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In this paper we investigate how intrinsic camera calibration and hand-eye calibration can be performed on a robot vision system using the simplest possible motions and a planar calibration object. The standard methods on plane-based camera calibration are extended with theory on how to use pure translational motions for the intrinsic calibration and we see how hand-eye calibration can be performed within the same framework. The calibration of two cameras in a stereo head configuration is shown to be an interesting application of the developed theory. Results of experiments on a real robot vision system are presented.