A mechanism for laying a strip on a receiving surface rotating about a first axis. The mechanism includes a laying head moving along a second axis oriented parallel to the axis of rotation of the surface and along a third axis oriented parallel to a radial direction passing through the point of contact between the receiving surface and a strip applicator of the laying head. The laying head is rotatable about a front axis oriented substantially perpendicular to the second and third axes and passing through the contact point. the laying includes a device for estimating the value of the of the angle α formed by a tangent to the transverse profile of the surface and the second axis. The movements of the laying head are determined by the value of the angle α in such a way as to displace the laying head in a direction parallel to the tangent following the transverse profile of the receiving surface.