth surfaces.

And of course there’s a final twist to the story. It seems that the natural world already got there well before Domokos, Varkonyi or Arnold. Take a closer look at the shape of the Gömböc and you’ll notice a remarkable resemblance to certain species of terrestrial tortoise.

These ancient creatures, already pretty much locked into their present day body shape a staggering 200 million years ago, were probably making use of the Gömböc principle all this time to help right themselves after a heavy night out on the swamp. Evolution? Design by Plan? I leave it to your better judgment…

In the meantime you can read the full in-depth story and download some interesting PDF’s here on the Objet website. The Gömböc has already received lots of media attention, with over 4.5 million hits on it’s own website.