Abstract: Gymnastic machine including an epicycloidal mechanism (2) for connecting an application member (3) of a driving device to resistive means (36); the mechanism (2) being provided with a satellite member (4) connected to the application member (3) by means of a first crank (5) having a pin (6); with a planetary member (7); with a second crank (8) which rotationally connects a movable rotation centre (9) on the satellite member (4) to a fixed centre (10) on the planetary member (7); and with transmission devices (11, 12, 13) for transmitting a relative motion between the satellite member (4) and the planetary member (7); the planetary member (7) being supported in freely rotatable manner around an axis (14) passing through the fixed centre (10); actuating members (15) being provided for imparting to planetary member (7) an angular movement (?) around the fixed centre (10) which corresponds to a relative angular variation (?) of the first and second cranks (5, 8), and a corresponding variation of the orientation o