Principle of The Linear Planimeter
The working of the linear planimeter may be explained by measuring the area of a rectangle ABCD (see image). Moving with the pointer from A to B the arm EM moves through the yellow parallelogram, with area equal to PQ×EM. This area is also equal to the area of the parallelogram A"ABB". The measuring wheel measures the distance PQ (perpendicular to EM). Moving from C to D the arm EM moves through the green parallelogram, with area equal to the area of the rectangle D"DCC". The measuring wheel now moves in the opposite direction, subtracting this reading from the former. The net result is the measuring of the difference of the yellow and green areas, which is the area of ABCD. There are of course the movements along BC and DA, but as they are the same but opposite, they cancel each other on the reading of the wheel.
Read more about this topic: Planimeter
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