A camera under general motions allows the absolute quadric to be determined uniquely for self-calibration. For turntable motions, the absolute quadric cannot be determined uniquely, and will lead to ambiguities in 3D reconstruction. However, some fixed points and lines will arise as a result of turntable motions, and can be related to the calibration matrix. In this article, we have made two contributions for self-calibration under turntable motions. First, a detailed theoretical analysis on ambiguities based on absolute quadric is given. The ambiguities are derived. Second, using constraints on the physical characteristics of the camera, the ambiguities are removed up to a single parameter family. Experiments on real turntable image sequences verified our findings, which we used to perform a 3D reconstruction.