This paper presents the electromagnetic design and experimental validation of a new framework for linear permanent-magnet (PM) machines with magnetic levitation. In this framework, a single forcer, which can generate two force components in two perpendicular directions, consists of a stationary Halbach magnet array and two Lorentz coils with a phase difference of 90° or 270°. Any number of coil pairs can be attached on the same moving frame to work with a common magnet array or matrix, forming a linear or planar permanent-magnet motor. Key advantages of this framework are simple force calculation, linear force, and a reduced number of coils for force generation and allocation in multi-axis positioners. The proposed framework effectively allows for decoupled dynamics of multi-axis stages, simplifying their linear controller design and real-time implementation. This framework is experimentally verified by a high-precision 6-degree-of-freedom (6-DOF) magnetically–levitated (maglev) stage.

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