Ufuk Öztürk, Gülay Erdal

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This paper presents a study on the motion of the Darboux rotation axis for curves in three-dimensional Lie groups a bi-invariant metric using the Frenet frame. Our findings reveal that the motion of the axis can be resolved into two simultaneous rotational motions. Additionally, we develop a sequence of Darboux vectors that are useful in constructing uncomplicated mechanisms. We also introduce a curve with constant precession and conduct an exhaustive analysis of its characteristics.


Darboux axis, slant helix, a curve of constant precession, Lie groups

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DOI: https://doi.org/10.22190/FUMI230404041O


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