The first step in the synchronous reluctance machine design is the selection of rotor flux barrier type. The literature provides various barrier construction methods with a common goal of reducing parametric complexity. However, too excessive simplification can lead to decreased performance, while overly complex geometries tend to increase optimization time. This paper presents a set of novel flux barrier construction methods with an increased degree of freedom and minimal geometrical complexity. The paper proposes four topologies based on circular, hyperbolic, and original Zhukovsky lines. When considering parametrization complexity, the original Zhukovsky type is the simplest, but it has barrier depth limitations. Other topologies have equal complexity. The paper proposes a novel Modified Zhukovsky variable depth type based on geometrical conformal mapping of the original Zhukovsky lines. The step-by-step construction of each topology is presented in a form of pseudo-code with detailed comments and illustrations. Overall, the presented research provides a valuable starting point for the designer who wants to investigate different smooth rotor barrier topologies.