# Planimeter: Colin Ledsome CEng FIED draws out the qualities of an old-fashioned drafting tool.

A planimeter is one of those old, apparently simple drawing-office gadgets, which does a complex task with ease (and no batteries). There are several types, but they all work on similar principles. The one shown here is from the IED calculator collection. It uses Polar or "Amsler" geometry. In construction, they are just a couple of metal rods, connected by a movable pivot and a small box of gears with a digital readout. At one end is a block or pin, which fixes the end of one rod; the other rod carries a pointer. If you have a scaled drawing--which can be the cross-section of a structural member, a graph of a function, or a map of a site--a planimeter will find its area.

On a map, it will give you the area of a piece of land, with suitable scaling. It can also be used to compare the areas under different graph lines, even if the scales do not allow you to find an absolute value. Combined with density values, the weight of a component can be calculated. Adjusting the position of the pivot along the rods allows different scales to be taken into account.

To use it, place the block at a convenient point at one side of the area, zero the counter, then move the pointer round the edge of the area. As you move, two small rubber wheels, set at right angles, roll along the paper. These turn the gears and the readout scales. When you complete the circuit, the digital readout gives you the area of the shape. For long narrow areas, the polar types are limited in their reach. You can use a linear version, which has a carriage on wheels with a cross track carrying the pointer. This is unlimited in the length it can cover.

Later electronic versions will give the position of the centre of mass and sometimes the second moment of area for structural calculations. With the advent of CAD systems, properties of areas and cross-sections can be carried out within the program, so few have need for planimeters any more. I still find them an interesting piece of mechanical magic.

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