Clearly a tricycle with gearlike wheels riding on a geared line would come pretty close. The theory of gears probably answers whether perfect linear motion can be obtained this way. --Dan On Jul 10, 2014, at 4:19 AM, James Propp <jamespropp@gmail.com> wrote:
This question (in a square-wheeled-tricycle vein) is probably easy, but I haven't had any coffee yet so it's not easy for me!
If you want a tricycle with wheels of some shape, riding on a terrain of some shape, so that turning the pedals with constant angular velocity (relative to the pedal-axle) imparts constant linear velocity to the rider, must the wheels be round and the terrain be flat?
On a square-wheeled tricycle, the forward speed of the tricycle varies; this is one reason why the ride does not feel as smooth as one might like.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun