Kit for a machine for the injection moulding of moulded parts, the moulding machine comprising a first platen and a second platen, the kit comprising: - a first support plate intended to be fixed on said first platen, - a second support plate intended to be fixed on said second platen, the two platens being designed to be able to move with respect to each other by sliding according to a translation direction so as to adopt successively an open position in which the two support plates (1104, 1154) are distant from each other and a closed position in which the two support plates (1104, 1154) are up against each other, - for the first support plate, at least one barrel of a first type, rotatably mounted on said first support plate about an axis perpendicular to the plane of said first support plate, and carrying at least two cavities (1114a, 1114d), - for the second support plate, at least one barrel of a second type, rotatably mounted on said second support plate about an axis perpendicular to the plane of said second support plate, and carrying at least three cavities (1164a-c), - for each of said cavities (1114a, 1114d, 1164a-c), a counter-cavity (1164a, 1164d, 1114a-c) disposed on the other support plate (1104, 1154), - driving means intended to rotate each barrel (1106, 1156) to allow the successive positioning of each cavity (1114a, 1114d, 1164a-c), opposite at least two different counter-cavities (1164a, 1164d, 1114a-c) and so that, at each rotation movement of each barrel (1106, 1156), one of the cavities of said barrel of the first type is opposite one of the counter-cavities of said barrel of the second type and so that, at each rotation movement of each barrel (1106, 1156), the other cavity of said barrel of the first type and the associated counter-cavity of said second support plate constitute a moulding pair for a first element of the part to be moulded, one of the other cavities of said barrel of the second type and the associated counter-cavity of said first support plate constitute a moulding pair for a second element of the part to be moulded, one of the other cavities of said barrel of the second type and the associated counter-cavity of said first support plate constitute an overmoulding pair for said second element, and said pair consisting of the cavity of said barrel of the first type and the counter-cavity of said barrel of the second type constitute an assembly pair for said first element thus moulded and for said second element thus moulded and overmoulded. - a first support plate intended to be fixed on said first platen, - a second support plate intended to be fixed on said second platen, the two platens being designed to be able to move with respect to each other by sliding according to a translation direction so as to adopt successively an open position in which the two support plates (1104, 1154) are distant from each other and a closed position in which the two support plates (1104, 1154) are up against each other, - for the first support plate, at least one barrel of a first type, rotatably mounted on said first support plate about an axis perpendicular to the plane of said first support plate, and carrying at least two cavities (1114a, 1114d), - for the second support plate, at least one barrel of a second type, rotatably mounted on said second support plate about an axis perpendicular to the plane of said second support plate, and carrying at least three cavities (1164a-c), - for each of said cavities (1114a, 1114d, 1164a-c), a counter-cavity (1164a, 1164d, 1114a-c) disposed on the other support plate (1104, 1154), - driving means intended to rotate each barrel (1106, 1156) to allow the successive positioning of each cavity (1114a, 1114d, 1164a-c), opposite at least two different counter-cavities (1164a, 1164d, 1114a-c) and so that, at each rotation movement of each barrel (1106, 1156), one of the cavities of said barrel of the first type is opposite one of the counter-cavities of said barrel of the second type and so that, at each rotation movement of each barrel (1106, 1156), the other cavity of said barrel of the first type and the associated counter-cavity of said second support plate constitute a moulding pair for a first element of the part to be moulded, one of the other cavities of said barrel of the second type and the associated counter-cavity of said first support plate constitute a moulding pair for a second element of the part to be moulded, one of the other cavities of said barrel of the second type and the associated counter-cavity of said first support plate constitute an overmoulding pair for said second element, and said pair consisting of the cavity of said barrel of the first type and the counter-cavity of said barrel of the second type constitute an assembly pair for said first element thus moulded and for said second element thus moulded and overmoulded.