On the Invariants of Ruled Surfaces Generated by the Dual Involute Frenet Trihedron

Abstract

The purpose of this paper is to describe ruled surfaces generated by a Frenet trihedron of closed dual involute for a given dual curve. We identify relations between the pitch, the angle of the pitch, and the drall of these surfaces. Some new results related to the developability of these surfaces are also obtained. Finally, we illustrate these surfaces by presenting one example.