The hardware for the swivel office chair dictates some parameters such as lean back (which is 3 degrees).
The part that I copied from the article is the back splat fitting assembly:
In the above photo we see how the assembly can be tilted back as necessary with the use of hinges. However, a way is needed to support the assembly - the first photo above shows how the assembly is supported using plywood bolted to the sides of the side rails and a top piece that is clamped to support the back assembly. It works, although there is a lot of weight overhanging the back of the chair which makes the chair want to lean back too easily when sitting. Not sure how to get around that.
For the final chair, the back splat will meet and mortise into the top crest rail. The crest rail will be proud of the back splat about 3/16" of an inch. With the chair fitting rig I simulate this fact by clamping a 3/16" plywood to the top back support. The goal is to make sure that the 3/16" bump does not end up digging into the client's back - very important since the Blacker House arm chair I built last year has this issue - the bottom of the crest rail digs into the back a bit and is not very comfortable. Lesson learned!
Another question is what distance must the wheels be from the center for stability? I drilled a couple holes so that I could test different distances for the wheels:
