A riveting machine which makes it possible to rivet two parts (81, 82), such as metal plates, to one another, the machine comprising: - a motorization system, for example a step motor which is associated with a reduction gear, comprising an output shaft; - a set of connection rods which are articulated on one another, characterized in that said set of connection rods comprises a first connection rod which is fitted such as to be integral in rotation with the output shaft of the motorization system, and a second connection rod which is articulated on the first connection rod; and in that said machine also comprises: - a ram which is articulated on the second connection rod, and is provided at its end opposite the one articulated on the second connection rod with a tool for retention of the rivet and putting it into place, known as the upper rivet die; - a guide device which is configured to guide the displacement of the ram along a guide axis; - a thrust element, known as the lower rivet die, which can be displaced in a direction parallel to the guide axis of the guide device, in order to cooperate with the upper rivet die, such as to upset the rivet, when said rivet is positioned in the interior of an orifice pierced through the parts (81, 82) to be riveted, between said upper and lower rivet dies; and - a control unit which is configured to rotate the output shaft of the motorization system, such as to make the connection rods (31, 32) of the system of connection rods go from a folded position to a deployed position, in which the connection rods (31, 32) are aligned along an axis which intersects the axis of the output shaft of the motorization system. - a motorization system, for example a step motor which is associated with a reduction gear, comprising an output shaft; - a set of connection rods which are articulated on one another, characterized in that said set of connection rods comprises a first connection rod which is fitted such as to be integral in rotation with the output shaft of the motorization system, and a second connection rod which is articulated on the first connection rod; and in that said machine also comprises: - a ram which is articulated on the second connection rod, and is provided at its end opposite the one articulated on the second connection rod with a tool for retention of the rivet and putting it into place, known as the upper rivet die; - a guide device which is configured to guide the displacement of the ram along a guide axis; - a thrust element, known as the lower rivet die, which can be displaced in a direction parallel to the guide axis of the guide device, in order to cooperate with the upper rivet die, such as to upset the rivet, when said rivet is positioned in the interior of an orifice pierced through the parts (81, 82) to be riveted, between said upper and lower rivet dies; and - a control unit which is configured to rotate the output shaft of the motorization system, such as to make the connection rods (31, 32) of the system of connection rods go from a folded position to a deployed position, in which the connection rods (31, 32) are aligned along an axis which intersects the axis of the output shaft of the motorization system. - a ram which is articulated on the second connection rod, and is provided at its end opposite the one articulated on the second connection rod with a tool for retention of the rivet and putting it into place, known as the upper rivet die; - a guide device which is configured to guide the displacement of the ram along a guide axis; - a thrust element, known as the lower rivet die, which can be displaced in a direction parallel to the guide axis of the guide device, in order to cooperate with the upper rivet die, such as to upset the rivet, when said rivet is positioned in the interior of an orifice pierced through the parts (81, 82) to be riveted, between said upper and lower rivet dies; and - a control unit which is configured to rotate the output shaft of the motorization system, such as to make the connection rods (31, 32) of the system of connection rods go from a folded position to a deployed position, in which the connection rods (31, 32) are aligned along an axis which intersects the axis of the output shaft of the motorization system.