On point-line displacement with elliptic screw motion

The objective of this paper is to develop the concept of point-line displacement within the framework of elliptic space, denoted as Ra1,a2,a3. The study begins by summarizing the fundamental principles of elliptic dual quaternions and elliptic screw motion. Next, the notion of point-line displacement is rigorously defined in the context of elliptic inner product spaces, and its algebraic properties are thoroughly analyzed. Finally, the practical relevance of the proposed approach is demonstrated through an illustrative example that establishes the relationship between point-line geometry and the elliptic dual Euler-Rodrigues formula. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.