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You might like this video about the US Navy fire control computer. Mechanical yet also programmable. Eg with cam-based calculation modules like 1/x or differential gearings to perform addition : https://m.youtube.com/watch?v=gwf5mAlI7Ug

Thanks for the link! I had meant to look these up after watching videos of some Hamming lectures (https://www.youtube.com/playlist?list=PL2FF649D0C4407B30) where he mentions using "gun directors" for various problems.

Check this out.

https://en.m.wikipedia.org/wiki/MONIAC

The Globus IMP mechanical navigation computer was used in every manned Russian space mission from 1961 to 2002.

https://en.wikipedia.org/wiki/Voskhod_Spacecraft_%22Globus%2...