The Tusi-couple is a mathematical device in which a small circle rotates inside a larger circle twice thediameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.
The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusiin his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets,[1] and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.[2][3]