All this talk about antikytheras led me to think about a cycloidal escapement for a clock. The problem is that the rolling circle has to roll on the _ceiling_, not on the floor, according to Lawlor's Brachistochrone paper. Ok, so we put a "rack" (a linear gear) on the ceiling & parallel to the ceiling. Then we _hang_ a gear wheel from a rail which runs parallel to the ceiling. The hanger has a small rolling mechanism similar to that in a "sliding" door. The gear teeth of the hanging gear wheel engages the teeth in the linear gear rack on the ceiling. Now, if we push the entire gear wheel slide forward, the engaged gear teeth will rotate the gear wheel. So far, so good. We now make the wheel extremely light with as low a moment of inertia as possible -- e.g., magnesium. We also make the sliding hanger mechanism as light as possible, with as little friction as possible. We then mount a lead weight on the gear wheel. With small-to-medium displacements of the wheel, the lead weight will now move in a cycloidal path, similar to Huygens's path. We can now arrange for some other mechanism (light actuated, e.g.) which notices when the amount of motion becomes too small, and gives the wheel a small additional kick to add energy. This is what I came up with in a few minutes. Perhaps someone here can come up with a more elegant version.