The Integraph: An Integrating Mechanism

input: function curve

linear

quadratic

sinusoidal

sinc

output: integral curve

		input pen		output pen
		trolley		main arm
		differential curve		integral curve
		tangential wheel

Before the Differential Analyzer and long before Mathematica or Wolfram|Alpha, mechanical instruments were used to perform computations. The "Integraph" [1] in this Demonstration plots the integral curve

F(x)

starting from a given curve

f(x)

.

This mechanism was first designed by Bruno Abakanowicz [2] and further perfected by Gottlieb Coradi [3] in Zurich around 1905 using a carriage in the shape of a parallelogram. These instruments are similar, in principle, to the planimeter, a device that can measure the area inside a closed curve.

According to the manufacturer: "By means of the integraph many of the most difficult calculations and problems occurring in the practice of an engineer in shipbuilding, bridge and iron constructions, earth transports, electronics, technical optics and ballistics can be solved in a simple and reliable manner with much saving of time and the operator need not possess any knowledge of higher mathematics." [4].

Move the input pen along the curve for the function

f(x)

to generate the integral curve.