You can upholster the final chair like I did or just paint it and fill it with pillows. The plans for this instructable are for a 4' diameter chair that will (just barely) fit through a 30" doorway. You could scale it up or down easily depending on the size of person it's for and how much "surround" you want.
The chair stands on the base by gravity alone and the unattached design allows for easy readjustment of the ball. I like sitting in it more upright, and my daughter likes it kicked farther back.
I made this for my daughter's 13th birthday and it was a big hit. She's an avid reader and it makes a perfect cozy zone to open a book in. When she saw it she called me a "mad genius" which is high praise from a 13 year old. One of her first questions was "how will I get it to college?" I think she likes it and plans to have it around for a long time. It was a big project, but well worth the effort.
Step 1: Sphere Cutting Jig
The turntable doesn't need to be perfectly circular since it's the rotation, not the shape, that cuts the circle. In fact, an octagon shape would be preferable to a circle as the corners on the octagon would make for easier turning during a cut. An octagon shape would also be easier to layout and cut.
I used a few pieces of leftover 3/4 inch melamine for the turntable and base and standard 2 x 4 lumber for the swing arm and mounts. Some 3/4 inch plywood would work fine for the turntable and base. Don't use 1/2 inch or thinner material due to the weight it'll need to support. To make a round turntable use a router mounted on a long strip of material such as fiber board, screwed loosely to the radius point. Measure carefully for the center, mount the radius board and cut a perfect circle.
The swing arm arrangement is connected to its mounting points with 1/2 inch lag screws. These fasteners can be loosened to allow the arm to swing freely, or tightened to hold it in place.
Both cutters are simple utility knife blades. I used blades with holes so they could be mounted to their bases with small screws. These blades are inexpensive and easily replaced as they dull.
The inner cutter arm is made with a 2 inch by 3/4 inch piece of wood with a slot cut in one end for the swivel. Use an extra piece of stock on the other end, held in place with 2 screws. The inner cutter blade is trapped between the two pieces of wood and clamped in place by tightening the screws. The distance from the swivel mount hole to the blade clamp will determine the inner radius of the sphere. To get a 4 inch thick wall use a 24 inch outer radius and a 20 inch inner.
I am 6' tall and this inner diameter is comfortable enough when sitting in the chair with a papasan cushion. I would've preferred to make the ball slightly larger, but getting the finished chair through doorways was the limiting factor. A larger radius is more comfortable. It's less likely to feel like your head is being tipped forward.
A point I can't stress enough is take careful measurements. Measure your doorways very carefully or you will make a cool chair that will live forever in your shop.
See the instructions on step 8 for additional tips and considerations on how big the chair could/should be.
The swivel mount for the inner cutting arm is made with a 3/8 or 1/2 inch thumb screw with a 1/4 inch hole drilled in the center of the flat portion. The swivel mounts to the turntable using nylon-insert nuts and washers. These nuts allow for a precise adjustment without slipping. The swivel must spin freely, but not wobble. Use a thumb screw long enough to go through a pivot hole in the base. In this way the swivel mount also functions as the turntable axle.
The width of the base doesn't need to be exactly as noted in the plans (72") but beware that having too small a gap between the edge of the turntable and horizontal mounts will make for frustrating cutting before the layers of cardboard get higher than the mounts. Too close and your glued cardboard will keep bumping into the mounts and have to be cut away to spin the turntable.