It is important to accurately construct a data-driven geometric model for the electric machine (EM) to avoid parts overlapping, which can result in the failure of performance analysis using finite element method (FEM) tools. This paper presents a novel approach that combines Latin hypercube sampling (LHS) and geometric repair operators to generate samples for the design of experiments (DoE). Firstly, the parametric geometric model, constraints, and the corresponding geometric reparations for EM are introduced. Then, the proposed approach is employed to address the geometric constraints when constructing the EM models for DoE. The proposed approach is numerically validated using a surface mounted permanent magnet synchronous machine, demonstrating the effectiveness in improving space-filling characteristics and feasibility through constrained LHS. Furthermore, the correlation analysis results based on the DoE can be used to reduce the design variables for multi-objective optimization and support surrogate modelling for EM performance prediction.