Figure 8 shows the response in the vertical load application test when a vertical force of 95 N is applied to the sensor. Here, the response is shown as the rate of change of the resistance of the strain gage to that without load. The graph shows that the resistance increases linearly for all cantilevers in a large load range such as gripping force. The sensitivity is calculated from the sensor response to be 0.66, 0.81, and 0.80 ppm/N for cantilevers 1, 2, and 3, respectively.
Figure 9 and Table 1 show the response as a function of the curvature of the elastomer sheet and sensitivity (gradient of response to curvature) of the sensor in the bending test, respectively. In Fig. 9, the elastomer sheet was placed with (a) the front side up and (b) the back side up, respectively. It is found that the response is proportional to the curvature of the elastomer sheet. The sensitivity of the sensor increases at 0 deg for cantilever 1, while it increases at 90 deg and 270 deg for cantilevers 2 and 3, as shown in Table 1. This indicates that the response is larger when the direction of strain caused by bending is close to the direction of the cantilever placement. Since cantilevers 2 and 3 make the same angles for the 0 deg, 90 deg, and 270 deg bending directions, their sensitivities to these curvatures are nearly identical. Furthermore, the positive and negative responses to curvature are reversed depending on the front and back of the elastomer sheet of the sensor arrangement. Figure 10 shows schematic illustrations of (a) the strain distribution in bending, and the cantilever behavior in the case of the (b) front and (c) back sides of the sensor chip being up, respectively. The deflection of the cantilever changes inversely depending on the front and back of the elastomer sheet, thus, it is suggested that the positive and negative responses are reversed. As mentioned earlier, the tip surface where the cantilever is located is 3.5 mm from the elastomer surface, which is below the neutral plane (2.5 mm) of the elastomer, so that when the front side is up, compressive strain occurs and the deflection of the cantilever is reduced, resulting in increased resistance. On the other hand, with the back side up, the cantilever deflection increases, and resistance decreases due to tensile strain because it is above the neutral plane. This indicates that the sensor can detect not only curvature but also bending direction.
Finally, the results of the torsional deformation test are discussed. Figure 11 shows the results of the torsional deformation test. Cantilevers 2 and 3 respond significantly at all angles of alignment, while the response of cantilever 1 is relatively small. For placement angles of 0 deg and 180 deg, the resistance of cantilever 2 increases, and that of cantilever 3 decreases. On the other hand, when the placement angles are 0 deg and 270 deg, the resistance of cantilever 2 decreases, and that of cantilever 3 decreases. Table 2 shows the response at each placement angle for a 3000 µm indentation. It is found that the magnitudes of the responses of cantilevers 2 and 3 are almost the same when the placement angles are 0 deg and 90 deg, and the positive and negative responses are opposite.
Figure 12 shows a schematic diagram of the direction of the torsional moment and internal shear stress when viewed from the front. The direction of the internal shear stress in the elastomer coincides with the direction of the torsional moment. When the placement angle is 0 deg, the torsional moment is counterclockwise when viewed from the front, thus the shear force acts from left to right at the bottom of the elastomer where the sensor is placed. On the other hand, when viewed from the left side, the torsional moment acts in a clockwise direction, so that when viewed from the front, the shear force acts from the front to the back at the bottom of the elastomer. Furthermore, considering the torsional moments at the back and right faces and the resulting shear forces, the direction of the shear forces acting due to each torsional moment is shown in Fig. 12(c). From these combined forces and the cantilever arrangement, it is expected that for a placement angle of 0 deg, the shear force acts on cantilever 2 from the fixed end toward the free end (diagonally upward to the right), resulting in reduced deflection and increased resistance. On the other hand, the shear force acts on cantilever 3 from the free end toward the fixed end (diagonally upward to the left), increasing the deflection and decreasing the resistance. Since cantilever 1 is equidistant from the front and back, no shear forces are expected to act in the longitudinal direction of the cantilever. Based on this expectation, the experimental values from Table 2 show that the resistance of cantilever 2 increases at a placement angle of 0 deg, the resistance of cantilever 3 decreases, and the resistance of cantilever 1 changes very little compared to them, indicating that the internal shear stress distribution due to torsion and the sensor response match.
Table 1
Sensitivity of the sensor to curvature
(a)

θ = 0 (deg)

θ = 90 (deg)

θ = 270 (deg)

Cantilever1

5.63

1.77

1.70

Cantilever2

1.98

6.36

6.04

Cantilever3

1.99

6.60

6.47

(b)

θ = 0 (deg)

θ = 90 (deg)

θ = 270 (deg)

Cantilever1

4.42

1.30

1.30

Cantilever2

0.02

5.09

4.77

Cantilever3

1.57

4.16

4.42

(a) front side up and (b) back side up (unit: ppm/m− 1)
Table 2
Resistance change rate of the sensor at 3000 µm pushing in the torsion test

θ = 0

θ = 90

θ = 180

θ = 270

Cantilever1

34.1

32.6

38.8

47.0

Cantilever2

325.0

346.3

345.0

328.0

Cantilever3

327.6

313.4

346.0

312.7
