Bicycle Riding on Square Wheels

Roland Piquepaille writes "Before starting our long working week, let's relax with this story of a bicycle with square wheels. No, it's not a joke. And it even rides smoothly. But there is a trick: the road must have a specific shape. The Math Trek section of Science News Online tells us more about this strange bicycle -- actually a tricycle with two front wheels and one back wheel. Read this overview for some excerpts and a picture of the tricycle, or the original article for an additional animation."

The answer is - A circle!

[DR SoB]

The question at the bottom that states they don't have a wheel the same shape as the surface, I tend to disagree, wouldn't a common circular wheel, while going over a steep hill both be circular shapes? What about tank tracks? They are both flat? A flat wheel and a flat surface = the same!

Re:Junior school physics

[greenhide]

For the challenge in the year we took part, we had to construct (entirely from cardboard) a device that would travel forward under its own power

So, how'd you make it move on it's own power? I'm intrigued.

Web design with Mathematica?!?

[Just Some Guy]

If you follow the link to the designer's own web page [stanwagon.com], and scroll to the bottom, you see:

Created by Mathematica (February 3, 2004)

I just realized that any geek cred I thought I had was just an illusion. I don't ever want to hear jokes about Emacs again. Understand?

Tricycle sounds like the Dymaxion Car

[G4from128k]

That backwards tricycle sounds like the Buckminster Fuler's Dymaxian Car [washedashore.com]. That beast was designed for minimum air resistance. Also having the two wheels in front provides better stability when cornering during hard braking. Still, tricycles do have some roll-over stability problems because the CG is closer to the sides of the wheelbase.

Elegant solution-

[baudilus]

While a mathematical solution is technically perfect, I can think of an easy way to determine the requisite road shape: use a square wooden block, cut a hole in teh center so you can roll it, then do so over a reasonably soft surface. You can even observe how the shape of the catenaries elongates as the rotational speed stays constant but the horizontal velocity increases. Would be fun for downhill rides. :)

Duh, physics class 101

[192939495969798999]

Every college physics class has one day where they talk about this,where the road is lumpy in a specific way, and then the bicycle with square wheels can drive. You know what else has a smooth ride? the space shuttle crawler. If you weigh enough, you just crush anything that would otherwise be a bump. I'll be happy when I see a vehicle besides a tank whose method of ground contact changes shape to accommodate for the road (i.e. tank tread on a bicycle). That would be sweet!

http://www.fulcrumgallery.com

Reminds me of the british 20p coin

[Funkitup]

This coin has 7 sides so you wouldn't expect it to roll smoothly.

However, they are cleverly made so that the diameter is equal right the way around the coin. Therefore, since the center of mass doesn't move, the coin will roll smoothly in slot machines etc. Try it!

I'm not sure whether the 50p is the same or not. I don't have one in my wallet to test as I used it to buy a packet of wine gums...

MMmmmm wine gums...

It's open to the public -- you can go ride it!

[melquiades]

I believe it's still sitting in the basement-level lobby of the Olin/Rice building at Macalester. You can just walk up and give it a ride.

In practice, it doesn't work perfectly: the wheels slip a bit on the upslope. But if you get a bit of speed, it rolls along nicely! Quite fun.

Reuleaux Triangle

[ortholattice]

Also neat is the Reuleaux Triangle [whistleralley.com] that is not round but even so has a constant width as it rotates. If it is used as a roller between two planks, it will roll smoothly and the distance between the planks will remain constant. This java applet [whistleralley.com] demonstrates it.

Alternative Transport

[Anonymous Coward]

the square bicycle could only ride straight line... predetermine road track... well... does that sound like a train to you? have the inverted thigie lay-out in straight - but it can be curve to left and right a bit, put the bicycle or a bicycle with an engine with it, get it to drag some coach at the back, and it is a new train design. :-)

--
baganjermal[at]gawab[dot]com

huge nitpick: you are both wrong

[mattyp]

movement of the center of mass nor axle has anything to do with smoothness: it's movement of the rider.

20 or 30 years ago (i searched the web, sorry, couldn't find) honda (an engineer there, for an internal contest) built a bicycle with square wheels that rode smoothly on a flat surface. It worked with a cam on the swingarm, so the axle could move up and down while rolling, and the bike frame (and rider) stayed level. I'm sure the center of mass also moved.

Finally!

[freeze128]

YES! Finally a way to take the speedbumps as fast as I want!

Re:Web design with Mathematica?!?

[Anonymous Coward]

I'm a former student of Stan's... he does *everything* in Mathematica (Except for spell it out... he refers only to Mma). If I remember right he's on some sort of advisory board for Wolfram Research.

Once upon a time, because my first college math course was taught by Prof. Wagon, all of my math papers were done in Mma... the highest compliment he ever paid me was that I had learned Mma typesetting "very well". It's not hard once you get used to it by placing your head in a microwave...

Re:Read the whole article?

[Lodragandraoidh]

I wonder what shape my wheels have to be to ride smoothly over the screwed up roads that my town refuses to fix?

Actually, several non-wheel ideas come to mind:

Tracked vehicles - make your own potholes - with a smooth ride...
Walking vehicles - who cares about potholes - or roads for that matter?...
Flying vehicles - this is my personal favorite - where is that flying car they promissed us?...

Re:Duh, physics class 101

[el-spectre]

Check this out [mattracks.com]. So far as I know, you still use the original shocks and stuff, so the ride would be fairly smooth...

Re:wheels are closed topology, roads are open

[L0C0loco]

"I don't get this part. A wheel is a small closed shape, you go once around it and you're back where you started from. On the other hand, a road has to GO somewhere along the ground - if it was a closed shape suspended in the air then you would fall off when you come around to the bottom side of it - so of COURSE they can't be the same shape - one has to have open topology and one has to have closed topology."

Well, no. The wheel is merely a periodic shape that repeats every 2*pi radians in polar coordinates. It can be just as "open" and the road.

Re:Allrighty then

[merlin_jim]

Actually, this research does have real world applications.

In the early parts of the industrial age it was found that a certain shape [allelectronics.com] of gear teeth (both along the axle of the gear, and the tooth's profile seen edge on), removed gear slip allowing for much smoother operation, to the point where bevelled gears are used in all car transmissions today.

This research may lead to innovative and new ways to mesh gears together; for instance, I could imagine one application to allow gears with teeth numbers that aren't strictly in ratio to their diameters to mesh properly. If that were the case, then we could make transmissions and gear boxes an order of magnitude or so smaller...

Re:Web design with Mathematica?!?

[passion]

Actually, it appears that he's not alone...

http://www.google.com/search?q=%22Converted+by+Mat hematica%22 [google.com]

google returns 10,000+ results for that phrase...

Leno

[comron]

This was done years ago on the Tonight Show by Leno's science guy.