Grinding head with flap wheels that can be used in a machining station of at least one mechanical piece, comprising: - at least one basic frame associable with at least one movement device adapted to move said grinding head inside said machining station; the grinding head being characterized in that it further comprises: - at least one operating assembly provided with at least one gripping and rotation unit (16, 17) of at least one flap wheel around at least one operational axis for the machining of said mechanical piece, in which said operating assembly is associated with said basic frame and movable in rotation in both directions of rotation around at least one axis of rotation, during said machining, between a balance position, wherein said operating assembly and said basic frame are aligned along an axis of equilibrium substantially perpendicular to said axis of rotation, and an unbalance position, wherein said operating assembly is rotated relative to said axis of equilibrium by an angle of rotation (α); and - bi-directional pneumatic compensation means adapted to counteract the rotation of said operating assembly around said axis of rotation from said balance position to said unbalance position in both directions of rotation. - at least one basic frame associable with at least one movement device adapted to move said grinding head inside said machining station; the grinding head being characterized in that it further comprises: - at least one operating assembly provided with at least one gripping and rotation unit (16, 17) of at least one flap wheel around at least one operational axis for the machining of said mechanical piece, in which said operating assembly is associated with said basic frame and movable in rotation in both directions of rotation around at least one axis of rotation, during said machining, between a balance position, wherein said operating assembly and said basic frame are aligned along an axis of equilibrium substantially perpendicular to said axis of rotation, and an unbalance position, wherein said operating assembly is rotated relative to said axis of equilibrium by an angle of rotation (α); and - bi-directional pneumatic compensation means adapted to counteract the rotation of said operating assembly around said axis of rotation from said balance position to said unbalance position in both directions of rotation. - at least one operating assembly provided with at least one gripping and rotation unit (16, 17) of at least one flap wheel around at least one operational axis for the machining of said mechanical piece, in which said operating assembly is associated with said basic frame and movable in rotation in both directions of rotation around at least one axis of rotation, during said machining, between a balance position, wherein said operating assembly and said basic frame are aligned along an axis of equilibrium substantially perpendicular to said axis of rotation, and an unbalance position, wherein said operating assembly is rotated relative to said axis of equilibrium by an angle of rotation (α); and - bi-directional pneumatic compensation means adapted to counteract the rotation of said operating assembly around said axis of rotation from said balance position to said unbalance position in both directions of rotation.