On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces

Abstract

In this study, ruled surfaces formed by Frenet's trihedral of involute curve$beta $ of a given curve $alpha $ are discussed. These surfaces are named as involute trajectory ruled surfaces. These type of ruled surfaces are expressed depending on the angle $theta $ between the binormal vector $b$ and Darboux vector $D$ of the main curve (evolute) $alpha $. Also, some new results and theorems related to the developability of the involute trajectory ruled surfaces are obtained. Finally we illustrate these surfaces by presenting some examples.