The story of the Gömböc | Hacker News Reader

The story of the Gömböc

plus.maths.org

165 pointsignifero45 comments

If a Gömböc is built to 10 micron tolerances, does that mean I need a cleanroom and the world's flattest table to be assured it will work?

I wondered the same thing when I saw the wooden table, which surely has deviations > 10 microns. Possibly there are approximate Gömböc shapes that are "good enough" without being mathematically perfect.

The implication of the result is that all the real "Gömböcs" are really such "almost Gömböcs", since any deviation at all from the correct shape technically destroys it.

Not necessarily: the Gömböc-shape could be a envelope of similar shapes. Any object within that envelope is a Gömböc, and ones just outside it are "almost Gömböcs"

It could be, but it isn't, which is part of what's so interesting about it.

(And that's leaving aside the more fundamental point that the very definition of a Gömböc isn't applicable in the physical world, where objects do not have precisely defined edges and cannot be completely homogenous).

According to Wikipedia, yes:

The balancing properties of a gömböc are affected by mechanical defects and dust both on its body and on the surface on which it rests. If damaged, the process of restoring the original shape is more complex than producing a new one.

So do the self-righting properties simply degrade or fail completely, if say an eyelash drops on it?

The self-righting properties degrade in imprecise environments -- from the level of "100% mathematical certainty it can right itself" -- to something sort of absolute mathematical certainty. Not from self-righting to complete failure.

Dropping an eyelash on it, and using a standard kitchen table probably won't make it fail, and it will probably still work -- but it does impact it at the theoretical absolute level.

I bet if that eyelash were on the stable equilibrium point, you'd now have two stable equilibrium points (one on either side of the eyelash, basically), and possibly an additional unstable point (balanced on the eyelash).

The self-righting property would be completely unaffected if the surface imperfection is smaller than a certain threshold value. This value is a function of the "equilibrium-ity" for any point of the surface.

Close to the stable and unstable equilibrium points, any imperfections create additional equilibrium points, like someone else mentioned.

The threshold will grow with the distance to equilibrium points, so in some places, an eye lash, a grain of sand or the inscribed logo makes absolutely no difference.

In the linked video they appear to demo it on a wood table which almost certainly doesn't meet the 10micron flatness.

For an interesting analysis of a practical application of this, namely turtles and tortoises righting themselves, there's a full text analysis of the dynamics involved available here: http://rspb.royalsocietypublishing.org/content/275/1630/11.f...

The article states that the machines are accurate to that tolerance, but not whether that level of precision is required.

Yeah that was a bit deceptive. A typical desktop CNC machine can easily do precisions in the thousands of an inch, or about 25 microns.

If you look at the close up of picture #2, they are nowhere near a 10 micron finish, which you would be able see your reflection in - all those tool marks (not to mention the logo) are an order of magnitude above 10 microns. http://www.gomboc-shop.com/app/urwfilter/catalog/do/action/S...

Not true: Here in the UK the BBC have a quiz show hosted by Stephen Fry - QI which featured the Gömböc. Fry placed it in front of him to show it in action, albeit on a mirror, but it certainly wsn't a dust free environment.

Here's the actual clip on Youtube http://www.youtube.com/watch?v=XCAg5_vHFmI

Hmm... you can buy a variety of these starting at €119 here:

http://www.gomboc-shop.com/app/urwfilter/catalog/do/action/S...

I've played with one. Domokos gave a lecture at Trinity College, Cambridge. Most ways that you place it, it behaves unremarkably, but there's one way of placing it such that it rocks back and forth and has almost settled down to the almost-stable point when it falls over perpendicular and ends up at the single stable point. This is the way to demonstrate it.

I'm interested in the tolerances on that 10 micron distance...if you could build an approximation that works most of the time with much less precision, then you might be able to make sale-able objects that do such...

> if you could build an approximation that works most of the time with much less precision, then you might be able to make sale-able objects that do such...

They're called turtles.

http://www.naturalhistorymag.com/biomechanics/10309/the-livi...

I am suprised we dont make ships with this general shape.

I am surprised we dont make ships with this general shape.

Why? So they'll right themselves if they're capsized? If a ship (not a boat) capsizes you've got pretty serious problems already.

Besides, self-righting is a very different sort of problem when you're floating.

It is fairly standard for lifeboats to be self-righting. Google "self-righting boat" for examples. The typical shape is not a gömböc, though. A gömböc would self-right, even when completely under water.

The self righting designs I'm familiar with for (large) dinghies have a lot of lead in the bottom of the boat combined with a lot of built in buoyancy - they'd probably self right deep underwater.

I'm sure a gomboc would self-right when completely underwater, but what about a floating gomboc half-submerged? Different problem.

Also, ships are not solid (as in 'filled'), let alone uniform in density. On top of that, hydrodynamics imposes more important constraints on shape. You can make a ship pretty stable by loading its keel heavily.

Ships don't have a mathematical requirement that their internal structure be one homogenous material, thus it's a trivial matter to put a weight at the lowest point of the ship so that it acts like a weeble: http://en.wikipedia.org/wiki/Weeble

There is an episode of QI : http://www.youtube.com/watch?v=XCAg5_vHFmI where in they discuss about this , and also a brief interview with the mathematician involved.

If anyone can find a cad model, I'll machine one out of aluminum or print an SLA.

Would be OK for personal use, but for commercial production it looks like they've put a variety of legal protections on the shape/design of it:

http://www.gomboc-shop.com/app/urwfilter/license/do/action/S...

So much for not being able to patent math.

How fault tolerant are they? What if I made one to within 100 microns - I imagine it would still self-balance itself pretty well, and that specific shape would probably not be covered.

From http://www.gomboc-shop.com/app/urwfilter/faq/do/index.html Is there only one Gömböc shape?

No, in fact, there are infinitely many Gömböc shapes. However, the overwhelming majority of these shapes could never be manufactured because these shapes are much too close to the sphere. Currently we manufacture two different shapes ( 8005 and 8205 ). Both are quite similar and have a substantial deviation from the sphere.

They could potentially get a design patent on each of the specific shapes they make and certainly on their name, but good luck on anything beyond that.

I can see possibilities of simulating a Gomboc surface on the back of a four-legged robot. However, the robot will either need small "legs" or some servo's to bring the "legs" inside the body (like a turtle) to correct its position

You'd have to recalculate the shape after that, as the interior density is no longer uniform.

Yes, you are right. Given this consideration, I think maybe the surface needs to be configurable? Not sure but it will be pretty complicated to dynamically adjust to changing density.

Am I the only one who thought about food?

If you don't speak Hungarian you could just reply "yes".

http://www.google.com/search?q=gomboc+food

Nice :) But still, there is a bit difference with or without the umlauts on the o's:

there's gombóc (=dumpling), probably from gomb (=button, knot) plus diminutive,

and

gömböc, from gömb (=sphere) with diminutive. "Kis gömböc" is the "meatball" that eats up everyone, until he bursts, in an old folk tale, probably the source of the name here. Ultimately I guess both words are from the same root.

http://www.google.com/search?q=A+kis+g%C3%B6mb%C3%B6c

http://en.wiktionary.org/wiki/gomb%C3%B3c

You're not, but apparently it's sacrilege to have done so, hence the downvotes LOL.

interesing variation in reactions to previous postings: http://www.hnsearch.com/search#request/all&q=gömböc&... and http://www.hnsearch.com/search#request/all&q=gomboc

There's a scifi story begging to be written about building a perpetual motion machine or trying to generate energy from an unbalanced Gömböc.

Isn't a sphere with it's centre of gravity shifted from it's geometrical center a gömlöck ?

>Gömböcs are not much to look at, and seem like they could be children's toys. Don't try to buy one, though. They're actually upwards of a thousand dollars each. They may look like they were knocked together in a toy shop, but the different angles and proportions have to be measured to within ten microns – one tenth of the thickness of a human hair - to make the shape work. So it's unlikely anyone will get to use one as a paperweight.

Sounds like the best reason to makerbot these things.

Sounds like the best reason one can't makerbot these things. Makerbots have a nozzle size of 0,5mm according to the makerbot wiki.

Oh, that. I know it by its more common name/appearance; a lump of bocconcini cheese. :) At least that's what immediately came to mind.

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