Any helmet sized mold is small enough to rotate by hand, provided that the material kicks off fast enough. Your shoulders would give out if the material took 30 minutes to kick. I cast helmets by hand with resin that kicks in 3 minutes.
I have been sitting here drawing this up,
I think everyone can picture the two concentric frames that pivot on the X and Y axis. Let me say that the frames need to be strong enough to carry the weight of the mold + material. (up to 50 lbs) So they should be steel or aluminum box tubing. Anyone who is adventurous might try 2" plumbing. All the 90 deg angles and Ts are Off-the Shelf. If someone wants to try this, post pics.
Does this need to be motorized? No, not if we are going to keep it simple.
Starting with the outer frame that rotates about the X axis, the frame is supported at both ends by its axle rods that are supported by bearings supported by vertical supports*. connect one axle to a hand crank, and you have rotation on the X axis.
The inner frame rotates on the Y axis. It also is supported at each end by axles that pass though bearings in the outer frame. One axle that passes through the outer frame is connected to a pulley wheel. (Size of pulley will determine the rotational speed of the inner frame with respect to the outer frame)
What is that pulley connected to that spins the inner frame? (There is more than one answer to this)
Answer: At the outside of the outer frame is a second bearing and shaft. On the shaft is another pulley, (in line with the first) and a wheel that rides on the vertical support*.
As the handle is cranked, the outer frame rotates and the wheel riding on the vertical support turns, which causes the inner frame to rotate.
*the vertical support mentioned above needs to be large enough to allow the wheel to make a complete revolution. It could be a piece of plywood, but it should be strong enough to support the frames and not lose contact with the drive wheel.
I picture a wheel similar to a Razor Scooter wheel, but any type of rubber wheel work.
Does that read well? I can't tell.