The thumbrings help a lot in the cutting motions, hence its prevalence in primarily cutting weapons, curved or straight. It helps to "lock" the grip when impacting, reducing the vibration and helping in the "slicing" effect, with a motion led more by the elbow and the shoulder than by the wrist, a similar effect in fact than the one produced by the disc-shaped pommel on talwars.
One has to take into account, though, that the grip is a dynamic feature in fencing, so "locking" the wrist is an option, not an obligation. Playing with the "loosensess" of the thumb there's different positions of the hand available to the user, so allowing for different cutting options and also for the use of the point. The thumbrings aren't seen in swords that don't feature a good cutting blade (not necessarily curved), and although they are indeed very usual in Eastern-Europe sabres since the 17th century, they're also frequent in other weapons, like these 16th- 17th c. schiavonas.
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