This article proposes a design process for a flux modulated (FM) permanent-magnet linear actuator for a five-axis gantry robot system by investigating the parameters affecting working harmonics. A detailed design process using the magnetic gearing effect was developed by considering the magnetic equivalent circuit and finite element analysis models of the FM-linear actuator. Considering natural cooling, the design process includes the effect of irreversible demagnetization when selecting the design parameters. Using the design parameters, a final simulation model was created to check the electromagnetic performance under both no-load and full-load conditions. A prototype was built to validate the results obtained using the proposed analytical model.