In my early teens I ran across plans to build something similar to this in a Popular Mechanics magazine.
I've long been interested in building one of my own but just never got around to it. In recent months I've begun thinking about an electronic version where the gears would be replaced with stepper motors. Three steppers would be required, a primary gear stepper, a secondary (driven) gear stepper, and a stepper to drive the center rotating table. More steppers and even linear motions could be added to increase the movement variations.
Each Stepper motor "gear" would be contained in a separate little box with a magnetic base. Since the steppers don't need to touch each other, they could be positioned at various locations around the center table using a steel plate for the base to hold the motors firmly. An Arduino will drive the steppers using mathematics to maintain the gear ratios much like gears with teeth. The number of teeth on each "gear" can be changed dynamically and each of the motors can be reversed independently of the others.
I'm working through the user interface at the moment. Programming will be next and actual construction of the moving parts should be dirt simple. Stay tuned.