In this paper, we propose a new approach for recovering 3D geometry from uncalibrated and unknown rotation angles of single axis motions. Unlike previous approaches, the computation of trifocal tensor is not required. The new approach is based on fitting a conic to the corresponding points in different images of the same space point. It is then shown that the essential geometry of single axis motion is encoded by a conic. Since we are determining only 5 parameters from N views instead of 18 parameters from a subsequence of 3 views, our approach is much more simple and robust. The experiments on a real image sequence demonstrate the accuracy and robustness of the new algorithm.