The invention concerns a convertible gym training device intended to be removably connected to a weight-training device that permits training of lower and upper body limbs.According to the invention, such a convertible gym training device in particular comprises: an essentially quadrangular frame (1014); an arm actuator (107) rotatably connected to the said frame (1014); resilient return means (40) opposing a force against the rotation of the said arm actuator (107) relatively to the said frame (1014); mechanical link means (400) connecting the said arm actuator (107) with the said resilient return means (40), said mechanical link means (400) being designed to oppose a variable back moving force against the said arm actuator (107), all along its rotation travel, said back moving force being variable according to a predetermined load curve.