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The Zeiss planetarium was originally conceived as a "Ptolemaic" display just like this.

Since planet and sun locations were projected onto a dome, the mechanical approach was to use a little Copernican models for each planet: each consisted of a moving pivot point for Earth and one for the particular planet. The line between the two planets/points designated the direction in which the attached projector sent the image of the planet.

By using eccentric pin-and-slot mechanisms, Keplerian orbits could be accurately recreated. Orbital inclination was incorporated as well.

So the Zeiss projectors had a stack of nine little two-planet orreries to handle simulating the appearance of the solar system from Earth 

The Internet Archive has a digitised copy of the book Geared to the Stars, which gives a fairly good description of the mechanism. https://archive.org/details/gearedtostarsevo00king