A machine for physically exercising the limbs, comprising a translational-rotary machine comprising motor means (4, 4') and translational-rotary members, wherein the translational-rotary members comprise: - a movable carriage; - a lower shaft passing through the carriage; - a first return pulley integrally keyed onto the lower shaft on the front side of the machine; - a first toothed wheel integrally keyed onto the lower shaft on the rear side of the machine; - an upper shaft passing through the carriage, said upper shaft being vertically aligned with the lower shaft; - a second return pulley idly mounted onto the upper shaft on the rear side of the machine; - a first transmission member arranged on a front side of the machine, said first transmission member being adapted to operatively connect the motor means (4, 4') to the first return pulley; - a second transmission member arranged on a rear side of the machine, said second transmission member being adapted to operatively connect the motor means (4, 4') to the second return pulley; wherein the second return pulley is operatively connected to the first toothed wheel by means of a second toothed wheel, so that the force transmitted by the second transmission member acts on the upper section of the first toothed wheel, and wherein the force transmitted by the first transmission member acts on the lower section of the first return pulley, wherein shaped seats, ' adapted to insert and connect various types of tools to the machine are formed at the ends of the upper shaft, and wherein a pair of handles, ', or accessories of other type, are connected to the upper shaft by means of corresponding cranks (34, 34'), wherein a toothing is formed on the lower shaft, at the centerline of the lower shaft, and wherein a toothed reduction wheel is integrally keyed onto the upper shaft, at the centerline of the upper shaft, so as to mesh with the toothing on the lower shaft, and wherein the toothing and the toothed reduction wheel have different diameters from each other so as to form a motion reduction system. - a movable carriage; - a lower shaft passing through the carriage; - a first return pulley integrally keyed onto the lower shaft on the front side of the machine; - a first toothed wheel integrally keyed onto the lower shaft on the rear side of the machine; - an upper shaft passing through the carriage, said upper shaft being vertically aligned with the lower shaft; - a second return pulley idly mounted onto the upper shaft on the rear side of the machine; - a first transmission member arranged on a front side of the machine, said first transmission member being adapted to operatively connect the motor means (4, 4') to the first return pulley; - a second transmission member arranged on a rear side of the machine, said second transmission member being adapted to operatively connect the motor means (4, 4') to the second return pulley; wherein the second return pulley is operatively connected to the first toothed wheel by means of a second toothed wheel, so that the force transmitted by the second transmission member acts on the upper section of the first toothed wheel, and wherein the force transmitted by the first transmission member acts on the lower section of the first return pulley, wherein shaped seats, ' adapted to insert and connect various types of tools to the machine are formed at the ends of the upper shaft, and wherein a pair of handles, ', or accessories of other type, are connected to the upper shaft by means of corresponding cranks (34, 34'), wherein a toothing is formed on the lower shaft, at the centerline of the lower shaft, and wherein a toothed reduction wheel is integrally keyed onto the upper shaft, at the centerline of the upper shaft, so as to mesh with the toothing on the lower shaft, and wherein the toothing and the toothed reduction wheel have different diameters from each other so as to form a motion reduction system.