Power for a good melee attack comes from the body not the arms.
Thrusts can succeed when powered only by the arm, however, the arms are primarily used to GUIDE the sword blow and act as the transmission device to bring power from the body into the target.
I first discovered this while doing kinetic energy tests with different weapons in the 1980s. I was amazed to discover that the kinetic energy from a two-handed weapon was not significantly higher than from a one-handed weapon of the same weight and length. This may be hard to understand, because most of your experience may tell you that you normally are hit harder by a two-handed weapon. This is because most two-handed weapons have much more mass and a longer lever for a blade and handle. Even beginning fighters often instinctively throw blows with their body instead of their arms when handling a two-handed weapon. Remember that using two hands on a weapon allows you to place the fulcrum and effort points of control further away from each other. This extra control leverage contributes a great deal to better handling of the tip movement. However the extra pushing force from the leverage is almost insignificant for impact because it is so slow. As such, on it’s own this additional (but slow) pushing force creates very poor impulse (less efficient transfer of force).
Grabbing a "one handed" weapon with 2 hands will give you more tip control (accuracy, that is why baseball batters and golfer use two hands ) and that extra control can also be better for feints and it can give you more blocking power.
But not really all that much extra hitting force.
If you are fighting your own weapon for control because it is very long or top heavy that can "waste" power that would have gone into your attack, thus supporting the misconception that using two hands gives you more power.
See here for more information like this:
http://www.spookyfx.com/book/tromp.html
I thought they said that you could also use two hands for a single handed weapon, which makes it do more damage while still being quicker than a two handed weapon.