A Digital Planimeter by Ryan Epp
A planimeter is an analogue device created for measuring the area of any arbitrary shape.
This project looked to create a functional prototype, that may or may not have been used before.
The first step was physical desgin, as both the math calculations and building it require it. As for a planimeter, there are many variants, but in this case I used a wheeled variant, making use of one angle encoder, two arms of equal length, and a base and pivot point. The arms move with one another, that being the first arm in connected at both ends to the base and the second arm, while the second arm is only attached to the first, making use of the other end to pinpoint the position at which the user wishes to measure. The only reading given to the user is a wheel that sits on the second arm .
The second step was the math behind the design. Unfortunately, wheeled planimeters have no easily available math constructs, however digital and other designs need only use addition and integration. That being said, there is no derivation, only theory towards the area. For this to work however, both arms still need be the same length. The equation used to area is as follows:
Area = (Reading of wheel) * (Length of second arm)^2
With room for error, a multiplier is used after a calibration test of a square measuring 100cm^2.
The resulting equation uses modified versions of the base values for the Reading and Length.