P.S. Apparently Euler discovered that shaping each side of a gear tooth as the involute of a circle leads to exact constant rotary motion transmitted between circular gears -- and this is still the main design of circular gears today. It *appears* that circular-to-linear motion, as transmitted by what's called rack-and-pinion gears (one circular, one straight), each using the Euler design, also maintains the same constant speed as a limit of the circular-circular case as one radius -> oo. But I haven't found anything authoritative that asserts this convincingly. --Dan On Jul 10, 2014, at 7:18 AM, Dan Asimov <dasimov@earthlink.net> wrote:
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.
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