## 2 Vibration Actuator Capable of Reciprocating Movement  
The reciprocating movement of the vibration actuator proposed by the authors was examined. The actuator moves in the tilted direction of the vibration component. To apply this principle, a newly designed slider mechanism that can move on a semi-cylinder was placed on the support of the vibration component. Four shape memory alloy springs were used to move the slider. Figure 1 shows the structure of the vibration actuator capable of reciprocating movement prototyped in the present study. This vibration actuator consistsof a vibration component, a holder unit for reciprocating movement, a permanent magnet attached to the lower part of the holder unit, and natural rubber sheet. Figure 2 shows the dimensions of the vibration actuator. This actuator has a length of 40 mm, a width of 38 mm, a total height of 42 mm, and is manufactured with dimensions smaller than 50 mm. As shown in Figure 3, the vibration component is composed of a coil spring, a ring-type permanent magnet, and an electromagnet with a bobbin-type iron core proposed in a previous paper [15]. The coil spring is a compression coil spring with a free length of 25 mm, an outer diameter of 12 mm, and a spring constant of k = 2689 N/m. The ring-type permanent magnet is an NdFeB magnet with an outer diameter of 12 mm, an inner diameter of 9 mm, and a thickness of 8 mm that is magnetized in the height direction. For the electromagnet, the experimental results of optimization of the bobbin-type iron core  
Figure 1: Structure of the vibration actuator capable of reciprocating movement. (**a**) Plan view of the actuator, (**b**) Front view of the actuator, (**c**) Details of holder unit of the actuator, (**d**) Photograph of the actuator. Figure 2: Dimensions of vibration actuator. (**a**) Plan view of the actuator, (**b**) Front view of the actuator. shape and the number of turns in a previous study [17] were applied. As shown in Figure 3, the diameter of the iron disk is D = 8 mm, the thickness is h = 1 mm, and the shaft diameter and length are d = 3 mm and H = 15.5 mm, respectively. The electromagnet was produced by winding a copper wire with an outer diameter of 0.2 mm around a bobbin-type iron core, creating a coil with a total of 810 turns. Details of the electromagnet are shown in Table 1.  
An NdFeB magnet having a length of M\({}_{1}\) (mm), a width of M\({}_{2}\) (mm), and a thickness of M\({}_{3}\) (mm) was used as a permanent magnet below the holder unit. In this paper, two types I and II permanent magnets were used for the holder unit. In addition, a natural rubber sheet with a thickness of 1 mm was attached to the lower part of the permanent magnet to increase the frictional force. The vibration components are mounted at an angle of 60 degrees from the horizontal plane. When this actuator is placed on a magnetic substance, such as an iron rail, the holder unit of the actuator receives an attractive force due to the permanent magnet, and the vibration component vibrates as a result of the electromagnetic force. The inertial force generated by the vibration component mounted at 60 degrees changes the frictional force between the magnetic material and the surface of the permanent magnet. Therefore, this actuator can move in the inclined direction of the vibration component [16]. Applying this principle of operation, the proposed vibration actuator with a holder unit capable of reciprocating movement was prototyped, as shown in Figure 4. As shown in Figure 1, the holder unit consists of an acrylic semi-cylinder, an acrylic base frame, four permanent magnets, four shape-memory alloy (SMA) coil springs, and an acrylic slider. In the holder unit, the acrylic semi-cylinder was attached to the base frame. The acrylic slider connected by two metal pins can rotate on the cylinder. Four SMA coil springs are attached to the frame and the slider via eight conductors. The SMA coil spring has a length of 30 mm and an outer diameter of 0.15 mm.