Scaling of a compliant mechanism for high-precision force measurement applications

This paper is dedicated to the mechanical structure of a force transducer for the measurement of very small forces in the nanonewton range with highest resolution and lowest measurement uncertainty. To achieve this, a low stiffness in one direction of motion, but high stiffness in all other directions of motion is required. Existing solutions that meet the requirements are not suitable because of their overall dimensions. This results in a need for miniaturization. For this purpose, the scaling behavior of an existing monolithic compliant mechanism is investigated and it is verified which joint contour provides an optimal stiffness ratio. It is shown that the corner-filleted contour in general has lower bending stiffnesses, but also lower cross stiffnesses compared to the semi-circular contour. A nonlinear scaling effect for the ratio of bending stiffness and cross stiffness in corner-filleted contour offers optimization potential. Based on a simplified rigid body model, additionally, the miniaturization of the mechanism is optimized. The stiffness in the desired direction of motion is reduced by about 85% compared to a semi-circular contour. The result is promising for the further development of a miniaturized force transducer. The findings of this work contribute to the advancement of the measurement of low forces and offer new perspectives for future research in miniaturized force sensors.