Ozturk, UfukErdal, Gulay2024-09-252024-09-2520230352-96652406-047Xhttps://doi.org/10.22190/FUMI230404041Ohttps://hdl.handle.net/20.500.12491/13490This 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.eninfo:eu-repo/semantics/closedAccessDarboux axisslant helixa curve of constant precessionLie groupsArticle10.22190/FUMI230404041O383649658WOS:001133108700007Q3