Recent research has compared the numerical efficiency of magnetic equivalent circuit (MEC) models based upon Kirchhoff's voltage law (mesh equations) and Kirchhoff's current law (nodal equations). For stationary magnetic components, it was shown that mesh-based methods converge in significantly fewer iterations. Although the numerical advantages would seemingly apply to electric machines, two issues have limited the application of mesh-based MEC models to electric machines. With movement, the number of meshes (unlike the number of nodes) is position dependent. Additionally, the loss of an airgap element creates an infinite reluctance. In this paper, both issues are addressed. Specifically, it is first shown that a relatively straightforward algorithm can be used to dynamically update meshes with rotor position. In addition, it is shown that the mesh model remains stable for very large values of tube reluctance. Tube reluctance values that are large enough to cause numerical issues can be easily avoided by excluding a very narrow range of rotor positions. Based upon these results, a mesh-based MEC model of a wound-rotor synchronous machine is developed and is shown to provide a significant advantage over its nodal-based model equivalent.