Influence of the geometric parameters of two-axis rectangular flexure hinges on the coupling of the force sensor

Abstract When a multi-component force sensor calibrated in the build-up type multi-component force calibration machine, its deformation caused by the load applied in one direction would induce the deflections in the series connection components in other directions, in which case the lateral forces would generate and applied to the reference sensor of the machine leading to deviations in the sensor readings. To address the above problems, this study adopted a two-axis rectangular flexure hinge as a series connection component and investigated how its geometric parameters influence the coupling effects in force sensors (reference sensors). The findings reveal a clear relationship between the hinge of each parameter and the coupling effects, providing valuable insights for optimizing the design of multi-component force sensor calibration machines and reducing inter-component coupling. Firstly, a mechanical model of the flexure hinges is derived based on material mechanics. Finite element method (FEM) simulations are then employed to investigate the influence of geometric sizes—width ( b ), thickness ( h ), and length ( l )—on the reaction forces at the fixed end. Subsequently, 15 flexure hinges with varying geometric sizes are designed and mounted on the force sensor to conduct coupling experiments. The variations in the coupling rate are quantitatively analyzed, and the accuracy of the FEM results is verified. The results show that the greater the deflection applied at the loading end of the two-axis rectangular flexure hinges is, the larger the reaction force at the fixed end will be, thereby intensifying the coupling effect on the force sensor output. Flexure hinges with more minor b and h , as well as longer l , reduce the coupling effects introduced by the deflection at the loading end. Among the above elements, reducing h is the most effective approach of minimizing coupling. Furthermore, two-axis rectangular flexure hinges exhibit directional compliance around the radial direction, which results in different coupling rates in the y and z directions when deflections are the same.