I had, and sold, a "Chair to Suitcase" when I worked for Buma. I remember it in great detail, because I had to replace some parts to make it work again.
It was made in England, and I believe it was from the twenties. As I recall, Buma represented it as coming from Davenport's, but I don't recall him specifying a maker. It was wood, painted brown. The seat was wider at the front than the back, but only by an inch or so. It was hinged in the center, as was the back. The legs were hinged in the middle as well, so they folded up, in half, then up again, into the seat itself. You picked the chair up by the seat, at the sides, and from behind. Then, the legs snapped up and you tilted the thing toward the audience. This caused the back to fall down and into the seat as you turned the whole thing upside down, (everything goes into the bottom or underside of the seat), and then brought the sides of the seat together. Voila! It is now a "suitcase"!
In fact, suitcase may be a generous description of the thing. It was actually about 18"x10"x5" when closed (So, the seat was 18"x20"x5" open).
You wouldn't want to sit on the thing, or let anyone other than a very small child do so. It would have supported fifty or sixty pounds at the most. The legs were 1"x2" finished, I think. They wouldn't support much weight, but they looked substantial from the front.
The back was two frames, basically, hinged in the center to fold with the seat, and also hinged at the base, where they connected to the seat. I hope all of this is clear. With an illustration I am sure you'd "see" it instantly.
It worked by combining gravity and rubber bands. The bands snapped the legs in half, then up into the base, and gravity "pulled" the back down. As for the rest of it, you turned it over and closed it! I always thought we should have kept that original as a model for an updated edition, but Buma wanted to sell, and we had an anxious buyer. Pete, do you remember this? You might, I sold it to Matt Corin. It is one of the ten or twelve things I have always wished I bought myself...