The area of the shape is proportional to the number of turns through which the measuring wheel rotates when the planimeter is traced along the complete perimeter of the shape.
The pictures show a linear and a polar planimeter.
Developments of the planimeter can establish the position of the first moment of area (center of mass), and even the second moment of area.
The other end of the linkage is fixed for a polar planimeter and restricted to a line for a linear planimeter.
Originally a radial planimeter was of academic interest only, but ten years later clock driven recording instruments started being used.
That means the planimeter measures the distance that its measuring wheel travels, projected perpendicularly to the measuring wheel's axis of rotation.
The planimeter was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage.
Bay dimensions were extracted by planimeter from topographic maps.
