Tusi couple

The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets[4] and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.

Historians suspect that Copernicus or another European author had access to an Arabic astronomical text, but an exact chain of transmission has not yet been identified,[10] The 16th century scientist and traveler Guillaume Postel has been suggested as one possible facilitator.

It has been suggested[13][14] that the idea of the Tusi couple may have arrived in Europe leaving few manuscript traces, since it could have occurred without the translation of any Arabic text into Latin.

Oresme's description is unclear and it is not certain whether this represents an independent invention or an attempt to come to grips with a poorly understood Arabic text.

[19] Nineteenth-century engineers James White,[20] Matthew Murray,[21] as well as later designers, developed practical applications of the hypocycloid straight-line mechanism.

A practical and mechanically simple version of the Tusi couple, which avoids the use of an external rim gear, was developed in 2021 by John Goodman in order to provide linear motion.