Turkish Journal of Mathematics
Author ORCID Identifier
SELAHATTİN ASLAN: 0000-0001-5322-3265
Abstract
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.
DOI
10.55730/1300-0098.3673
Keywords
Moment curves, Plücker coordinates, rigid transformations, ruled surfaces, real quaternions
First Page
636
Last Page
650
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
ASLAN, S (2026). The kinematic relationship between Plücker coordinates, moments of ruled surfaces, and real quaternion algebra. Turkish Journal of Mathematics 50 (4): 636-650. https://doi.org/10.55730/1300-0098.3673
