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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."
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!
This story is almost as interesting as the latest case-mod story or the latest news about the state of the Linux x-box port.
they are both radio blog themes, based on Bryan Bell's Woodland's Theme
It actually has 1 front wheel and two rear wheels.
My beliefs do not require that you agree with them.
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.
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
They are a jelly candy, fruit flavors. Well, OK, they are like really tough jelly candy (think OLD jujubes), with really good fruit flavours. They are delicious, but can rip out your fillings, and will stay stuck in your teeth for all eternity.