## 1 Introduction  
A linear induction motor (LIM) is a type of asynchronous machine that in comparison with the traditionally rotary induction machine does not develop an electromagnetic torque [1]. The electromagnetic forces in an LIM operate along two directions: horizontal and vertical, instead of rotating. Figure 1 illustrates the process for generating the electromagnetic forces in an LIM [2]. As shown in Figure 1, a, LIM has two different parts, which produce two different magnetic fields. The first part is a ferromagnetic steel (called stator or primary part). Inside this part, is located an alternating current (AC) three-phase winding that generates a traveling magnetic field. The second part is composed of two joined layers of aluminum and iron (called rotor or secondary part), where the generated eddy currents produce a new magnetic field. The interaction between the two magnetic fields created in both parts causes the motion of the secondary part. The relevance of LIMs in the industry is huge because there are a lot of applications in different areas [3], such as transportation systems (propulsion of wheel-on-rail vehicles and magnetic levitation high-speed trains), vertical drives (passenger elevator or an elevator without ropes), industrial drives (impact machine and machine tools), or automotive control and robotic. Additionally, these motors are relevant in military applications [4], such as electromagnetic aircraft launch or electromagnetic rail gun systems. Besides, LIMs are very important in all magneto-hydrodynamic applications because under low-velocity conditions, an LIM can be used as an electromagnetic pump where the liquid metal represents the moving part. A general classification of LIMs [1], divides these electrical induction machines into two different families depending on two criteria: the configuration of the magnetic flux and the geometry of the machine. The first family can be divided into two categories depending on the number of primary parts. Hence, an LIM that operates with only a primary part is called single-sided linear induction motor (SSLIM) and an LIM with two primary parts is called double-sided linear induction motor (DSLIM). The second family can be also divided into two different categories. First, an LIM with a magnetic flux that circulates along the direction of the movement called a longitudinal flux linear induction motor (LFLIM). Second, an LIM with a magnetic flux closed to a perpendicular plane to the direction of the movement called a transverse flux linear induction motor (TFLIM) [5; 6]. The most popular topology in the literature is LFLIM. However, TFLIM presents some advantages [1], such as a magnetic flux that crosses the airgap twice, a reduction of the consumed magnetization current, and a reduction in the weight of the device. In the literature, there are several techniques to increase the efficiency of LIM's which can be classified into the three following strategies. The first strategy is called winding skew and it is oriented to reduce the ripple whose effects are unwished [7]. The second strategy is focused on employing the third-order harmonics current injection to improve the thrust and the levitation force [8] and the third strategy modifies the geometric parameters of the LIM [9; 10; 11; 12; 13]. Our paper is focused on the third strategy that allows us to modify the magnetic flux configuration inside the armature on the LIM and redesign the paths available for the eddy currents induced inside the aluminum plate. The starting point is a prototype of an LIM that will be called model 1. Model 1 is an SSLIM with a configuration of TFLIM, whose geometry has been modified in both parts (primary and secondary part) in order to improve the efficiency of the LIM. Changes in the geometry have been introduced to configure a relevant three dimensions main magnetic circuit (3D-MMC). Our goal is to search two useful paths in perpendicular planes available for the magnetic fluxes.