A machine for physically exercising the limbs, comprising a translational-rotary machine comprising motor means 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 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 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 , 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 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 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 , 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. <EOS>