The kinematic relationship between Plücker coordinates, moments of ruled surfaces, and real quaternion algebra
TURKISH JOURNAL OF MATHEMATICS, cilt.50, sa.4, ss.636-650, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3673
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Academic Search Ultimate (EBSCO), Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.636-650
- Ankara Üniversitesi Adresli: Evet
Özet
This paper introduces a new kinematic method for generating ruled surfaces in Euclidean 3-space. We demonstrate that the Plücker coordinate method for straight lines can be extended to ruled surfaces. We prove that the moment of a ruled surface is a unique curve, which is independent of the chosen base curve. Moreover, we introduce a novel and distinctive base curve that is defined as the set of points on the rulings of the ruled surface such that these points are closest to the origin. Thus, we prove that each ruled surface can be generated using a real quaternion and a moment curve. Consequently, we express the ruled surface as a rigid transformation. We show that the moment curve is the axis of rotation in the generation of the ruled surface. Finally, we provide a geometric interpretation of the generation of ruled surfaces, along with some examples featuring their respective moment curves and figures.