I know that siege engines were usually built at the site of a siege but I've read that these engines were often pre-fabricated.

Were there specialized workshops or factories where craftsmen would build a trebuchet or a mangonel or a siege tower, and then break it down for transport? Would there be a private guild of engineers that I would contract for the work? Would I be recruiting engineers as part of my royal court or in my standing army (if I had one)?

I would also appreciate views from around the world; would it be a different process in Arabia than in England? Or in China vs Germany?