We establish a motion trajectory model for the principal point of a camera when it rotates with the rotating device. We also propose a calibration method based on the two-dimensional planar calibration of the camera to determine the distance between the camera's principal point and the turntable axis; the resulting translation matrix allows the calculation of the position relation between the principal point and the rotating center, providing a guidance for the camera installation. Further, the proposed motion trajectory model and calibration method are experimentally validated. The principal point of camera lens crosses the center of the rotation axis, and the standard deviation of the measured changes in translation matrix is 0.0826 mm. The results of this study can be used to support the installation of rotating measurement systems.