from point h this results in point a2 39 further a line is drawn through the second contour point u1 which has an inclination gamma 2 which equals alpha 2 relative to the zero position of the axis another contour point u2 is located in the point where the perpendicular line extended from the point a2 39 on the zero position of the axis 17 intersects this line the perpendicular lines on the zero position of the axis in the respective points a1 39 and a2 39 represent each the radii r1 and r2 of the roll in the normal plane the projection of which is represented by the respective perpendicular lines if only two pivotal angles are given the false twist roll will obtain a discontinuous contour line however a steady contour line may be obtained if the pivotal angles are closely stepped fig4 discloses a second embodiment of the invention in this embodiment the roll is supported in a mounting support 10 rotatable about a pivot 12 the roll is driven by a motor 11 the pivoted position of the roll can be secured by a locking mechanism 16 in a slot 23 which is concentric to the pivotal axis and provided in base plate 27 a yarn advances from cooling plate 7 and travels without deflection over yarn guide 8 onto false twisting roll 9 at the same time the false twisting roll is.