I came up with the idea for a simple mechanical adding machine and wondered whether anyone has designed complete computer modules that can be built from Tinkertoys or similar physical components. I'm especially interested in reusable designs for logic gates, adders, memory, or other basic computing parts—not necessarily a modern computer, just something practical and mechanically demonstrable.
4 Answers
A wooden-block computer would be extremely limited, but mechanical computing devices are possible. Start by looking into abacuses, half adders, full adders, and mechanical logic gates. For a more complete example, Ben Eater’s 8-bit computer project explains how the pieces of a simple computer fit together, even though it uses electronic components rather than wood.
You could design and test the logic in Logisim first, then translate the gates and connections into a physical Tinkertoy mechanism. That would make it much easier to experiment with adders and larger circuits before building everything by hand.
There have been historical and experimental Tinkertoy machines, including a tic-tac-toe-playing computer. That suggests more complex mechanical circuits can be made, although complete modular blueprints are uncommon. Most existing projects are demonstrations rather than standardized plans.
An abacus is probably the easiest useful starting point. From there, you could try building a mechanical counter, then a one-bit adder, and eventually connect several stages into a larger adding machine. A complete general-purpose computer would require enormous amounts of space and very careful construction.

There have also been demonstrations of surprisingly elaborate machines made from blocks, rods, and other simple mechanical parts. They’re usually educational or experimental, but they show that more than an abacus is possible.