Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve

A special Frenet motion with a one parameter has been given by Bottema [5] in E 3. In this study, we have given a generalization of [5] to Bishop motion in Euclidean 3-space. Firstly, Bishop motion is defined for space curve α and then Darboux vector of this motion is calculated for fixed and moving spaces in E 3.The Bishop darboux rotation for space curves in Euclidean space E 3 is decomposed into two simultaneous rotations. The axes of these simultaneous rotations are joined by a simple mechanism. One of these axes is a parallel of the tangent vector of the curve, the direction of the other is the direction of the Bishop darboux vector of the curve. This decomposition of the Bishop darboux rotation yields a necessary condition for the curve to be closed.