The armillary sphere, an astronomical observation device embodying the Orbital Heaven Theory of the Later Han Dynasty in China, holds both historical and scientific significance. It has been produced in various forms by many individuals since its inception in the era of King Sejong in the Joseon Dynasty. A prominent figure in this field was Nam Byeong-cheol (南秉哲, 1817-1863), known for his work 'Uigijipseol' (儀器輯說), published in 1859, which detailed the history, production methods, and usage of the armillary sphere. This text particularly highlights 21 applications of the armillary sphere, divided into 33 measurements, covering aspects like installation, time, and positional measurements, supplemented with explanations of spherical trigonometry. Despite numerous records of the armillary sphere's design during the Joseon Dynasty, detailed usage information remains scarce. In this study, the 33 measurements described in 'Uigijipseol' (儀器輯說) were systematically classified into six for installation, nineteen for position measurement, seven for time measurement, and one for other purposes. Additionally, the measurement methods were analyzed and organized by dividing them into the ecliptic ring, moving equatorial ring, and fixed equatorial ring of the armillary sphere. In other words, from a modern astronomical perspective, the results of schematization for each step were presented by analyzing it from the viewpoint of longitude, right ascension, and solar time. Through the analysis of Nam's armillary sphere, this study not only aims to validate the restoration model of the armillary sphere but also suggests the potential for its use in basic astronomical education based on the understanding of the 19th-century Joseon armillary sphere.

This study aims to develop a restoration model of an armillary sphere of Tongcheon-ui (Pan-celestial Armillary Sphere) by referring to the records of Damheonseo (Hong Dae-Yong Anthology) and the artifact of an armillary sphere in the Korean Christian Museum of Soongsil University. Between 1760 and 1762, Hong, Dae-Yong (1731-1783) built Tongcheon-ui, with Na, Kyung-Jeok (1690-1762) designing the basic structure and Ann, Cheo-In (1710-1787) completing the assembly. The model in this study is a spherical body with a diameter of 510 mm. Tongcheon-ui operates the armillary sphere by transmitting the rotational power from the lantern clock. The armillary sphere is constructed in the fashion of a two-layer sphere: the outer one is Yukhab-ui that is fixed; and the inner one, Samsin-ui, is rotated around the polar axis. In the equatorial ring possessed by Samsin-ui, an ecliptic ring and a lunar-path ring are successively fixed and are tilted by 23.5° and 28.5° over the equatorial ring, respectively. A solar miniature attached to a 365-toothed inner gear on the ecliptic ring reproduces the annual motion of the Sun. A lunar miniature installed on a 114-toothed inner gear of the lunar-path ring can also replay the moon's orbital motion and phase change. By the set of ‘a ratchet gear, a shaft and a spur gear’ installed in the solstice-colure double- ring, the inner gears in the ecliptic ring and lunar-path ring can be rotated in the opposite direction to the rotation of Samsin-ui and then the solar and lunar miniatures can simulate their revolution over the period of a year and a month, respectively. In order to indicate the change of the moon phases, 27 pins were arranged in a uniform circle around the lunar-path ring, and the 29-toothed wheel is fixed under the solar miniature. At the center of the armillary sphere, an earth plate representing a world map is fixed horizontally. Tongcheon-ui is the armillary sphere clock developed by Confucian scholars in the late Joseon Dynasty, and the technical level at which astronomical clocks could be produced at the time is of a high standard.

In this paper we have reconstructed an armillary sphere based on the Method of an Armillary Sphere Making described in the Volume 1 of The Collection of Writings on the Scientific Instruments-Uigijipsol (儀器輯說, two volumes) edited in the 1850's by Nam Byong-Chul (南秉哲, 1817-1863) who was a famous Korean states-man-scientist. Nam achieved convenience and accuracy in the measurements of stellar positions in the manner of selective setting the equatorial, ecliptic and horizontal poles by adding a pole axis exchange ring called Jaigeukkwon (載極圈) between the Three Arrangers of Time and Four Displacements. We made use of 3-dimensional graphic software for modelling Nam's armillary sphere which consisted of five layers-eight rings. Results of simulation showed that the pole axis exchange ring functioned properly in setting the equatorial, ecliptic and horizontal coordinates simply by exchange of positions of specified holes on the ring. We ascertained that the invention of Jaigeukkwon solved inherent problems in the conventional Chinese armillary sphere in computation of real ecliptic coordinates. It was revealed that Nam Byong-Chul made great contributions in the East Asian history of armillary sphere making.