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Compliant mechanisms are becoming increasingly important, especially in force measurement and weighing technology, due to their zero backlash, wear resistance, and zero friction. Their deformation under external forces can be analyzed well with analytical calculations and FEM simulations. Analytically, only mechanisms with symmetrical and longitudinally symmetrical hinges are described. This paper presents a method that allows transversally symmetric hinges to be described analytically. The model must be computed numerically due to the built neutral fiber and the nonlinearities in the used calculation method. The developed method is then compared with FEM calculations in a parameter study and considered to be validated. Finally, outlooks are formulated on how the created method can for instance be used to develop load cells for later calculations. Moreover, it is shown to what extent it is possible to implement this method for general calculations of compliant mechanisms.

The performance of tactile and optical surface sensors for nano and micro coordinate measuring machines is currently limited by the lack of precisely characterised micro spheres, since established strategies have mainly been developed for spheres in the range of millimetres or above. We have, therefore, recently focused our research efforts towards a novel strategy for the characterisation of spheres in the sub-millimetre range. It is based on a set of atomic force microscope (AFM) surface scans in conjunction with a stitching algorithm. To obtain an uncertainty statement, the uncertainty about the shape of the reference surface needs to be propagated via the shape of the AFM tip to the actual measurement object. However, the sampling process of an AFM is non-linear and the processing of AFM scans requires complex algorithms. We have, therefore, recently begun to model the characterisation of micro spheres through simulations. In this contribution, this model is extended by the influence of the tip and reference surface. The influence of the tip’s shape and reference surface is investigated through virtual and real experiments. The shape of the tip is varied by using tips with mean radii of 200 nm and 2 μm while sampling the same ruby sphere with a mean radius of 150 μm. In general, the simulation results imply that an uncertainty of less then 10 nm is achievable. However, an experimental validation of the model is still pending. The experimental investigations were limited by the lack of a suitable cleaning strategy for micro parts, which demonstrates the need for further investigations in this area. Although the characterisation of a full sphere has already been demonstrated, the investigations in this contribution are limited to equator measurements.

The article describes the possibilities of calibrating the force constant in an electromagnetic force compensation (EMFC) load cell using the electrostatic force compensation principle. The static and dynamic principles of calibration of the Kibble balance for the electrostatic force constant, as well as calibration by means of compensation of the electrostatic force by the electromagnetic force, are considered. The combination of the two compensation principles in the load cell allows the measurement of forces in the range of 20 pN to 2.2 mN and ensures traceability to national standards. The relative uncertainty in the measurement of forces of about 100 nN is estimated to be about 0.001.

Mass comparator weighing cells based on electromagnetic force compensation (EMFC) find application in the most demanding force and mass measurement applications. The centerpiece of these devices is a highly sensitive compliant mechanism with thin flexure hinges. The compliant mechanism forms the mechanical part of the mechatronic overall system. A novel mechanism based on an advanced adjustment concept has been developed, manufactured, and experimentally investigated. The adjustment is designed to further reduce the measurement uncertainty for mass comparisons by canceling out first-order error components. The focus is on the mechanical properties: stiffness, tilt sensitivity, and off-center load sensitivity. The elastic stiffness of the compliant mechanism is compensated by introducing a negative gravitational stiffness to enable the compensation of manufacturing deviations and to increase mass resolution.