I cant take a look at your file cause you posted it on pasteall (wich makes my firewall yell at me). You know you can upload the blend file directly to blenderartists right? Anyway, looking at your pictures i would say your bone placement is wrong.
Depending on which chair leg folds to the other i would start by placing a bone at the end of one of the legs up to where the chair legs meet, then extrude another bone to the other end of the chair leg. Then IK constrain it to a new bone. Like that… simple IK.blend (542.2 KB)
For the seating Area i would probably use drivers on the x-axis based on distance between IK and the IKt arget
Is this model based on a real world chair? I could be wrong but the rot that is connected to both legs should be slideable on one side for it to follow the folding of the chair.
Hey, this requires a basic parallelogram set up. The key for it to work properly lies in the dimensions, in other words the 2 perpendicular sides combined length must be close to the other 2 in length. Yours is a bit off, which will prevent it (legs) from being parallel when closed. Here is a pic of how I rigged it using an IK constraint…