I’m designing a laser-cut jewelry box for Genevieve, and one of the features I’m hoping to integrate is a cool hinge system that makes the lid sort of float back instead of just flap open. Basically imagine the trays you find inside of those unfolding tackle boxes, only with asymmetrical connection struts. I looked around the internet trying to figure out what this is called, but came up short. I can’t imagine I invented this – anyone have any leads on what this kind of construction is called?
Anyway, I’ve had a pretty clear idea of what I wanted for a few days now, but I was stuck puzzling over how to conceptualize all the trigonometry involved to predict the motion of the lid. I finally decided it wasn’t worth waiting for complete understanding and that I should just make a mockup instead. The video above is some cardboard and some #4-40 screws I had laying around thrown together with complete guesses for the dimensions.
To my surprise, it actually worked the way I hoped it would! I think I’ll be able to use this to connect the lid to the box with all laser-cut parts and possibly with no fasteners at all. Stay tuned for further details as I get farther into the design.
Bryan Duxbury's Blog 
That's a standard four bar linkage. It may be called something special in use as hinge, but it is a well studied arrangement in mechanical engineering.
Yep.. four-bar linkage.It's one of the most basic mechanisms there is, so kudos to you for inventing it on your own.. fundamental discoveries take serious thinking even if you aren't the first one to get the answer.For the sake of official names, each element with two joints is called a 'link'. The one that doesn't move at all (in this case, the box) is called the 'fixed link'. The two that connect to the fixed link are 'grounded links', and the one in the middle is called the 'floating link' or the 'coupler'. Grounded links are either 'cranks' (if they can rotate 360 degrees) or 'rockers' (if they're constrained to less than 360 degree rotation). The point at the center of the coupler is interesting for mathematical reasons, and is called the 'coupler point'.Four-bar linkages get used for a lot of things, and are named according to usage. If you care about the relative positions of the grounded links, you get things like 'drag links', 'crank-rockers' and 'double rockers'. In this case, you mostly care about the motion of the coupler, so you're doing 'coupler curve synthesis'.One of the neat things about four-bar linkages is that you always design one such that the coupler passes through any three positions you choose. The positions are called 'precision points', and there's a fairly simple geometric construction for designing the grounded and fixed links that will produce the required motion. You can also design a four-bar linkage that passes through four precision points, but that construction is more complicated.