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.

Keywords

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

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