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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."
I'll bet it stays smooth on turns. :P
I'll get right on that change-the-shape-of-all-of-the-roads project right away ...
The reason the trike has smooth motion is simple - the centre of mass (where the axle is attached) doesn't move vertically. It's exactly the same reason as for a hoop rolling on a plane surface except the hoop is more obvious.
When you turn, the square shape doesn't fit so well, so the c.o.m oscillates vertically, and you get a more bumpy ride - the larger the angle you turn through, the worse the fit, and the bumpier the ride. Wheels (round ones) don't have this turning problem so much; my vote goes to the round wheels
I remember doing a 'Granada power game' (schoolkid teams are set problems to do, and compete to produce the best solution). 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 for 5m, turn through 45 degrees, forward 1m, turn back through 45 degrees and throw a ball-bearing into a target, accuracy being rewarded. There were 2 walls at given positions that you had to get over as well, at 2.5m and 5.5m from the start. We just cut slots in our wheels - there were some really outlandish solutions to getting over the walls though
Simon
Physicists get Hadrons!
they did re-invent the wheel, not a good invention though...
See picture here
:)
Ya yew betcha! I wonder if that basket on the bike is to hold the hot dish? Only in Minnesota would we spend the time determining if square wheels would work... Perhaps from the potholes on 494?
I reside in Minnesota so I am permitted to make these important scientific observations
Perfect for Michigan roads.
The successor to the overly hyped Segway?
Wheels? Who needs wheels when rhombuses work perfectly fine!
Nothing disturbs me more than blind loyalism towards some unrealistic and over-idealistic notion of one's nationality.
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!
Mod +5 Drunk
It's the next Segway!
literally
An Indian-American Hindu committed to non-violent thought/speech/action alarmed by the global explosion of radical Islam
Will be be seeing pentagonal wheels or maybe even octogonal wheels? Or better yet n-gonal wheels where n is an incredibly large number?
EVERYDAY IS CATURDAY
This is basically the same principle as the odd-shaped pieces in your old Spirograph set....
I wonder what shape my wheels have to be to ride smoothly over the screwed up roads that my town refuses to fix?
Today in the news: Inventors discover new way to make road construction ( and repair ) even more expensive....
He's working on a water powered car I hear... just requires a really big hill.
No word if the car will support square wheels or not.
Economics
"The following theory assumes there are no external factors"
External Factor = People
Sociology
"The following theory is based on a majority sample"
Majority = 50 in a sample of 99.
Slashdot
"The following company/technology categorisation is correct given the sample data"
Sample data = Slashdot
And now we have
"The following design is correct for a given definition of road"
Reminds me of the old maths joke
"1+2=4 for sufficiently large values of 2 and small values of 4"
An Eye for an Eye will make the whole world blind - Gandhi
A catenary is the curve describing a rope or chain hanging loosely between two supports. At first glance, it looks like a parabola. In fact, it corresponds to the graph of a function called the hyperbolic cosine.
Yeah, I always get those confused...
[frink]Oy, with the wheels and the squares and the riding and the graphing, ng'hey, glaven.[/frink]
I want to drag this out as long as possible. Bring me my protractor.
Seems to me this is a good analog to proprietary file formats. Instead of having people pay tolls, maybe the government should build roads with inverted caternary bumps and sell the square wheels!
Don't you mean, fixing rounds?
...I'll procrastinate tomorrow...
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?
Dewey, what part of this looks like authorities should be involved?
"So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel."
That backwards tricycle sounds like the Buckminster Fuler's Dymaxian Car. 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.
Two wrongs don't make a right, but three lefts do.
I've seen the South Park kids travel to French Canada. They have square wheels on their bicycles as well as their cars. I really don't see what the big excitement is all about.
They should have used triangular wheels. One less bump.
they are both radio blog themes, based on Bryan Bell's Woodland's Theme
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. :)
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
stuff |
I was wondering when someone was going to get around to improving the wheel. The current version is so impractical, inefficient, and has such a limited range of applications it has been screaming for a face-lift. Someone get this guy a $250 million research grant ASAP!!!
Now if only the train to Chicago didn't run 1/3 as fast as the train to New York and leave 2 hours earlier.
Dear Esteemed Committee: I would like a million dollar grant. As a good geneticist I am going to see if I can cross a cat with a canary. I will call it "cantenary"! (Since you refused my grant for the monkey with four asses research) Part bird and part cat--that is something useful. Regards, Dr. Mephisto...
Harpo Tunnel Syndrome--my wrist feels funny.
It actually has 1 front wheel and two rear wheels.
My beliefs do not require that you agree with them.
The best ones conform the invention's design to fit the environment, not the other way round.
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
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...
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.
Also neat is the Reuleaux Triangle 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 demonstrates it.
Standard gear and rack interaction is well understood. Racks are usually straight-sided, while gear teeth are involute curves. Two gears which will mesh with the same straight-sided rack will mesh properly with each other. This fact reduces the size of simple gear inventories from O(N^2) to O(N).
"Mesh properly" has a specific meaning. There has to be contact on both sides of each gear tooth when the axes of the meshing gears are a constant distance apart. Getting this right improves gear life by orders of magnitude.
There's a nice little section in the back of every Boston Gear catalog which explains all this. Available online, too.
Nonstandard rack shapes are rare, but not unheard of. The drive system on the IBM RS-1 electrohydraulic gantry robot used a curved-sided rack.
way
too
much
time
on
his
hands.
Ok, I'm risk asking this, but by definition, a "wheel" cannot be "square...."
wheel
n.
1. A solid disk or a rigid circular ring connected by spokes to a hub, designed to turn around an axle passed through the center.
And, without pasting it too, a disk must be circular....
So, whatever those things are on that bicycle frame, they are not wheels
"All great things are simple & expressed in a single word: freedom, justice, honor, duty, mercy, hope." --Churchill
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.
YES! Finally a way to take the speedbumps as fast as I want!
If 4 wheels needs small hills to run on.... lets add a side so we have 5 sides. 5 sides will need smaller hills saving material in the rebiuld the road project.
And if 5 saves materal lets keep adding sides... 6, 8, 20, 100, 1000. Imagine how small the hills will be... we don't need to redo the roads as much.
Infact if we keep adding sides... we'll get.... a circular wheel... with no need to change the roads.
Well. That was easy.
What you're talking about is, in essence, a suspension system. Which is used to overcome a rough ride. What you're all trying to say is "The smoothness of a ride is determined by how much axle movement is passed along to the rider". Or something like that.
'Standards' in computing only impress those who are impressed by things like 'standards'.
"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.
-- Instant Karma's gonna get you! [320848 = 2*2*2*2*11*1823]
Eeghh, cmon Mods. +4 Interesting? At least it wasn't informative. Look at the coin, where is the center of mass? In the center! What happens when the coin rolls? The center moves up and down. What happens to the center of mass? It MOVES! What the equal diameter allows you to do is roll something flat over a coin and not have -that- move vertically, but the CM of the coin will move.
This was done years ago on the Tonight Show by Leno's science guy.
...to improve his "ride," Stan Wagon will be adding a "spoiler" (shaped like a rectangle) and a cylindrical exhaust "muffler" to make the vehicle more appealing to "the bitches."
If moderation could change anything, it would be illegal.
But if we use a fractal patterned tread, we'll need an infinite amount of road surface!
I vote for the smartwheels with zillions of radar-guided extending foot-spokes, a'la Hiro's motorcycle or Y.T's skateboard in Snow Crash.
I'd say being able to skateboard smoothly down stairs would probably give you the upper hand in the simpler conditions of municipal roadway battles.
"We have to go forth and crush every world view that doesn't believe in tolerance and free speech." - David Brin
OK, so the parent post was kind of silly, but it gives me a chance to mention Imre Lakatos, my favorite mathematical philosopher. (Yes, I have a favorite favorite mathematical philosopher. Don't you?)
He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context -- which present a very interesting very of the process of mathematical discovery: instead of accumulating an ever-increasing series of perfect truths, he argues, mathematicians are constantly shifting their perceptions of what is true, because they're constantly shifting the very definitions of the things they're writing the proofs about. (This happened in a major way with calculus during the 19th century, for example, when limits, derivatives and integrals were redefined more formally, giving birth to the field of analysis.)
The book is a lot of fun, and actually not such a hard read. It takes place in an imaginary classroom, where the students and the professor, having just proved a simple little theorem about polyhedra, start coming up with counterexamples by "stretching" their notion of what a polyhedron is. (Should a cylinder be a polyhedron? Why not? What about a box with a box-shaped hole on the inside? etc.)
Through their arguments, they end up sharpening the definition of "polyhedron", eventually replacing their naive notion with something clearer and more formalized through a process of proofs and refutations.
So, Stan Wagon challenges our definition of "wheel" with an apparent counterexample: Does the bike have no wheels? Or are wheels not round? We might propose sharpening the definition of "wheel" to account for the new counterexample:
A wheel is a solid object designed to rotate about an axle, with its perimeter in constant contact with some other surface.
(Make a ridiculous post, get a ridiculous reply!)