ON THE EVOLUTE OFFSETS OF RULED SURFACES USING THE DARBOUX FRAME

Abstract

In this study, using Darboux frame fT; g; ng of ruled surface '(s; v), the evolute o§sets ' (s; v) with Darboux frame fT; g ; n g of '(s; v) are deÖned. Characteristic properties of ' (s; v) as a striction curve, distribution parameter and orthogonal tra jectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces ' T ; ' g and ' n are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfa¢ an vectors of motions H=H0 and H=H 0 , where H = fT; g; ng be the moving space along the base curve of '(s; v), H = fT; g ; n g be the moving space along the base curve of ' (s; v), H0 and H 0 be Öxed Euclidean spaces.