Search results

The purpose of this paper is to propose a new way of prototyping surfaces, taking the mathematical background into account, without involving drawing environments.

The authors thicken surfaces from a mathematical point of view to obtain solids. Next they look for an operative procedure to build virtual models and interchange files. The authors build a sample of Enneper thickened surface by fused deposition modelling and verify the prototype by reverse engineering techniques.

The authors provide a formulation able to thicken surfaces in mathematical terms. An operative procedure generates virtual solids and interchange files in the same environment. The approximations necessary for additive fabrication, such as triangulations and mesh geometry, can be chosen at this stage.

The approach is useful at the product/process development stage, in which surfaces are delivered by theoretical analysis. At this stage a prototype can give useful advice permitting functional tests. The limitation is that, when the mathematical formulation is not available, it is difficult to translate a concept without fundamentals of differential geometry.

Approximations of drawing environments typically lead to fault models, not ready for fabrication by additive manufacturing (AM) technologies, needing empiric, not at all obvious and not rapid repair interventions. The authors' approach eliminates this stage, permitting a faster and simple managing of modifications due to functional and technological requirements, that are frequent at concept stage. This leads to a time‐to‐market reduction in the course of product/process development.

This paper extends the capability of a mathematical approach to solve surface prototyping problems. By reducing the required stages, the proposed methodology finds a theoretical and practical shorter route to direct fabrication.