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The subject of this paper is the feedback linearization of the input-output and input-state equations for a class of multi-link, three degrees-of-freedom manipulators with the last link flexible. This class includes the 5-bar-linkage and the elbow manipulator. It is shown that the input-output equations are only feedback linearizable if the output variables are chosen appropriately. However, the nonlinear dynamics made unobservable by this feedback are not asymptotically stable which is a severe drawback. It is then shown that the input-state equations are not feedback linearizable. These results indicate that feedback linearization techniques are not appropriate for this class of manipulators. Thus, alternate methodologies should be explored. That issue is tackled in Part II.