Rotational Vision System (RVS) is a common active vision system with only rotational degrees of freedom. Usually, the degree of freedom for rotation is provided by the turntable and pan head. Or the hand to eye (EIH) structure in articulated arm robots. Due to assembly deviations and manufacturing accuracy limitations, the ideal assumption that the rotation axis is fully aligned with the coordinate axis of the local camera is mostly violated. To address this issue, we propose a generalized deviation model that specifies a rotation axis that connects the rotational motion of the platform with the external orientation (EO) of the camera. On this basis, we propose a heuristic estimation algorithm to minimize global reprojection errors and fit circles in space under constraints of global optimization. The experiment shows that the translation and tilt average reprojection errors of dynamic EO reconstruction based on the reprojection error method are 0.14 and 0.08 pixels, respectively. In the absence of angle measurement, the results of the circle fitting method are similar to them (with a relative error of about 2%), meeting the application requirements of general visual measurement.