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.

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.