Hun,
I think your question might include a few extra people. In the medieval period the man in charge of the wagon was simply a driver. Most of the time two per wagon from what I can tell. Usually they carried whatever they were told to. In war you could have literally hundreds of wagons in use for a single campaign. So for that simply driver would do though there are a few other names as well.
The men working the siege engines were called various things, gynnors- gunners, for example, originally was a person who worked the trebuchets and such and had nothing to do with guns, guns getting their name from them. They are referred to as engineers or siege engineers often though a much more general term than today applying to anyone working the 'engines' as all war machines more or less were called. You find specialist carpenters as well in this group, often in contracts listing them as carpenters for the engines of war...
Hope that helps, if not just ask. Jim Bradbury's book on sieges is very good by the way.
http://books.google.co.uk/books?id=xVCR ... &ct=result
R
There ain't nothin' girlie about a tunic...