A machine that forms the heads of coils made of rectangular wire so that it fits within the slots of the stator of an electric machine. The machine receives a coil having unformed first and second heads separated by first and second legs and applies controlled deformation to yield properly shaped heads. The machine comprises first and second leg support mechanisms for gripping the first and second legs and head-forming elements mounted to the first and second leg support mechanisms for contacting portions of the heads of the coil while the first and second legs are gripped by the leg support. Actuators are provided for causing sequential actuated movements of one of the first and second legs to force the head-forming elements into contact with different portions of the first and second heads while allowing selective free movements of the other leg in response to the actuated movements.