In recent years, digitization of cultural heritage objects, for the purpose of creating virtual museums, is becoming increasingly popular. Moreover, cultural institutions use modern digitization methods to create three-dimensional (3D) models of objects of historical significance to form digital libraries and archives. This research aims to suggest a method for protecting these 3D models from abuse while making them available on the Internet. The proposed method was applied to a sculpture, an object of cultural heritage. It is based on the digitization of the sculpture altered by adding local clay details proposed by the sculptor and on sharing on the Internet a 3D model obtained by digitizing the sculpture with a built-in error. The clay details embedded in the sculpture are asymmetrical and discreet to be unnoticeable to an average observer. The original sculpture was also digitized and its 3D model created. The obtained 3D models were compared and the geometry deviation was measured to determine that the embedded error was invisible to an average observer and that the watermark can be extracted. The proposed method simultaneously protects the digitized image of the artwork while preserving its visual experience. Other methods cannot guarantee this.

A Mechanical Integrator is a mechanical device which can be used to obtain the continual integration of the input variable value. This paper explains the operational principles and discloses the simulation and motion study results of the mechanical integrator 3D model assembly. Specifically, 3D models of the input function generator, the ball and disc integrator and the output x-y plotter are created and their operations are simulated. This work is significant mainly for education in the fields of solid modelling, mechanism synthesis and scientific visualization of the mechanism motion and operation. In particular, the motion analysis presented in this paper visualizes and discloses the mutual relationship between the integration calculus as the mathematical operation and the geometrical and kinematical characteristics of one special type of mechanical computing device.

The escapement is a very important horological invention and it is commonly used in theory of clocks and chronometers. It transfers energy to the timekeeping element and allows the number of its oscillations to be counted. The chronometer detent escapement used in marine chronometers was modified and simplified by Thomas Earnshaw, English renowned watchmaker, in order to make it available to the public. This chapter deals with 3D modeling and assembling of all escapement parts in SolidWorks, as well as constructive geometry of mechanism and computer simulation. The whole process has been accomplished in program “SolidWorks 2016,” where all parts are assembled by using standard mates since this approach is suitable for motion and dynamical analysis. Generated simulation results are very close to the real ones, thereby using computationally strong kinematic solvers.

Gaspard Monge is known as the father of modern descriptive and differential geometry. In 1764, he was engaged to draw a detailed plan of a fortification in his hometown, which was seen by an officer at the École Royale du Génie de Mézières. This plan was a success and his techniques were marked as a military secret for a long period of time. In 1780, he was elected to the Academy of Science and participated in the work of the Commission for Weights and Measures, that was in charge of moving the system from imperial to metric. In 1794, Monge helped setting up the École Centrale des Travaux Publics (later École Polytechnique) where he was lecturing Descriptive Geometry. In 1798, Napoleon undertook a campaign in Egypt. The famous chemist Claude Louis Berthollet was asked to recruit prominent scientists. Among them were Fourier, Monge, Dolomieu and Malus. Institut d'Egypte was established by Napoleon and Monge was named as its first president. Monge passed away on July 28, 1818. His name is inscribed on the base of the Eiffel Tower and it is located on the third façade opposite the Military Academy. Besides descriptive geometry, he carried on many different researches in chemistry and physics.

This paper analyzes the geometrical and mechanical characteristics of balance springs, which have the most important influence on the oscillation rate of the balance wheel and, consequently, the most decisive effects on the timekeeper’s accuracy. These characteristics are obtained by a set of SolidWorks simulations of static structural studies based on the finite element model, which are performed and accomplished in a specific and original way. Our study demonstrates that the position of the balance spring center of mass and its momentum of inertia are not constant but depend on the angular displacement of the spring collet end. It also shows that the torque spring rate (the spring stiffness) varies as a function of angular displacement during the balanced spring twist. All results are presented numerically and graphically by a set of diagrams and can contribute to the better understanding of the balance spring geometrical and mechanical features and, therefore, be applied for improving a timepiece’s accuracy. Moreover, the method of simulation study disclosed and explained in this paper provides general suggestions and guidance for similar studies. The accuracy of the presented results, as well as the validity of the complete simulation-based method, is proven by the experimentally determined relationship between balance spring restoring torque, stiffness, and spring angular displacement.

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.