Medieval Torsion Catapults

[Sean Manning]

Anyone knows the earliest unequivocal (re)appearance of
(a) the torsion arrow-shooter and
...
in
...(2) Latin West and
...
after 600 AD?

I would have a look at a book called Springalds and Great Crossbows which I have not read (French original; English translation available). It focuses on arrow-shooting engines in the second half of the middle ages. You can also read Abbo's poem on the Viking siege of Paris and decide whether he just cribbed his artillery scenes from Ammianus and Lucian.