A device for the locking of pieces on machine tools, comprising: - at least one base body fixable to a machine tool (M); and - at least one gripping assembly for gripping a piece (P) to be machined having at least one cavity (C) with a cavity axis (A1), said gripping assembly being adapted to lock said piece (P) on said machine tool (M) and comprising: - a main head having a main axis (A3) and insertable into said cavity (C) in an insertion configuration wherein said main axis (A3) is substantially parallel to said cavity axis (A1); - at least two self-centering locking elements associated with said main head in a movable way along sliding directions (D) substantially transverse to said main axis (A3) to abut on the inner surface (S) of said cavity (C) when said main head is in said insertion configuration; and - movement means of said self-centering locking elements between a retraction position and an extraction position; characterized by the fact that: - said main head is associated with said base body with a lateral play adapted to allow the shift of said main head along a plane of alignment (B) substantially orthogonal to said main axis (A3) to allow the placement of said gripping assembly in an alignment configuration wherein said main axis (A3) is aligned with said cavity axis (A1); and - said device comprises removable locking means adapted to temporarily lock said main head with respect to said base body in said alignment configuration. - at least one base body fixable to a machine tool (M); and - at least one gripping assembly for gripping a piece (P) to be machined having at least one cavity (C) with a cavity axis (A1), said gripping assembly being adapted to lock said piece (P) on said machine tool (M) and comprising: - a main head having a main axis (A3) and insertable into said cavity (C) in an insertion configuration wherein said main axis (A3) is substantially parallel to said cavity axis (A1); - at least two self-centering locking elements associated with said main head in a movable way along sliding directions (D) substantially transverse to said main axis (A3) to abut on the inner surface (S) of said cavity (C) when said main head is in said insertion configuration; and - movement means of said self-centering locking elements between a retraction position and an extraction position; - a main head having a main axis (A3) and insertable into said cavity (C) in an insertion configuration wherein said main axis (A3) is substantially parallel to said cavity axis (A1); - at least two self-centering locking elements associated with said main head in a movable way along sliding directions (D) substantially transverse to said main axis (A3) to abut on the inner surface (S) of said cavity (C) when said main head is in said insertion configuration; and - movement means of said self-centering locking elements between a retraction position and an extraction position; - said main head is associated with said base body with a lateral play adapted to allow the shift of said main head along a plane of alignment (B) substantially orthogonal to said main axis (A3) to allow the placement of said gripping assembly in an alignment configuration wherein said main axis (A3) is aligned with said cavity axis (A1); and - said device comprises removable locking means adapted to temporarily lock said main head with respect to said base body in said alignment configuration. <EOS>