The Tusi couple is a device constisting of two circles, one half the size of the other.
The smaller circle is rolled inside the circumferance of the larger circle. A point on
the smaller circle will trace, back and forth, the diameter of the larger circle,
creating a linear harmonic motion out of constant circular motion.
The clever invention of a very clever man by the name of Nasir al-Din al-Tusi
it was originally invented to solve the problem of the latitidunal (north/south) motions
of the heavens. Al-Tusi's predecessors had used simple epicycles to push orbits north
or south over the course of the year, but such an epicycle also pushes
the orbits an equal distance east and west as they do north and south, knocking
them out of alignment with the longtitudinal motions. The couple solved this problem, and
a great many more, in geometric astronomy.