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Weighing cells with electromagnetic force compensation are frequently used in precision balances and mass comparators. The kinematic structure is given by a compliant mechanism with concentrated compliances. Thin flexure hinges enable highly reproducible motion but limit the sensitivity to mass changes due to their rotational stiffness. To achieve the desired sensitivity, the stiffness of the mechanism must be further reduced by mechanical adjustments. To optimize the adjustment parameters, the initial stiffness of the mechanism needs to be characterized accurately. For this purpose, a novel self-testing method was developed. It allows accurate determination of the elastic stiffness of the weighing cell and the geometric stiffness caused by the masses of the linkages. The method uses static stiffness measurements in three orientations. The gravity vector must be orthogonal to the plane of motion to characterize the elastic stiffness. Determining the geometric stiffness requires the system to be in the working orientation. The upside-down orientation is used to confirm the results. This paper considers the novel method analytically and simulates using a rigid body model and the finite element method. The measurement of the stiffness of a weighing cell prototype is taken to validate the method.

Monolithic compliant mechanisms with concentrated compliances are often used in high-resolution force sensors and precision balances. Since the measurement resolution is vastly limited by the bending stiffness of the compliant joints, the thinnest part of the joints is reduced to down to 50 µm. A further reduction encounters technological limitations and creates new side effects. Compensation for the "positive" stiffness of the mechanism can be achieved by integrating an element with "negative" stiffness that generates a counteracting force or torque when deflected. In the literature, preloaded tension springs, buckled leaf springs as well as trim masses are predominantly for that purpose. However, most existing approaches are either not monolithic, elaborate to readjust, associated with parasitic forces and torques, or only applicable in a defined orientation relative to the vector of gravity. This paper presents a new concept of monolithic stiffness-compensated mechanisms for use in high-resolution force sensors that is independent of spatial orientation. The negative stiffness is generated by a preloaded spring element of an integrated compensation mechanism. The preload force can be easily adjusted. The compensation force is generated simultaneously with the deflection and transmitted to the main mechanism by a lever and a dedicated coupling element to avoid parasitic effects as much as possible. A suitable design minimizes parasitic motions and avoids buckling of the thin joints as a result of the relatively high preloading force. Finite element simulations are performed to investigate the behavior of the mechanism and to validate the concept.