Term for hinge that allows trapdoor to rise and move aside while remaining near-level

What terms describe / can be used to locate a hinge that allows a trapdoor to rise and move aside while remaining near-level?

I have a project where a cantilevered* shelf of 3/4 inch plywood will need to be able to simultaneously rise and move aside while remaining near-level.

The maximum design load for the shelf is 30 pounds + the plywood.

[*] “Cantilevered” in this sense means it is supported on one end by the hinges I’m attempting to describe, and that the hinges either mount to plywood adjacent to the closed (lowered) shelf position like an “—“, or mount to a ~60 degree sloped mount point below the shelf area like the stem of a “T”.

What is the name of this type of hinge so that I can locate and purchase a set?

I’m looking for a hinge type that would put the floating section of the table below off to the side as a “leaf” (where the closed position is the same level as the tabletop) then lift over the existing “tabletop” into roughly the position shown.

Searching for “Folding coffee table hinge” got me to a class of product described as “lift up top table mechanism.”

The difference is:

• A “- -“ shape seems to be required unless there is a “ T “ shaped hinge that allows the level-ish-rise path. The only level-ish hinges I’ve found form a “z” shape when fully closed instead.
• The form factor I’m looking for would fold flat so that the lift-able portion and stationary mount point are in the same plane.

I have checked with my local home centers. While a few employees recalled having seen or heard of a hinge that moves as needed, they all reported being unaware of anyone carrying such a product and suggested I look online.

Unfortunately, they also could not remember the words to describe one in order to search and order online.

Surely such hinges exist?