Gravity is well tested on several length scales, but some unified theories predictdeviations in the region below 1 mm. In this thesis I will present a methodto search for such deviations in the sub-micrometre length scale. Below 1 μm,the electrostatic and the Casimir force are stronger than the gravitationalforce by some magnitudes. To distinguish these forces, I have designed a newforce measurement setup based on the frequency modulation AFM technique.Utilizing a quartz based parallelogram cantilever, it is feasible to measurethese forces with sufficient accuracy for us to set new constraints for possibledeviations of gravity. In this thesis I will present a new method of measuringsuch deviations of gravity, and show the initial results I have obtained using it.This will show that the measurement concept works, but that improvementsare necessary before we can achieve optimum measurement uncertainty.