Medieval Trebuchets didn't move. You hired engineers to cut down trees and build Trebuchets for a particular siege.
Honestly, "Castle Drops" in AOE2 are more akin to how Trebuchets were used. You build an army, the army gains control of an area, and then you use your engineers to build a long-range siege device at that location.
My impression was that they were assembled on site, but they were pre-made and could be dissembled. From this thread, it looks like both methods could have been used:
Honestly, "Castle Drops" in AOE2 are more akin to how Trebuchets were used. You build an army, the army gains control of an area, and then you use your engineers to build a long-range siege device at that location.
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https://en.wikipedia.org/wiki/Trebuchet#/media/File:Ms.Thott...
See? No wheels. Those things couldn't move at all.