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This paper presents the visual servoing of a six degrees of freedom (6-DOF) manipulator for unknown three-dimensional profile following. The profile has an unknown curvature, but its cross section is known. The visual servoing keeps the transformation between a cross section of the profile and the camera constant with respect to 6 DOE The position of the profile with respect to only five degrees of freedom can be measured with the camera since the image does not provide position information along the profile. The kinematic model of the robot is used to reconstruct the displacement along the profile, i.e., the sixth degree of freedom, and allows to control the profile-following velocity. Experiments show good accuracy for positioning at a sampling rate of 50 Hz. Two control strategies are tested: proportional-integral control and generalized predictive control (GPC). The visual servoing exhibits better accuracy with the GPC in simulations and in real experiments on a 6-DOF manipulator due to the predictive property of the algorithm.