| To relate measurements made by a sensor mounted on a mechanical link to the robot's coordinate frame, we must first estimate the transformation between these two frames. Many algorithms have been proposed for this so-called hand-eye calibration, but they do not treat the relative position and orientation in a unified way. In this paper, we introduce the use of dual quaternions, which are the algebraic counterpart of screws. Then we show how a line transformation can be written with the dual-quaternion product. We algebraically prove that if we consider the camera and motor transformations as screws, then only the line coefficients of the screw axes are relevant regarding the hand-eye calibration. The dual-quaternion parameterization facilitates a new simultaneous solution for the hand-eye rotation and translation using the singular value decomposition. Real-world performance is assessed directly in the application of hand-eye in-formation for stereo reconstruction, as well as in the positioning of cameras. Both real and synthetic experiments show the superiority of the approach over two other proposed methods.