As a writer of steampunk (and general science/engineering nerd) the most entertaining theories I come up with tend to involve making a piece of equipment steam powered when it wasn't originally. Well, those and some of the nutball ideas that pop into my head where my characters are concerned ... but I digress.
The polybolos, as you may or may not know, was a siege engine in use during antiquity that could fire multiple arrows in rapid succession through use of its chain drive. The mechanism in question is a flat-link chain attached to a windlass, the oldest known use of a system that was considered an invention of Signore da Vinci's.
From (where else?) Wikipedia:
"When loading a new bolt, the windlass is rotated counter-clockwise with the trigger claw raised; this drives the mensa forward towards the bow string, where a metal lug pushes the trigger under the trigger claw, which is closed over the string.
Once the string is locked into the trigger mechanism, the windlass is then rotated clockwise, drawing the mensa back, drawing the bow string with it.
A round wooden pole in the bottom of the magazine is rotated down toward the mensa (cradle that holds the bolt) as it is drawn to the back of the polybolos, dropping a single bolt into the tray, ready to be fired. As the mensa is pulled farther back, it meets another lug like the one that locked the string into position, this one pushes the trigger and automatically fires the polybolos, and the process is repeated. The repetition provides the weapon's name, from the Greek πολύ - poly "multiple, many" and -βόλος - -bolos "thrower" (from βάλλω - ballo "to throw, to hurl"), or simply a repeating weapon."
As the above description shows, the polybolos already operated with mechanical action, which makes it a little easier to adapt steam power onto it.
My theory (and yes, this will be used in the new project) is to attach a steam-powered mechanism to the base of the machine accompanied by piping and gear work that turns the windlass at a speed greater than regular mechanical motion can achieve. Also, a steam-powered polybolos could be made to rotate automatically on a horizontal axis, which would thus eliminate a suggested complaint of it being "too accurate."
There's also the potential for steam power in ballistas and gastraphetes (a belly bow) among other possibilities.
As always, your thoughts are appreciated.