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The hand-eye problem consists in computing the poses between pairs of different coordinate frames fixed to the same rigid body from measurements of such poses as the body moves. Various procedures have been proposed over the past two decades for solving this problem in presence of noise, especially for a robot as the moving body. As a matter of fact, different formulations of the problem in terms of the well known AX=XB or AX=ZB equations implement different flavors of an error minimization procedure, either least-square or non-linear, on the basis of a common algebra. It is shown in this paper that better results in terms of accuracy can be obtained outside the conventional approach. Rather than fitting the calibration matrices out of a number of random poses, the presented method superimposes easily programmable robot poses in order to attain a set of constant manifolds, like points, circles and axes, among the different coordinate frames. Such manifolds are used for identifying the constant relationships between the coordinate frames that are in fact the poses under estimation. The proposed method presents the implementation of a simple robot motion routine for generating the manifolds. Standard mathematical tools are used for fitting the manifolds out of an actual realization of the procedure with tracked markers. The geometry of the proposed manifolds also reduces the propagation of the measurement noise that usually affects the conventional computation based on relative poses. Results are given in simulation and with a real setup in comparison with the most popular state-of-the-art algorithms.