The Tusi couple (also known as Tusi's mechanism[1][2][3]) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter 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 Tusi couple is a 2-cusped hypocycloid.
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.[5][6]
^Roshdi Rashed (ed.). Encyclopedia Of The History Of Arabic Science.
^Saliba, George (2002-07-01). "Greek astronomy and the medieval Arabic tradition: the medieval Islamic astronomers were not merely translators. They may also have played a key role in the Copernican revolution". American Scientist. 90 (4): 360–368. doi:10.1511/2002.27.360.
^Nosonovsky, Michael (2018-08-14). "Abner of Burgos: The Missing Link between Nasir al-Din al-Tusi and Nicolaus Copernicus?". Zutot. 15 (1): 25–30. doi:10.1163/18750214-12151070. ISSN 1571-7283. S2CID 135358186.
^George Saliba (1995), "A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam", pp. 152–155.
^"Late Medieval Planetary Theory", E. S. Kennedy, Isis57, #3 (Autumn 1966), 365–378, JSTOR 228366.
^Craig G. Fraser, "The cosmos: a historical perspective", Greenwood Publishing Group, 2006 p. 39.
The Tusicouple (also known as Tusi's mechanism) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of...
hypocycloid called Tusicouple was first described by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in Tahrir al-Majisti...
translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusi-couple are still extant in...
celestial worlds. In the late 13th century, Nasir al-Din al-Tusi created the Tusicouple, as pictured above. Other notable astronomers from the later...
translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusicouple are still extant in...
translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusi-couple are still extant in...
Nasir Al-Din al-Tusi was the lead astronomer and first director of the observatory. His most notable work was the creation of the Tusi-couple, a geometric...
dissatisfying and replaced it by adding a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions....
motion for the Tusicouple. Although it seems that Copernicus used Albert's ideas, he highly relied on Islamic sources for the Tusicouple. Copernicus's...
lemma". Nasīr al-Dīn al-Tūsī (1201–1274) resolved significant problems in the Ptolemaic system by developing the Tusi-couple as an alternative to the...
technical realization of the motion of the paper strip can be achieved by a Tusicouple (see animation). The device is able to draw any ellipse with a fixed...
{2{\sqrt {d/r}}}{1+(d/r)}}} becoming 1 when d = r {\displaystyle d=r} (see Tusicouple). The classic Spirograph toy traces out hypotrochoid and epitrochoid...
such straight lines. This circle corresponds to the smaller circle in a Tusicouple. The point midway between the pivots orbits in a circle around the point...
innovative mathematical device called the Tusicouple. The Maragheh Observatory held around 400,000 books salvaged by Tusi from the siege of Baghdad and other...
are slightly offset along the crankshaft axis (which creates a rocking couple). Another solution is to use master-and-slave connecting rods, where the...
equant and eccentrics at Maragheh observatory, and introduction of Tusi-couple by Al-Tusi. Alternative models later proposed, including the first accurate...
al-Tusi was the director of the Maragheh observatory, and made many new discoveries while he was there. Such discoveries include the Tusi-couple, a system...
a planetary nebula that displays delicate, spirograph-like filigree. Tusicouple Knight, John I. (1828). "Mechanics Magazine". Knight; Lacey – via Google...
independently developed the Tusicouple remains open, since no researcher has yet demonstrated that he knew about Tusi's work or that of the Maragha school...
motion". Nasir al-Din al-Tusi (1201–1274), a Persian astronomer and mathematician who died in Baghdad introduced the Tusicouple. Copernicus later drew...
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