In this paper, an approach for the automatic structural synthesis of serial robot manipulators is proposed. Unlike existing methods, the parameters that can be used subsequently in a geometrical synthesis are obtained for every architecture as result of the presented approach. A modified motion vector is introduced in order to take into account different orientations of the robot base. This vector is used to generate a set of feasible architectures. Additionally, conditions for the evaluation of the presence of isomorphisms in this set of architectures are introduced. Finally, an example of a manipulator with four degrees of freedom is given to clarify the advantage of the proposed method.