A novel algorithm for estimating motion and structure from orthographic projections is presented. The estimate is based on the image locations of a set of points on a rigid object viewed in many frames. The object can have an arbitrary shape. Motion is assumed to consist of rotation about a fixed-direction axis and linear translation, each at a constant rate. The algorithm uses closed-form expressions to find estimates of the motion and the structure parameters and can accept any number of points over any number of frames as input. The performance of the algorithm on synthetic data generated to represent a range of motion and structure conditions and on data extracted from real images is evaluated. It is shown that the algorithm produces accurate results from synthetic data given the positions of 10 points over 10 frames, with a total rotation of 90° and with uniformly distributed noise of 0.9%.