Tusi Couple

By Spencer Connor

This mesmerizing arrangement producing purely sinusoidal motion is a specialized case of a hypocycloid, which generally don’t produce motions anything close to linear. But if the inner gear has half the tooth count of the outer gear the motion produced from anywhere on the inner gear is elliptical. Additionally, if the attachment point is located on the pitch diameter of the inner gear that ellipse goes to an infinite eccentricity and becomes rectilinear. It is a well supported assembly not needing much stabilization and has reasonably low friction due to mainly rolling motion.

In practice, producing an internal gear is such an annoyance/difficulty that a series of pins are often used instead. Such is the case on the Jen’s Olsen clock.