Any examples of 'two stage' pulley mechanisms?

Sorry if this is against the rules. I certainly don't want anyone to design something for me. I just want to know if it's possible, and to be pointed in the right direction :-)

I have a DIY home project where I need to be able to raise some acoustic panels (1'x4') up out of the way to access my windows. I was originally thinking of just building a simple garage door style overhead track to roll them up. But then I started thinking about folding them up like an accordion instead. The only issue is that the panels need to 'collapse' only at the ceiling, not at the bottom, and not continuously on all panels (If the bottom panels fold up first they will bump into all the gear on my desk!). The idea is to have the bottom panels raise vertically like a garage door, but fold into the ceiling instead of rotating up like a garage door.

Here's some ridiculous ASCII art that tries to illustrate the folding mechanism I'm looking for:

------- -------- -------- -------- -------- | \ == == == | / | \ == | | | / | | 

I only have 4 panels that need to fold, so I'm looking for a mechanism that would allow the first pair to raise and fold up against the ceiling, and the second pair only folds up once the first pair is done. It seems to me that there should be a fairly simple mechanism to make something like this happen, but I'm not seeing it. Anyone have an example of a pulley (or gear) mechanism that would make this work?

The only reason I think it's possible is that I have a memory of solving a physics problem like this as an undergraduate. I just cant remember whether the mechanism depended on differences in friction, mass, or some kind of counterweight that kept the bottom pair from folding first. It was not a complex mechanism, or it wouldn't have been in an undergraduate mechanics class. It was just the result of the physics that produced this two-stage behavior. I don't think the class even realized that it would happen that way except that the professor pointed it out. I'd ask him if he remembers the problem, but unfortunately he passed away 10 years ago,

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