Nasir al-Din al-Tusi Invents the Tusi-couple Mechanism

In his work 'Tahrir al-Majisti,' Persian polymath Nasir al-Din al-Tusi introduced a mathematical device called the 'Tusi-couple.' This geometric construction demonstrated how linear motion could result from combining two circular motions by placing a small circle inside a larger circle with twice its diameter. The mechanism addressed problems in Ptolemaic astronomy by eliminating the need for the equant, which violated uniform circular motion principles. Copernicus later incorporated a similar mechanism in his heliocentric model, suggesting the Tusi-couple influenced subsequent astronomical developments and contributed to more accurate planetary models.