I enjoyed all the comments on my first post about the stool project, including the humorous ones; I'm really having fun with this.
With the seat made and attached to the seat post--a scrap 1 1/4" dowel 16" long--I had to figure out a base. Since I wanted the stool to be 34" tall, I obviously had to attach the seatpost to a platform and add legs for this prototype. I had two ideas for the platform: a triangle with three legs or a square with four legs. I tried the triangle first and it worked fairly well. I splayed the legs slightly and put the middle leg in the back so I wouldn't fall over backward. There is no need for forward stability when the stool is in use because my feet are flat on the floor in front and I am nearly standing up anyway. Any force I apply with tools will push me backward. Dry fit, it was very stable to sit on but it tipped over easily if I bumped it when not in use. The center of gravity of the seat was too high and too far forward because of where I attached the seatpost to the platform.
The next option I tried was a square with the seatpost in the exact center, four legs and the seat oriented on the diagonal. My reasoning was that then the platform wouldn't interfere with my legs and it would be very stable when I am on or off the stool. Here it is:
The platform is 1 1/2" thick to allow for strong attachments of the seatpost and legs. I didn't like the way it looked very much though, to me like a giraffe. I think the triangle looked better for some reason--maybe because the seat is triangular--and I have a preference for three legs. Looking back, I wish I had made the platform an equilateral triangle to increase its depth and allow the seatpost to attach further back. Hmmmm, might have to make another version from scratch. What to do.
Then a brain shower happened (a brain shower is to a brainstorm as a rain shower is to a rainstorm--a passing event that may or may not amount to anything much). A problem with my first version was that the height isn't adjustable, which is OK for me because I know the exact height I want, but not OK for most. A bicycle seat is adjusted by sliding the seatpost up and down inside the downtube and gets locked in place. I could modify my prototype and still use only scraps by creating a "downtube." So, I decapitated the giraffe and cut off its legs:
Then I laminated a down column and inserted it between the platform and the seatpost:
I like this much better and the lower center of gravity is more stable, but I think the way to go is to lower the platform to be just off the floor, shorten the seatpost and have a longer column. I am going to use this one awhile before making another version.
The two main ideas in my design that I very strongly urge you to consider if you want to make a shop stool are to make the seat shaped like a bicycle seat and make the stool very high, just low enough to keep a very slight bend in your knees. I think you will be surprised at how well this works. It does take some getting used to but you'll quickly get accustomed to it. I suppose this is more familiar to a bicycle rider though and this certainly isn't a stool for everyone. I concede that it doesn't push the upper bound of the woodworking aesthetic. :( I have an idea for the next version that I think would look fantastic while retaining the functionality of this one.
NB: Ralph, the Accidental Woodworker, comments that it looks like the stool would fall over backward easily. Obviously, the bigger the base the less likely this is; it's a tradeoff. If you build one, make your own decision. I was concerned about this and tested my prototype in a safe place before using it. You should too. This stool depends in part on your legs for stability so keep them flat on the floor.