Optimized Design and Characterization of a Non-Linear 3D Misalignment Measurement System

This work proposes a framework for the optimization of the metrological performances of a system that measures the relative position and orientation between two rigid bodies using the International Organization for Standardization (ISO) guide to the expression of uncertainty in measurement as a reference for the analysis. The developed method identifies a nonlinear measurement model of the instrument. The procedure uses the Monte Carlo method (MCM) and the design of experiments (DOE) techniques for determining the instrument uncertainty and the uncertainty sensitivity versus the geometrical and metrological instrument's characteristics. The innovative result of the proposed approach lies in the derivation of nonlinear numerical models of the measurement uncertainty and the bias error components. A case study related to a misalignment measurement system based on a universal joint is presented. The measurement uncertainty computed with the proposed method is compared with the one obtained in fit-to-purpose experiments performed with a robotic manipulator. An optimal calibration procedure is then developed to identify the parameters of the system by minimizing the overall uncertainty. Results evidenced that the uncertainty of the misalignment, in the tested configuration, mainly depends on the uncertainty of the rotational measurements. The model has also been used to improve the design of the system by increasing the mounting and manufacturing tolerances of the most critical components.