|On display at||National Museum of Mathematics|
The Square-Wheeled Tricycle is an iconic exhibit at MoMath, where the visitor can ride a tricycle with square wheels on circles over a special track so that the ride is smooth.
A square wheel with the axis of rotation at its center can rotate over a special (straight) track, making the rotation axis stay at constant height (without bumping). In order to achieve that, the track must have the shape of a sequence of inverted catenaries with appropriate size.
MoMath exhibit makes the ride not in a straight line, but in a circle. The three wheels of the tricycle have different sizes, depending on the radius distance to the center of the circle track. The front wheel of the tricycle has pedals that the visitor can use to impulse the vehicle, while the two rear wheels are driven.
The two rear wheels are connected through a gearbox, which makes the two axes of the wheels parallel but not at the same height (to compensate for the different sizes of the wheels), and linking through gears the two rear wheels to rotate at the same angular speed.