Prior to the advent of computers, draftsmen had to use dedicated mechanisms to plot curves. One such instrument was the parabolograph [1], simulated in this Demonstration and on display in the London Science Museum [2].
The red pen is connected to a series of bars and sliders. As the pen moves from left to right, it plots the parabola . You can vary the parameter with its slider to move the green bar in the mechanism. You can vary the angle with a slider to rotate the magenta bar.


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[1] DMG-Lib. "Vyatkin Link-Gear Parabolograph." (Nov 11, 2014) www.dmg-lib.org/dmglib/main/portal.jsp?mainNaviState=browsen.images.viewer&id=16750023.
[2] Science Museum, London. "Payne-Coradi Parabolograph." (Nov 11, 2014) collectionsonline.nmsi.ac.uk/detail.php?type=related&kv=60143&t=objects.


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