[schiffern]

>the weight could take a more direct path downward as the frame moves.

That should change how long it takes the arm to drop, but it shouldn't change the amount of potential energy released (and thus, projectile speed).

[jcims]

Projectile velocity is a function of power rather than energy alone because you only have so much time to accelerate it.

[foota]

It does, another commenter posted the same person's explanation. But, the idea is that it doesn't matter how much GPE is released, it matters what the velocity of the projectile at release is. If the trebuchet can't move then the weight starts to slow down before all it's GPE is used up. When it can move, it coincides with the time that the projectile is at maximum velocity.