The popularity of mystery clocks is no mystery at all. They’re novelties and great conversation pieces. They are mind-boggling at first glance, and amusingly fascinating once you understand what’s going on. They’re triumphs of imagination and craftsmanship, and they’re often works of decorative art as well.

The mystery comes in how these clocks work. They’re sometimes called impossible clocks because they seem to have either no workings at all, or floaters because the clock hands don’t seem to be connected to any workings. With more conventional clocks, it’s easy to see where the hands are attached to the workings that move them, whether powered by a mechanical pendulum or an electric motor. But in mystery clocks, the hands seem to move with no apparent mechanism to drive them. Turn the clock over, examine the back, and you still won’t be able to tell what makes it tick and keep accurate time.

It’s an Illusion

Mystery clocks are tricks. They’re illusions and spectacles of magic, so it’s no wonder that their history is entwined with that of famous magicians.
The mystery lies in the movement of the clock’s hands. The creator of a mystery clock fools the observer by hiding the workings so that the hands appear to move on their own. Over the years, clever clockmakers have devised many ways to achieve this illusion. Mechanisms were closely guarded secrets — in fact, they were often patented.
Fittingly, Jean Eugene Robert-Houdin, a 19th-century French magician and clockmaker, is widely hailed as the inventor of the mystery clock, but even his name is something of an enigma. (Houdin’s last name at his birth in 1806 was Robert. Young Jean Eugene added “Houdin” to his name when he married the daughter of a prominent Paris maker of clocks and watches with that name.) Coincidentally, he had also become interested in conjuring and magic. He combined his two passions in the making of mystery clocks. His first mystery clock won a bronze medal at the Exhibition of the French Industry of 1839. Houdin used various optical tricks in his mystery clocks, including a rod that ran up through the ornate clock base and along the right of the top of the case, attaching to a screw that was connected to a second, invisible glass dial that turned behind the visible dial [source: Horologist].
In many of his mystery clocks, Houdin used some variation of secreting the mechanism the clock base and attaching the hands to a second, transparent, serrated-edge dial that was turned by pinions inside the frame of the case [source: Kolesnikov-Jessop]. Many other clock makers have used similar tricks involving transparent dials that look round but really have cogs hidden inside the clock’s frame.
For more Detail: How mystery clock works