Flexure-based inverted pendulum mechanical inclinometer

This article presents a novel fully mechanical flexure-based single axis inclinometer with degressive sensitivity based on an inverted pendulum with visual readout. The mechanism comprises a cantilever beam with a tip mass attached to its free end inducing axial compression load in the beam, thus reducing its bending stiffness. By adjusting the mass, the sensitivity of the mechanism-defined as the ratio between the beam deflection and the inclinometer inclination-can be tailored. In theory, this sensitivity can approach infinity when the load exerted by the tip mass approaches the critical buckling load of the beam. However, increased sensitivity comes at the cost of reduced measurement range, increased nonlinearity and higher impact of manufacturing tolerances. An analytical model based on Euler-Bernoulli beam theory is developed to describe the degressive nonlinear relationship between beam deflection and inclination angle. The analytical model is validated through finite element modeling and experimental testing on a mesoscale titanium alloy prototype fabricated via wire electrical discharge machining. A graduated scale is integrated for direct visual readout of the deflection of the mass, enabling estimation of the inclination angle. Experimental results demonstrate that the designed inclinometer can be used to measure inclinations up to ±35°, with a sensitivity of 1.16 near the nominal position, degressively reducing to 0.425 near ±35°. The adjustable tip mass allows the sensitivity to be tuned for specific application requirements.