The depiction itself can be found searching " siege of Syracuse" which happened about 200BC, this painting is a Homage to the inventions or Archimedes. I do think you are right they are more like trebuchets in the distance, and could be part projection from the artist but they did seem to have done some research into the other engines in the picture so we can not rule out they had other sources too from ancient designs. When I was originally foraging for trireme designs this picture came up because it was part of a naval battle and because it is so jumbled I thought they were on rows of ships with different engines on them and were part of the Roman side hitting Syracuse from the sea. Well after further study I was wrong that they were on ships but went with it anyway since catapult siege ships are mentioned but are not really ever shown in surviving art (except for a double bow version with a large deck and tower.... hmm.....)
From my research Romans and further back were aware of trebuchet technology (yet not perfected or nearly as large enough to change the game like the 1400's). They seemed to prefer to use the type that 30+ men would pull on ropes to fire them for a pretty fast rate of fire, which is a big advantage and gives something for your troops to do who might get anxious to charge out for glory. I also wonder to what extent was taken to hide these designs since they are not very proprietary and after 10 good minutes of study a spy could describe something enough for others to replicate and maybe they did not use them very much because they were effective enough with torsion artillery which is more sophisticated and harder to reproduce and did not want to find these new engines at their walls later.
These designs even go back further to ancient Greek and who knows from pre-bronze age collapse. Our history is much lost to us and we collectively seem to under estimate life at these times, but there were machine shops, glass of incredible making, and so many other OP arts (out of place artifacts) that seems to suggest History is just it forgetting and rediscovering itself again.
So the world in which my minis are created is like the golden age of antiquity in all its high form. I grew up playing Age of Empires so I do not mind merging some of the time lines to have it all fit together.
As to my own question,
I did a little trekking for Archimedes siege engines and found this representation which I think answers my question. It confused me to see a bent arm but apparently that's where this engine stores the energy.
Note: it fires 2 projectiles, one in the arm and another in a sling like a trebuchet.
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