[math-fun] Constant velocity implies round wheels?

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