Dual-speed tightening/untightening device with floating ring gear

A tightening device comprising:

• a casing;
• a motor with a rotor;
• an output member that is drivable in rotation to drive a drive element of an element to be tightened;
• a transmission connecting said rotor to said output member, said transmission comprising at least one additional gear train that can be engaged/disengaged, said at least one additional gear train comprising at least one epicyclic train with a toothed inner ring gear;
• and
• engaging elements for engaging said at least one additional gear train, said engaging elements being able to take at least:
• an engaged state in which the at least one additional gear train is engaged, and
• a disengaged state in which said at least one additional gear train is not engaged,
• a speed reducing ratio of said transmission between said rotor and said output member being different depending on whether or not said additional gear train is engaged, and
• wherein said ring gear is mounted so as to be mobile in translation along the axis of said rotor inside said casing between at least:
• a free position, taken when said engaging elements is in said disengaged state, and in which said ring gear is mobile in rotation relative to said casing in such a way that said at least one additional gear train is disengaged, and
• a locked position, taken when said engaging elements are in said engaged state, and in which said ring gear is locked in rotation relative to said casing in such a way that said at least one additional gear train is engaged.