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

Year 2021, Volume: 13 Issue: 1, 94 - 105, 30.06.2021

Mustafa Bilici

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.

Keywords

Trajectory ruled surface, developable ruled surface, involute-evolute, Frenet frame, Euclidean 3-space

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