Systems and methods for measurement of geometrical parameters of threaded joints

Thread parameters for a threaded object are determined. Spatial reference systems (X, Y, Z) and (X′, Y′, Z′) are respectively identified for a position sensor and the threaded object. A transformation matrix describing a quadratic form representing the threaded object in (X, Y, Z) may be determined to relate the reference systems. For example, a sensor trajectory on the threaded object may be determined, along with measurement points on the threaded object. The measurement points may be selected so the matrix, evaluated on these values, has maximum rank. Position data at measurement points in the second reference system may be transformed into the first reference system, yielding first results. After coating the threaded object, position data at the measurement points may be acquired again and transformed into the first reference system, yielding second results. Comparisons between the first and second results may provide thickness of the coating and quality verification.