This paper describes and explains the synthesis of an astronomical clock mechanism which displays the mean position of the Sun, the Moon, the lunar node and zodiac circle as well as the Moon phases and their motion during the year as seen from the Earth. The clock face represents the stereographic projection of the celestial equator, celestial tropics, zodiac circle (ecliptic) and horizon for the latitude of Belgrade from the north celestial pole to the equator plane. The observed motions of celestial objects are realized by a set of clock gear trains with properly calculated gear ratios. The method of continued fraction is applied in the computation of proper and practically applicable gear ratios of the clock gear trains. The fully operational 3D model of the astronomical clock is created and the motion study of its operation is accomplished by using the SolidWorks 2016 application. The simulation results are compared with the ephemeris data and the detected differences are used to evaluate the long-term accuracy of the astronomical clock operation. The presented methods of the clock mechanism synthesis can be useful for the design, maintenance and conservation of large-scale city astronomical clocks since these clocks represent a precious historical and cultural heritage of European civilization.