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."

Comments

Web design with Mathematica?!?

[Just Some Guy]

If you follow the link to the designer's own web page, 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?

Reuleaux Triangle

[ortholattice]

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.

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.

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 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...