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Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 1

A New Approach to Generating Ruled Surfaces with Rigid Body Motion

Selahattin Aslan(ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİ)0000-0001-5322-3265
Pages
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Publication Date
2026-04-22
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that this developable ruled surface also represents a generalized cylinder.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new method for building ruled surfaces using dual quaternion curves and straight lines.
📊
Key Findings & Data:We proved that the rigid body motion, arranged from any straight line in Euclidean 3-space and any dual quaternion curve, produces a ruled surface in Euclidean 3-space when the parameter of the straight line is different from the parameter of the dual quaternion curve.
💡
Conclusion & Impact:We show that this developable ruled surface also represents a generalized cylinder.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ruled surface · developable surface · dual quaternion curve

Abstract

In this paper, we introduce a new method for building ruled surfaces using dual quaternion curves and straight lines. We proved that the rigid body motion, arranged from any straight line in Euclidean 3-space and any dual quaternion curve, produces a ruled surface in Euclidean 3-space when the parameter of the straight line is different from the parameter of the dual quaternion curve. We show that the ruled surface can be expressed by two separate rigid transformations. Moreover, we show that if the rotation part of the dual quaternion curve is a constant unit real quaternion, then the rigid body motion creates a developable ruled surface in Euclidean 3-space. We show that this developable ruled surface also represents a generalized cylinder.

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Cite This Article

Aslan, S. (2026). A New Approach to Generating Ruled Surfaces with Rigid Body Motion. International Electronic Journal of Geometry, Volume: 19 Issue: 1. https://doi.org/10.36890/iejg.1796953

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