Yes, I do mean that - they have to hang upside down in order to start the process of spinning a cocoon.
As I mentioned before ours seem to prefer the top of whatever type of container they end up in as opposed to a nice, sturdy twig put there just for them.
So, when your caterpillar looks like this:
You will probably have a cocoon within a day or two. (This one hung there for a whole day before finally making its cocoon while his buddy took all of an afternoon (or was it evening?) to make his.)
If you watch really closely (and don't mind sitting in one position staring fixedly at your caterpillar for longer than 10 minutes) you will be able to watch how the cocoon is actually formed. I won't tell just in case you want to watch (but I will say your brothers will probably get a kick out of it), but be prepared to sit staring at the caterpillar for a LONG time before you finally see what is happening because it is a very slow process.
I'll keep a close eye on the cocoons now and keep you updated. These two are the only ones so far (not counting the one we've had for almost a week already) and still three that haven't started theirs yet.
Oh, and before I forget . . . . I was serious when I said they really like to find little open places and sneak out of their new homes. Here is an illustration of what I mean.
Needless to say I didn't appreciate him 'hanging out' on my boots and he didn't get to stay there long before being unceremoniously escorted back into the bucket.