.....so, not a war throwing simple machine , but a possible gravity powered simple machine ,if we take a look at :
https://www.real-world-physics-problems.com/trebuchet-physics.html (https://www.real-world-physics-problems.com/trebuchet-physics.html)
.....but play a vertical accelerating track ,as Eric Limer's model :
https://gizmodo.com/9-gifs-that-make-perpetual-motion-machines-a-reality-5994377 (https://gizmodo.com/9-gifs-that-make-perpetual-motion-machines-a-reality-5994377)
With a simplified leverage (one constant arm-one variable arm) , we can tumble the torque difference on the same side of the fulcrum and...have we a continuous gravity unbalance ("self" motion)?!
For the modified trebuchet we can play the variable arm ,if we take a look at :
https://en.m.wikipedia.org/wiki/Perpetual_motion#/media/File%3APerpetuum1png (https://en.m.wikipedia.org/wiki/Perpetual_motion#/media/File%3APerpetuum1png)
.....but play a SINGLE ARM !
The wheel concept is "minimized" as a lever concept...
Al_ex