In 1837, Charles Babbage was the first to design a general-purpose computer, a mechanical analytical engine. The design anticipated the first completed general-purpose computer by about 100 years.
It has been proven that the technology of his day was sufficient to produce the relatively high strength and precision parts necessary for Babbage's designs to function.
Alas, as of 2010, the current RepRap Options are not yet able to make parts with enough strength and precision to produce a computer according to Babbage's original design. However, we hope that someday the RepRap will be able to produce practically all the parts for a mechanical computer, by attacking this problem in two directions:
- making new RepRap designs that are "better" in the sense that they can produce stronger and more precise parts.
- We now know that a general-purpose computer can do extremely high-precision calculations even when built out of relatively low-precision components. By adapting the ideas of Babbage and later inventors, we can make new mechanical computer designs that are "better" in the sense that they are at least as "powerful" as Babbage's original design, but have more relaxed requirements on strength and precision.
It would appear that we have reached the limits of what is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in five years. -- John von Neumann, computer inventor, 1949
Everything below this point is working notes.
printing a computer: http://forums.reprap.org/read.php?88,32387
- Jeffrey Winters. "remember the adding machine". Mentions a calculating machine built by Thomas Fowler in 1840 that used base 3 so that it could be built from simpler and lower-precision parts (but more of them).; 
- Andrew Carol. "Building Complex Machines Using LEGO". "Babbage Difference Engine made with LEGO".
- Michael Freeman. "Difference Engine 0.5" . Designed using OpenScad and Blender ; printed on "the 3D printer". OpenSCAD source files available for download.
- Sydney Padua. "The Marvellous Analytical Engine - How It Works". (A video illustrating the motion of some of the key parts of Babbage’s Analytical Engine).
- "The Logical Engine: A project to create the world's first steam-powered all-mechanical computer, which could also be considered a 6,000,000:1 scale model of a nano-computer." Suggests that a binary rod computer would be easier to build and require fewer kinds of parts than a decimal rotating computer.
- "rod logic" at everything2.
- The "Microprocessor Design" wikibook says a "relay computer" (the CPU, not including memory) can be built with less than 450 relays, and gives some examples.
- A steampowered mechanical Turing machine and CAD models for making said Turing machine:
- (Who should I credit?). The "Babbage-Boole Rodulator", aka the "Logical Engine". One possible answer to the question, "what if Babbage ditched decimal representation in favor of binary?". "My rule is that I can use any material as long as it doesn't have some essential property that was not available in Babbage's time.". 
Love Of the Art
Mechanical Computing is inherently beautiful and interesting.
This brings a number of fabrication technologies under the RepRap Umbrella:
Files and Parts
Photos and Drawings
Links can be put in captions.