This paper investigates using constant inter-frame motion for self-calibration from an image sequence of an object rotating around a single axis with varying camera internal parameters. Our approach is based on the facts that in many commercial systems rotation angles are often controlled by an electromechanical system, and the inter-frame essential matrices are invariant if the rotation angles are constant but not necessarily known. It is shown that recovering camera internal parameters is possible by making use of the equivalence of essential matrices, which relate the unknown calibration matrices to the fundamental matrices computed from the point correspondences. Experimental results on both synthetic and real sequences are presented to determine the accuracy and the robustness of the proposed algorithm.