Rigid mass m is connected to the fixed world via 2 parallel leaf springs. 2 Parallel leaf springs are well-known for a play-free linear guidance that comprise the following stiffness:
A contactless displacement sensor measures the displacement of m in relation to fixed world as a consequence of the applied force. The sensor used is a laser interferometer with nm resolution. With a stiffness of 1e5 N/m, the resolution becomes 0.1 mN. In the application in which the force sensor was used, 1e5 N/m was the lowest acceptable value (in relation to the dynamics of the application) but if a lower stiffness of the leaf springs is acceptable even better resolutions can be reached.
Manufacturing tolerances influence the stiffness. E.g. the stiffness changes with the leaf spring thickness to the 3rd power. Therefore the sensor is calibrated using precision weights; first the moving mass m is determined with the use of a precision weight () and the resulting 2 eigen frequencies ( and ): . Hereafter the force cell is placed in multiple angular configurations (with and without extra weights) to determine the stiffness curve (F vs. x) with .
The derived stiffness-linearity of the 2 parallel leaf springs is within 2%.
When the 2 parallel leaf springs move in x, the sag (z) in height is: . In this particular case the maximum sag is 1.8 μm at end-of-stroke (which is negligible).