A METHOD FOR MANNHEIM OFFSETS OF RULED SURFACES

Abstract

In this paper, using Darboux frame {T, g, n} of ruled surface phi(s,v), Mannheim offsets phi* (s, v) with Darboux frame {T*, g*, n*} of phi(s,v) are defined. The striction curve, distribution parameter and orthogonal trajectory of phi* (s, v) are investigated by using the Darboux frame {T, g, n} . The distribution parameters of ruled surfaces phi*(T*),phi*(g*), and phi*(n*) are calculated. Finally, the relation between the instantaneous Pfaffian vectors of motions H / H' and H* / H*' are given, 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.