Bicycle Riding on Square Wheels 406
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."
Smooth ride (Score:2, Troll)
Read the whole article? (Score:5, Funny)
I wonder what shape my wheels have to be to ride smoothly over the screwed up roads that my town refuses to fix?
Re:Read the whole article? (Score:4, Insightful)
Re:Read the whole article? (Score:2)
But what would the radius be then?
Re:Read the whole article? (Score:4, Funny)
Duh! Infinity over 2!
</humor>
Re:Read the whole article? (Score:2)
Also, looking at this pic:0 _4958.jpg
It was originally stated in the original post that:
http://www.sciencenews.org/articles/20040403/f472
actually a tricycle with two front wheels and one back wheel
From this picture it looks like it's the other way around, two back wheels and one front.
Re:Read the whole article? (Score:3, Interesting)
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?...
Smartwheels! (Score:3, Insightful)
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.
Allrighty then (Score:5, Funny)
Re:Allrighty then (Score:4, Funny)
Re:Allrighty then (Score:5, Interesting)
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...
Junior school physics (Score:5, Informative)
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
Re:Junior school physics (Score:3, Interesting)
So, how'd you make it move on it's own power? I'm intrigued.
Re:Junior school physics (Score:5, Funny)
Cardboard fueled boiler for the steam engine I would assume.
Re:Junior school physics (Score:2)
huge nitpick: you are both wrong (Score:5, Interesting)
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.
Bigger nitpick, you're confused. (Score:3, Insightful)
Re:Bigger nitpick, you're confused. (Score:4, Insightful)
A rotating cam designed to smooth out bumps inherent to the wheel isn't fundamentally much different than a spring designed to smooth out bumps inherent to the road, except that because the bumps inherent to the wheel are calculated and predictable, a spring would be a poor solution. The road bumps, on the other hand, can't really be predicted, so it needs a more flexible (no pun intended) method of shock absorption.
Pointless little sidenote: As far as I can see, if you had a square-wheel bike with a correcting cam, and ran it over the bumpy road described in the article, the wheel would ride smoothly, and the cam would overcorrect, so you would still need a shock absorber to go over that road. It'd just be bumping in the opposite phase compared to a normal tire.
Re:Junior school physics (Score:2)
I should have written: "The vertical motion of the c.o.m. does not necessarily have a noticable effect on the smoothness of the ride".
Better>
I guess... (Score:5, Funny)
Re:I guess... (Score:2, Funny)
Re:I guess... (Score:3, Funny)
Unfortunately, two years before Microsoft introduced flying cars, so nobody's using MSroads anymore anyway. However, OS users get to feel superior because, even though they get to their destination slower, they're not nearly as likely to blow up in midair.
hot dish? (Score:2, Funny)
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
It's open to the public -- you can go ride it! (Score:5, Interesting)
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.
Re:hot dish? (Score:2)
ingenious concept (Score:3, Funny)
Re:ingenious concept (Score:2, Funny)
Re:ingenious concept (Score:2, Funny)
Woohoo! (Score:2, Redundant)
Great!
Now all we need is to lay some curved roads all over the place, make loads of these bikes, and we can all ride bicycles with square-shaped wheels!
I'm calling my Senator right now!
Could it be... (Score:5, Funny)
Wheels? Who needs wheels when rhombuses work perfectly fine!
The answer is - A circle! (Score:3, Interesting)
Re:The answer is - A circle! (Score:3, Insightful)
No, because the hill is really at best a half circle.
I'm not sure if tank tracks count as a wheel since they don't orbit a central axis. Even if they were, the tank treads aren't flat when they are in use. They're a sort of oblong shape. You might as well say a wheel is also a line because if you cut the inner tube in half it lies down and becomes a line.
If the wheel is circular, then the road would have to be circular as well. Like goin
Re:The answer is - A circle! (Score:3, Funny)
Yeah, but the Earth is a circle ;)
Re:The answer is - A circle! (Score:2)
Actually, the wheels are inside the tank tracks. The tracks themselves are a sort of 'moving platform' on which the wheels roll. It's like they make their own traction, which is why they work so well in all sorts of terrain.
Re:The answer is - A circle! (Score:2)
Cities Will Be Redesigned Around This... (Score:2, Funny)
reinventing the wheel (Score:2, Funny)
Re:reinventing the wheel (Score:2)
Before starting our long working week,
The "normal" person's workweek in ET started about 4 hours earlier.... 1 hour earlier in PST, but they still missed the "before we start" window for most people.
What next? (Score:5, Funny)
Spirograph (Score:5, Insightful)
Re:Spirograph (Score:2)
Only when JavaScript is enabled...hmm. Where do I go to submit this as a bug?
OT I know...
Re:Spirograph (Score:5, Funny)
And I wanted to see the new Spirograph stuff!
Now the road.... (Score:5, Funny)
Before the square wheel... (Score:5, Funny)
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.
If you want to build your own bicycle... (Score:2)
Re:If you want to build your own bicycle... (Score:2)
The wonder of assumptions... (Score:4, Funny)
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"
From the article (Score:5, Funny)
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]
Re:From the article (Score:2)
Re:From the article (Score:2)
Re:From the article (Score:2)
zach
So much for (Score:2, Redundant)
And I was always told that was the wrong approach to use.
Proprietary Roads! (Score:3, Insightful)
Isle of misfit toys (Score:2)
Re:Isle of misfit toys (Score:2)
I'm sticking with the wheel (Score:2)
Also, steering with this would be impossible. Basically, this goes in a straight line only.
And, this is good food for thought. Perhaps this priciple can be applied to other things.
Web design with Mathematica?!? (Score:5, Interesting)
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?
Re:Web design with Mathematica?!? (Score:5, Funny)
Re:Web design with Mathematica?!? (Score:3, Funny)
If he uses Mathematica for his "real" website, I wonder if he blogs with Octave?
Re:Web design with Mathematica?!? (Score:3, Interesting)
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...
*BOOM* (Score:5, Funny)
"So far, no one has found a road-and wheel combination in which the road has the same shape as the wheel."
Re:*BOOM* (Score:2, Insightful)
Tricycle sounds like the Dymaxion Car (Score:4, Interesting)
Re:Tricycle sounds like the Dymaxion Car (Score:2)
Greenspeed [greenspeed.com.au]
Windcheetah [windcheetah.co.uk]
Catrike [catrike.com]
Build your own [ihpva.org]
Many others [ihpva.org]
The Dymaxion suffered from having rear wheel steering. Tends to be very, very unstable at anything over walking speed. Too easy to overcorrect, swinging the back end wide.
Re:Tricycle sounds like the Dymaxion Car (Score:3, Insightful)
Now I know (Score:2)
Old News! (Score:5, Funny)
Re:Old News! (Score:2)
old joke (Score:3, Funny)
Elegant solution- (Score:2, Interesting)
Duh, physics class 101 (Score:5, Interesting)
http://www.fulcrumgallery.com
Re:Duh, physics class 101 (Score:3, Interesting)
Finally we get some improvements! (Score:4, Funny)
Re:Finally we get some improvements! (Score:2)
He did, this was the solution to Seattles Washingtons Pothole problem.
On the bandwagon (Score:2)
Is it me or do others find it amusing that a chap researching vehicles with square wheels has a surname "Wagon" ?
nick
Meow/Chirp, Meow/Chirp (Score:5, Funny)
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...
wrong description of the trike (Score:5, Informative)
It actually has 1 front wheel and two rear wheels.
A Lesson about Inventions (Score:3, Insightful)
Reminds me of the british 20p coin (Score:4, Interesting)
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...
Stupid American Question (Score:2)
Re:Stupid American Question (Score:2)
They're a little bit like ju-jubes but you probably don't know what those are either, heathen!
Farming.. (Score:2)
Reuleaux Triangle (Score:5, Interesting)
Gear and rack (Score:4, Informative)
Standard gear and rack interaction is well understood. Racks are usually straight-sided, while gear teeth are involute curves. [howstuffworks.com] 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 [bostongear.com], 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.
Let me be the one to point out the obvious, (Score:3, Insightful)
too
much
time
on
his
hands.
Square Wheel? (Score:5, Informative)
wheel [reference.com]
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
Re:Square Wheel? (Score:2, Funny)
Errant pedant prompts Lakatos reference (Score:3, Insightful)
He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context [wikipedia.org] -- 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 shif
Never understood... (Score:2)
Finally! (Score:3, Interesting)
Lets get wild with the sides. (Score:5, Funny)
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.
Re:Lets get wild with the sides - fractals (Score:3, Funny)
Wheel / Road Same Shape? (Score:2, Redundant)
Seems to me you could ride a bike with circular wheels on the inside (or outside) of a circular track (2001 space odyssey-style). The wheels and road would have the same shape then, right?
Re:Wheel / Road Same Shape? (Score:2)
Speedbumps (Score:2)
And... (Score:3, Funny)
Re:Good for elementary schoolers (Score:5, Funny)
Don't you mean, fixing rounds?
Re:Groklaw? (Score:3, Informative)
Re:WORTHLESS HORSESHIT! (Score:2, Funny)
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.
Re:brakes (Score:2)