Mike Davey presents his hand-built Turing Machine. The machine uses a Parallax Propeller chip for mechanical control, but actual computation is executed using the tape reel.
You can get more details about the construction of the machine at Mike's Site.
My goal in building this project was to create a machine that embodied the classic look and feel of the machine presented in Turing’s paper. I wanted to build a machine that would be immediately recognizable as a Turing machine to someone familiar with Turing's work.
Although this Turing machine is controlled by a Parallax Propeller microcontroller, its operation while running is based only on a set of state transformations loaded from an SD card and what is written to and read from the tape. While it may seem as if the tape is merely the input and output of the machine, it is not! Nor is the tape just the memory of the machine. In a way the tape is the computer. As the symbols on the tape are manipulated by simple rules, the computing happens. The output is really more of an artifact of the machine using the tape as the computer.