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The contribution of powerful numerical calculation methods in the design procedure of electrical actuators is usually restricted to the analysis of structures with known geometric dimensions. This paper describes a computer-aided design tool with a multiphysics design methodology starting from datasheet specifications. It is operational from the first design phases due to the association of analytical and numerical approaches that are performed by the coupling of two software tools. The analytical study associates a coupled electromagnetic-thermal model with a gradient optimization algorithm and provides a quick first solution. This solution is then optimized, according to other criteria, by a further numerical study that is based on a finite-element model that is linked to a simplex algorithm. The vibratory behavior of the obtained solution is finally studied using modal analysis. This methodology is applied to design a permanent-magnet synchronous machine.