Theoretical insights on the influence of the experimental plan in the calibration of multicomponent force and moment transducers

In recent years, the increasing demand of multicomponent force and moment transducers led the necessity to develop specific calibration procedures. Sensitivity and exploitation terms of these transducers are usually expressed in matrix form to evaluate cross-talks between the different components. According to the seminal work of Ronald Fisher in 1926, to provide accurate results, calibrations shall be performed with different combinations of forces and moments in order to minimize the correlation between them. In this work, a theoretical investigation, based on an ideal transducer, on the influence of the experimental plan in the evaluation of exploitation matrix terms and the associated uncertainties as function of the number of measurements and the correlation between the applied forces and moments is performed. It is found that at decreasing number of measurements and increasing correlations between the applied forces and moments, uncertainties increase, while exploitation matrix terms are poorly affected by the chosen experimental plan.