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Polar planimeter 1

Instrument for determining the area (F) of an arbitrary two- dimensional shape (in red).

Move stylus B along the periphery of the shape (one complete round), the green roller gives two values:

B1: initial position angle (in radians)

B2: final position angle (in radians)

F = L.R.(B1-B2)

L = BC

R: radius of rolling circle of the green roller.

The roller rotation axis must be parallel to BC.

Mathematical basis of the mechanism: intergration in polar coordinates.

There must be sufficient friction between the green roller and the ground to prevent slipping.

In real planimeters there is reduction gear drive to ease reading angle values.

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