Simultaneous normal and torsional force measurement by cantilever surface contour analysis

This study presents an alternative to the current Hooke's law-based force relation between rectangular cantilever deflection and applied force. In the new approach, a transduction constant is presented that (1) includes no cross-talk between torsion and normal force components, (2) is independent of the load application point, and (3) does not depend on the cantilever beam length. Rather than measuring the cantilever deformation at a single point (such as the tip location), it is measured at multiple adjacent points using scanning white light interferometry to provide a three-dimensional description of the cantilever deformation during loading. This measurement, processed by a force relation based on a superposition of deflections derived from Euler–Bernoulli bending theory and St Venant's torsion theory, provides the vertical, axial, and torsional force components simultaneously. Experimental results are compared to force predictions for the vertical and torsional components using macro-scale cantilevers under mass loading. An uncertainty analysis is also provided.