f is the friction coefficient between the thread and the ring 121 and u03b2 is the angle of winding of the thread on said ring the component h 39 a is added to the component ha which said thread discharges onto the body 120 at the points of tangency of said body with respect to the drum ta and significantly improves the elastic response of the truncated cone braking body to variations in the traction t the ring 121 fitted on the terminal section of the truncated cone braking body 120 is made of brass or steel plate with a thickness of 2 3 tenths of a millimeter and advantageously has a flared edge 122 fig1 which slightly protrudes inside the truncated cone body 120 as clearly shown in the figure the flared edge 122 keeps the thread f adjacent to but spaced from the inner surface of the body 120 with the advantage that the thread in its rotary unwinding motion does not slide on said surface and therefore is not subjected to uncontrolled braking and torsion but at the same time performs a cleaning action with regard to the lint which tends to deposit thereon the variations of fig1 and 12 show an improved elastic suspension means 330 for the truncated cone braking body 120 said suspension means by virtue of its greater axial elasticity further contributes to improve the modulation of the braking action of said truncated cone braking body on threads having a small count the suspension means.