Tusi Couple

The "Tusi Couple" was introduced by Nasir al-Din al-Tusi in his 1247 commentary on Ptolemy's Almagest. It was introduced as an alternative to Ptolemy's equant in order to provide cyclic linear motion from uniform circular motion.

The large circle rotates anticlockwise. The small circle rotates clockwise such that it maintains a tangent with the large circle at a fiex point of the large circle. A point on the circumference of the small circle moves in linear, cyclic motion.

Another way of looking at it is that the small circle is rolling around the inner circumference of the large circle.

Copernicus adopted the Tusi Couple to generate a linear cyclic motion from circular uniform motion. although it is not clear if he copied the Tusi mechanism from earlier philosophers or devised it himself.