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 β of a given curve α are discussed. These surfaces are named as involute trajectory ruled surfaces. These type of ruled surfaces are expressed depending on the angle θ between the binormal vector b and Darboux vector D of the main curve (evolute) α. 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. © MatDer.