Mathematical model of contacting freeform surface contour measurement

To unwind the requirement of a freeform surface for the position adjustment and to provide high precision measurement results in a high precision contacting freeform surface contour measurement, this paper proposes a mathematical model based on the least square method. The model can fit the measured dada to obtain optimized position parameters. After analysis of possible causes for the measurement error of Coordinate Measuring Machine (CMM), the model can be used to correct the errors caused by the rotation in the X, Y, Z axes and the eccentricity in the X, Y, Z direction that exist in the positioning of freeform surface. By mathematical simulations, it is proved that this model achieves high precision in correction of the errors for eccentricity less than 1 cm and inclination less than 0.1° and shows a very reliable and effective result. It provides loose workpiece positioning conditions, high precision and reliable measurement results. The analysis principles proposed also offer a reference for other contacting freeform surface contour measurement methods.