This paper presents a mathematical model which can fit a parameter in an optimal position by measuring data. The model can synchronously correct the measurement error caused by the small rotation about X, Y and Z axes and the small deviation along X, Y and Z directions. The measurement results of the surface show that the model is reliable and effective, which provides loose conditions for placing mirrors and reliable measurement results for contact Coordinate Measuring Machine(CMM) off-axis surface contour measurement. The basic principle of the data analysis is also of high reference value for contour measurement of other non-contact free-form surfaces. The validity of the model is verified by mathematical simulation and practical engineering application, which is of great help to the measurement of high precision contact free-form surface.
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