A robot arm having seven axes of actuation imparts to a toroidal support a circumferential distribution motion about its own geometric axis simultaneously with controlled transverse distribution displacements in front of a dispensing organ of a strip of elastomeric material. The strip thus forms a plurality of turns, the orientation and mutual superposition whereof are controlled in such a way as to control the thickness variations to be conferred to a component of a tyre being manufactured, based on a pre-determined laying scheme pre-set on an electronic computer. The rotation of the toroidal support is controlled in such a way as to obtain a peripheral speed of application exceeding the theoretical feeding rate of the strip, able to be increased or decreased as needed to form turns with reduced or, respectively, enlarged cross section.