A mechanical computer is built from mechanical components such as levers and gears, rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays. More complex examples could carry out multiplication and division -- Friden used a moving head which paused at each column -- and even differential analysis. One model sold in the 1960's calculated square roots.
Mechanical computers reached their zenith during World War II, when they formed the basis of complex bombsights including the Norden, as well as the similar devices for ship computations such as the US Torpedo Data Computer or British Admiralty Fire Control Table. Mechanical computers continued to be used into the 1960's, but were quickly replaced by electronic calculators, which -- with cathode-ray tube output -- emerged in the mid-1960's. The evolution culminated in the 1970s with the introduction of inexpensive handheld electronic calculators. Mechanical computers were ailing in 1970 and dead by 1980.
Noteworthy are mechanical flight instruments for early spacecraft, which provided their computed output not in the form of digits, but through the displacements of indicator surfaces. From Yuri Gagarin's first manned spaceflight until 2002, every manned Soviet and Russian spacecraft Vostok, Voskhod and Soyuz was equipped with a Globus instrument showing the apparent movement of the Earth under the spacecraft through the displacement of a miniature terrestrial globe, plus latitude and longitude indicators.
- The Antikythera mechanism, ca. 100 BC
- Pascaline, 1642 - Blaise Pascal's arithmetic machine primarily intended as an adding machine which could add and subtract two numbers directly, as well as multiply and divide by repetition.
- Stepped Reckoner, 1672 - Gottfried Wilhelm Leibniz's mechanical calculator that could add, subtract, multiply, and divide.
- Difference Engine, 1822 – Charles Babbage's mechanical device to calculate polynomials.
- Analytical Engine, 1837 – A later Charles Babbage device that could be said to encapsulate most of the elements of modern computers.
- Marchant Calculator, 1918 - Most advanced of the mechanical calculators. The key design was by Carl Friden.
- Kerrison Predictor ("late 1930s" ?)
- Z1, 1938 by Konrad Zuse
- Curta calculator, 1948
- Moniac, 1949 – An analog computer used to model or simulate the UK economy.
- Voskhod Spacecraft "Globus" IMP navigation instrument, early 1960s
- Automaton - Mechanical devices that, in some cases, can store data and perform calculations, and perform other complicated tasks.
Early electrically powered computers constructed from switches and relays rather than vacuum tubes (thermionic valves) or transistors (from which later electronic computers were constructed) are classified as electro-mechanical computers. Examples include:
- Z2, 1939
- Z3, 1941 – Designed by Konrad Zuse.
- Harvard Mark I, 1944 – Built by IBM. ("electro-mechanical counters")
- Harvard Mark II, 1947 ("electromagnetic relays")
- "Binary Arithmetic Relay Calculator" BARK, 1950
- Simon (computer), 1950
- University of Toronto Electronic Computer (UTEC), 1951
- "Binary Electronic Sequence Calculator" BESK, 1953
- Harry Porter's Relay Computer, Portland State University, 2005 
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