RE: Computing Linkages
Recent additions to the story of the computing linkages.
Torres y Quevedo
The Spanish engineer Torres y Quevedo designed, among many other devices, a linkage computer. Read more about it in the Mémoires présentés par divers savans à l'Académie royale des sciences de l'Institut de France 329 (1902).
A nice example of the use of linkages in the education of engineers can be found in The University of Pittsburgh's Skyscraper engineer, October 1963, p.24-29
Torres y Quevedo's linkage computer
The Stabilogauge.
The American Hydromath Company produced analog calculators for longitudinal ship stability: the Stabilogauge.
The loading of various parts of a ship is set by the micrometer screws. Deadweight, displacement, mean draft are read on the horizontal scale and the metacentric height GM on the vertical scale. If the needle on the vertical scale is covered by the red flag, the ship is not stable.
Note that the mechanism contains a curve-following part for curve segment on the arm with the red flag. Additionally, the springs (and the spring constants) play an essential role in the computation, as explained by the patent US2551440.
Therefore this device is not a pure computing linkage. The Trimogage, also produced by American Hydromath, might be a real computing linkage, but I have not yet seen its mechanism.
Kempe's Universality Theorem
In 1876 Alfred B. Kempe published an article "On a General Method of describing Plane Curves of the nth degree by Linkwork" in which he showed that linkages can be constructed to draw any algebraic plane curve. These linkages are quite complicated and usually not very practical. Some MIT students have created a stunning simulation of Kempe's theorem, in which you can enter your own equation!