Efficient numerical models have been already developed in 2D to take into account the movement of electromagnetic devices with rotating parts in the framework of the Finite Element Method (FEM). When the movement becomes complex it leads to large mesh distortions. A remeshing step is then required which increases the computational complexity and can also lead, in some cases, to numerical ripples on forces and torques due to the field projections between old and new meshes. Moreover, remeshing procedures in 3D remain an open topic. Meshless methods seem an appealing choice for alleviating the mesh constraints. The Natural Element Method (NEM) which, has known a growing interest in the domain of mechanics, allows to proceed in the meshless framework, avoiding one of the main drawbacks related to the vast majority of meshless techniques, as is the imposition of essential boundary conditions. In this paper, a variant of the NEM, known as constrained natural element method (C-NEM) is applied for simulating electromagnetic machines involving rotating parts. A new mixed strategy combining the finite element and the constrained natural element methods is proposed and then tested by using an appropriate error estimator.