Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories
Abstract
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories are well known, the case of line trajectories is more complicated and has not been studied. We explain when such motions exist and how to compute them. Our method gives explicit formulas for constructing these motions and shows that, in many cases, the solution is unique. We also show examples and explain how to use these results to design simple mechanisms that move a line in the desired way. This work helps to better understand the relationship between rational motions and ruled surfaces and may be useful for future research in mechanism design.
Cite
@article{arxiv.2506.18029,
title = {Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories},
author = {Zülal Derin Yaqub and Hans-Peter Schröcker},
journal= {arXiv preprint arXiv:2506.18029},
year = {2025}
}