that the screw end 131 opening is formed into a blocking edge 133 i e it forms with the locking device 2 to form an anti slip connection the locking device 2 is a screw body which is also provided with screw threads 21 at the screw end 131 the limiting hole 22 restricts the blocking edge 133 such that the displacement axle core screw end 131 will not dislocate from the locking device 2 referring to fig4 again when the braking device is at normal condition the tension spring 12 urges a tension force to push the displacement axle 13 at this point of time the steel balls 15 correspond to the converging face 142 each of the steel balls 15 will urge to the cable 3 thus fastening or engaging effect is formed at this point of time when the locking device 2 and the displacement axle core screw end 131 are connected a locking is formed between the locking device 2 and the braking body 14 which means an addition locking mechanism is provided in accordance with the present invention this equals to provide the displacement axle core 13 a strong pulling force which is converted into a strong engagement force to ensure the fastening strength of the braking device 1 this will fully prevent the inner push of the displacement axle core 13 as shown in fig1 and 6 referring to fig5 and 7.