Kinematic-geometry of a line trajectory and the invariants of the axodes-Reference-Cited by-同舟云学术

Kinematic-geometry of a line trajectory and the invariants of the axodes

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Li Yanlin¹,Mofarreh Fatemah²,Abdel-Baky Rashad A.³

Affiliation:

1. School of Mathematics, Hangzhou Normal University , Hangzhou 311120 , China

2. Mathematical Science Department, Faculty of Sciences, Princess Nourah Bint Abdulrahman , Riyadh 11546 , KSA

3. Department of Mathematics, Faculty of Science, University of Assiut , Assiut 71516 , Egypt

Abstract

Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0252/pdf

Reference36 articles.

1. O. Bottema and B. Roth, Theoretical Kinematics, North-Holland Press, New York, 1979.

2. A. Karger and J. Novak, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York, 1985.

3. H. Pottman and J. Wallner, Computational Line Geometry, Springer-Verlag, Berlin, Heidelberg, 2001.

4. R. Garnier, Cours de Cinématique, Tome II: Roulement et Vibration-La Formule de Savary et son Extension a laEspace, Gauthier-Villars, Paris, 1956.

5. J. Phillips and K. Hunt, On the theorem of three axes in the spatial motion of three bodies, J. Appl. Sci. 154 (1964), 267–287.

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