We are addressing the problem of Euclidean reconstruction with an uncalibrated affine camera and the calibration of this camera. We investigate constraints under which the Euclidean shape and motion problem becomes linear. The theoretical study described in this paper leads us to impose some practical constraints that the camera is mounted onto a robot arm and that the robot is executing controlled motions whose parameters are known. The affine camera model considered here is just an approximation of the true projective mapping. Nevertheless, there is a large number of applications for which the camera is allowed to be at some distance from the scene and under these circumstances the affine model is a good approximation. The fact that we deal with an uncalibrated camera is an advantage over previous methods because we do not rely any more on the tedious task of camera calibration. The experimental results obtained show that the method described compares favourably with other similar methods.