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Through trial and error, I found out that an old variable speed drill wasn't the best choice to spin this thing. Plenty of power, but the trigger was just too.... well...variable. I couldn't get it to spin the skull reliably at the same speed with any combination of wooden blocks and metal straps inside the wooden box that I put together.
I found a nice little 11W 120VAC motor at a surplus store for $6 that did the trick. It runs at 60 RPM and this spinning rate give a nice "look at the skull face about once per second" which is just what I wanted.
I found a skull that I wanted to use....but it was really just paper mache...and I had to spray some clear varnish on it to waterproof it. As a bonus, it was more realistic than a stryofoam skull....which would have been lighter in weight and easier on the motor...but I dealt with it. Tradeoffs, tradeoffs.
I screwed a small block of wood to the underside of the skull (it is hollow) and then drilled a hole in the center of the block of wood and put in a 3/8" bolt. Then, I epoxied the bolt to the wood. I mounted the motor in a block of wood and put that in my wood box (with silicon caulk in the junctions of the box for waterproofing). Then, I mounted the skull bolt onto the motor shaft with a nylon spacer with a screw to hold it to the shaft.
Here's a quick AVI video of the spinning skull in action (1.9 mb):
Spinning Skull in AVI format 904K