Abstract: A machine for the manufacture of rotational parts in a three-dimensional material is disclosed. A mandrel provided with rows of barbs is rotatably carried by the machine, whereby superimposed layers of threads are successively deposited in the longitudinal and circumferential corridors defined between the barbs. The machine additionally comprises a retractable member adapted to hold in place one extremity of a weft thread when the latter does not extend outside of the corresponding corridor, and a winding system which positions a holding thread in a circumferential corridor near the extremities of the weft threads to hold them in place when the retractable member has been retracted.