This paper presents a novel parametrization for the flux barrier profiles of synchronous reluctance and permanent magnet assisted reluctance machines. In literature there are several methods used to design rotor flux barriers of various types, however the vast majority use only a few parameters to characterize their shape. These approaches are proven to be effective in terms of simplicity and computational burden required to achieve an optimal design. However, simplified parametrizations certainly decrease the degrees of freedom when designing the whole barrier shape. In this paper, an attempt to increase the degrees of freedom, introducing a novel rotor flux barrier parametrization, is presented. The method proposed uses natural splines, defined by the positions of a set of control points, to form the shape of the flux barriers. The spline and state-of-the-art barrier profiles are compared from both electromagnetic and mechanical perspectives. The results of this investigation show that by increasing the degrees of freedom it is possible to obtain better performance characteristics. The proposed parametrization is applied to a 6-pole synchronous reluctance motor and its permanent magnet assisted variant, optimized for a traction application. A prototype has been manufactured and tested to experimentally validate the design methodology.