The first picture seems to be missing something. Shouldn't there be a crows foot or lever to pull the string?
Not all crossbows had to be spanned with a lever or windlass. Especially in the 13th century, and a little way into the 14th I think, crossbows had a stirrup like the one we see here. Hooks on the belt engaged the string and the crossbow could be spanned with a hefty downward stomp.
EDIT: Thinking about it, it was more common to start kneeling and straighten up than it was to start standing and stamp down.