Method and machine (18) to manufacture a coil (9-14) around a component (102) of an article (100). A main conveyor (19) moves, along a working path (P1), a carriage (20) provided with a seat (22, 23, 24) designed to house the component (102); the component (102) is arranged in the seat (22, 23, 24) of the carriage (20) in an input station (S1) arranged along the working path (P1); and in a winding station (S3, S6, S9, S12, S15, S18) arranged along the working path (P1), a wire (15) is directly wound around the component (102) to form a series of turns making up the coil (9-14) by making a movable finger (57), which engages the wire (15) in a sliding manner, revolving around the component (102) several times.