The Tusi couple is a geometric mechanism introduced by the Iranian scholar Nasir Tusi in the 13th century. In this mechanism, a smaller circle rotates inside a larger circle whose radius is twice as big. If a small gear rotates inside a fixed larger gear, and we track the motion of a point on the edge of the smaller gear, its path will not be circular but will instead become a straight line. As a result, this mechanism produces linear back-and-forth motion from purely rotational motion. #mathema