ON THE EVOLUTE OFFSETS OF RULED SURFACES USING THE DARBOUX FRAME

Abstract

In this study, using Darboux frame {T, g, n} of ruled surface phi(s, v), the evolute offsets phi*(s, v) with Darboux frame {T*, g*, n*} of phi(s, v ) are defined. Characteristic properties of phi*(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces phi*(T*), and phi*(g*) phi*(n*) are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfaffian vectors of motions H/H' and H*/H*' where H = {T, g, n} be the moving space along the base curve of phi(s,v), H* = {T*, g*, n*} be the moving space along the base curve of phi* (s, v), H' and H*' be fixed Euclidean spaces.