surrounding the layers of profiled member at several places on the circumference and in particular in the zones of covering of the start and end of the spiral formed by the profiled member or by any suitable means of fastening the hooks 31 and 32 can then be released this takes place due to the fingers 82 which maintain the bead ring 45 axially by their ends 820 which are directed towards the bottom and lowered axially on the inner side of the ring 45 while the support arms 2 are pushed back axially towards the core 7 this movement see fig5 makes it possible to release all the first hooks 31 the fingers 82 are then raised the device 8 moves axially away from the core 7 in order to be able to lower the ends 820 axially on the outside of the bead ring 45 fig6 and 7 the bead ring 45 is pushed against the core 7 by the axial movement of the device 8 towards the core 7 while the support arms 2 are moved axially away fig7 and 8 which releases the last hooks 32 the flexibility of the hooks 31 and 32 must be compatible with the necessity of their resuming precisely their position in each ring 1 after unhooking even if all the hooks of one and the same type are not unhooked all simultaneously at this stage the core 7 bearing the reinforcement anchored to bead rings 45 can be removed from the apparatus the manufacture of the.