On the Bertrand offsets for ruled and developable surfaces

Abstract

This work examines some classical results of Bertrand curves for ruled and developable surfaces using the E. Study’s dual line coordinates. In particular, a developable surface can have a developable Bertrand offset if a linear equation holds between the curvature and torsion of its edge of regression. From this result many of the classical results of closed space curve follow rather simply. Finally, an example of application is introduced and explained in detail.