Akademik Veri Yönetim Sistemi
20th INTERNATIONAL CONFERENCE ON ENGINEERING & NATURAL SCIENCES, Ohrid, Makedonya, 23 - 30 Mayıs 2026, ss.196-204, (Tam Metin Bildiri)
In this paper, the theoretical background and geometric properties of parallel Darboux equidistant ruled surfaces are examined by studying in detail the Twisted Cubic curve, which is considered one of the fundamental curves of differential geometry. Within the scope of the study, primarily, the Frenet-Serret moving frame elements, curvature, and torsion values of the base curve, along with the Darboux vectors that characterize the rotational dynamics of the surface, are calculated analytically.In order to provide the equidistance condition consistently in space, how the constant distance d between the central planes is dynamically balanced and preserved via the translation functions in the tangent and binormal directions is clearly demonstrated by the obtained equations.In order to prove the geometric validity of the theoretical findings, the created system is meticulously examined at different parameter values: In particular, that special case where the striction point goes to infinity and the surface locally exhibits a cylindrical character due to the instantaneous vanishing of the curvature and torsior derivatives is detailed.It is stated that even in this singular case, the parallelism between the central planes is flawlessly preserved in the principal normal direction without any deviation. Additionally, at further parameter values reflecting the general bending characteristic of the system, it is proven that despite the spatial asymmetry and complicating form of the surface, the equidistant structure uncompromisingly maintains its geometric integrity. 'The obtained analytical results and the created geometric structures are modeled in three-dimensional space using MATLAB software, and all figures presented in the study are drawn with high precision through this program. As a result, this comprehensive example clearly reveals the structural parallelism between the base ruled surface, the equidistant surface, striction lines, generator lines, and central planes.