The device comprises at least one conical roller, and a thread guide cooperating with the roller for orienting a thread at the circumference of the roller. The thread guide is in the form of a control arm which is provided with a thread eye and which is mounted for movement in a path such that the thread eye is displaced substantially parallel to a generatrix of the conical roller. A pivoted rocker arm is coupled to the control arm and is rocked by means of a cam mounted on a rotatable shaft.