Algorithms for Jewelry Industry 4.0

The industrial and technological revolution and the use of innovative software allowed to build a virtual world from which we can control the physical one. In particular, this development provided relevant benefits in the field of jewelry manufacturing industry using parametric modeling systems. This paper proposes a parametric design method to improve smart manufacturing in 4.0 jewelry industry. By using constrained collection of schemata, the so called Direct Acyclic Graphs (DAGs) and additive manufacturing technologies, we created a process by which customers are able to modify 3D virtual models and to visualize them, according to their preferences. In fact, by using the software packages Mathematica and Grasshopper, we exploited both the huge quantity of mathematical patterns (such as curves and knots), and the parametric space of these structures. A generic DAG, grouped into a unit called User Object, is a design tools shifting the focus from final shape to digital process. For this reason, it is capable to returns a huge number of unique combinations of the starting configurations, according to the customers preferences. The configurations chosen by the designer or by the customers, are 3D printed in wax-based resins and, later, ready to be merged, according to artisan jewelry handcraft. Two cases studio are proposed to show empirical evidences of the designed process to transform abstract mathematical equations into real physical forms.