ASIDES
Planimeter
Colin Ledsome CEng FIED draws out the
qualities of an old-fashioned drafting tool
Aplanimeter is one of those old, apparently simple drawing-of ce
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 xes 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 nd 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 nd 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 nd them an interesting piece of mechanical magic.
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