A disc assembly of disc brake adapted to cooperate with a brake caliper for exerting a braking action on a vehicle, said assembly being adapted to rotate about a rotation axis (X-X) coincident with or parallel to an axial direction (A-A), said assembly extending away from said rotation axis along radial directions (R-R) orthogonal to said axial direction (A-A) and along circumferential directions (C-C) orthogonal to said axial direction (A-A) and to said radial directions (R-R), and also locally defining tangential directions (T-T) precisely orthogonal to said axial direction (A-A) and orthogonal to the radial direction (R-R) passing through said point; wherein said assembly comprises: - a braking band; - a bell for connecting the disc assembly to a support of a vehicle; - at least one driving element; wherein - said bell rests on at least one surface (33, 34) of the braking band, or a plurality of surfaces (33, 34) of the braking band substantially coplanar with one another, thus avoiding a two-sided restraint at least between said bell and said braking band; - said braking band comprises at least one band driving surface (9; 10; 11; 12) extending along said axial (A-A) and radial (R-R) directions, thus forming a tangential abutment surface for the band; - said at least one driving element slidingly rests on said at least one band driving surface (9; 10; 11; 12); characterized in that - said bell comprises at least one bell driving surface (18; 19) extending along said axial (A-A) and radial (R-R) directions, thus forming a tangential abutment surface for the bell; - said at least one driving element is selectively movable along said at least one band driving surface (9; 10; 11; 12), at least passing: - from a position in which it avoids resting on the bell - to a position in which it rests on the bell and restrains said bell to said band in axial direction (A-A) and in circumferential direction (C-C); - thus avoiding said braking band from being restrained to said bell in radial direction (R-R). - a braking band; - a bell for connecting the disc assembly to a support of a vehicle; - at least one driving element; - said bell rests on at least one surface (33, 34) of the braking band, or a plurality of surfaces (33, 34) of the braking band substantially coplanar with one another, thus avoiding a two-sided restraint at least between said bell and said braking band; - said braking band comprises at least one band driving surface (9; 10; 11; 12) extending along said axial (A-A) and radial (R-R) directions, thus forming a tangential abutment surface for the band; - said at least one driving element slidingly rests on said at least one band driving surface (9; 10; 11; 12); - said bell comprises at least one bell driving surface (18; 19) extending along said axial (A-A) and radial (R-R) directions, thus forming a tangential abutment surface for the bell; - said at least one driving element is selectively movable along said at least one band driving surface (9; 10; 11; 12), at least passing: - from a position in which it avoids resting on the bell - to a position in which it rests on the bell and restrains said bell to said band in axial direction (A-A) and in circumferential direction (C-C); - thus avoiding said braking band from being restrained to said bell in radial direction (R-R). - from a position in which it avoids resting on the bell - to a position in which it rests on the bell and restrains said bell to said band in axial direction (A-A) and in circumferential direction (C-C); - thus avoiding said braking band from being restrained to said bell in radial direction (R-R).