The deformable driving band (3) or similar comprises passage means (2) passing through the band and opening out, towards the inside, at right angles to pockets (5) or similar provided in a compressible strip (6) extending over the whole driving band, the assembly being such that a suction phenomenon increasing grip is created by the compressible strip (6) and the packets (5) in deformation zone of the driving band (3) corresponding to an expansion phase of said pockets (5).