PAPAC-00, a Do-It-Yourself Paper Computer (1958)
ieeexplore.ieee.org
ieeexplore.ieee.org
In these modern times, it's more fun to program a virtual machine. The Dietel and Dietel "Java: How to program, 5th ed" had a project for the Simpletron computer simulator, which young me enjoyed. The projects around Simpletron included an assembler and later a compiler for a BASIC-like language.
[0] http://woodgears.ca/marbleadd/
EDIT: My google search results improved when I stopped searching for physical computer and instead searched for mechanical computer.
A sliding-plate computer is the Z1[2].
[1] https://en.wikipedia.org/wiki/E.S.R.,_Inc. [2] https://en.wikipedia.org/wiki/Z1_(computer)
https://www.kickstarter.com/projects/871405126/turing-tumble...
The FIBIAC: http://www.chrisfenton.com/the-fibiac/
The Calculating Machines of Sir Samuel Morland: http://history-computer.com/MechanicalCalculators/Pioneers/M...
Sadly not very repeatable :-)