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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 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...
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.
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.
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.
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."
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.
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.
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.
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.