coke can planimeter

A planimeter measures area; this is one made from a soft drink can.

The pointer projecting horizontally from the right-hand end of the can is moved round the shape to be measured, the total rotation of the can is proportional to the area. All the different coloured shapes (triangle, circle, two oblongs) have been drawn the same area. So moving the pointer round any one of them will cause the can to rotate by exactly the same amount.

Only one end of the can touches the paper, I found it works better if you put PTFE tape round this bit of the can. The blue-tack weight also seems to improve the accuracy, I stuck a bent paperclip in it to help read the rotation of the can. A bit of bent wire runs through holes in either end of the can & is bent down in a right-angle at the left-hand end where it is sellotaped to the bent card to form a hinge-bearing.

The other end of the card has a drawing pin stuck through it which is sellotaped to the table. You have to use both hands to work it: the left hand moves the cardboard linkage while the right hand guides the pointer round the shape. It's important that the right hand exerts no vertical force on the can. It's difficult to use but gives quite consistant results. It could be made more sophisticated by sticking a spiral paper scale to the can, so that the amount of rotation could be read, rather than just showing that different shapes had the same area.

Link to movie

plastic spoon planimeter

This is a much simpler way of measuring area

If the right-hand end is carefully traced round an outline using a pin & sellotape as a pointer the vertical displacement of the left-hand end is proportional to the area. This kind of works if you just push a teaspoon round carefully with your finger.

Link to movie

hatchet planimeter
Douglas Brown's explanation
mechanical computing
2000 year-old computer
make your own drawing instruments

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