Chapter 4 DESIGN, ANALYSIS AND OPTIMIZATION OF AN
4.2. Structural design of proposed displacement sensor
4.2.1. Mechanical design and working principle of a proposed displacement sensor
4.2.1.1. Description of the structure of the displacement sensor
A displacement sensor is developed in Figure 4. 1 a. The platform of the sensor is embedded with strain gauges to directly identify the working travel. In a realistic scenario, the platform of the sensor is intended to be used in conjunction with an asymmetrical compliant gripper, as portrayed in Figure 4. 1b. The gripper comprises a micro-pin, a stationary jaw, a movable jaw, and a PEA. However, since the platform's behavior is akin to that of the gripper, the focus of the study was on analyzing the quality characteristics of the platform instead of the gripper. The suggested platform is mainly composed of a mobile platform, four sets of FHs, rigid bodies, and twelve strain gauges that are integrated.
Figure 4. 1: Design structure: a) displacement sensor and b) asymmetrical compliant gripper.
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Table 4. 1: Initial design parameters.
Parameters Value Unit
L Length of the positioning platform 68.16 mm
H Height of the positioning platform 109.5 mm
W Width of the positioning platform 8.0 mm
tA Thickness of flexure hinge A 0.75 mm
lA Length of flexure hinge A 25 mm
tB Thickness of flexure hinge B 0.7 mm
lB Length of flexure hinge B 12 mm
tE Thickness of flexure hinge E 0.85 mm
lE Length of flexure hinge E 30.5 mm
tF Thickness of flexure hinge F 1.0 mm
lF Length of flexure hinge F 70.5 mm
To achieve a stable grasping structure and a broad range of displacement, the gripper is designed with a symmetrical structure. The FHs include A, B, E, and F types. The elastic bodies are glued by strain gauges on the FH surfaces. A flexure hinge group is linked with an F group through C rigid link. A force gauge or piezoelectric actuator applies a force, denoted Fy, on the D mobile platform. Material AL7075 with parameters as shown in Table 4. 2 was selected as a suitable material for compliant mechanism applications.
Table 4. 2: Mechanical characteristics of AL7075.
Yield strength (MPa)
Young’s modulus (MPa)
Density (kg/m3 )
Poisson’s ratio
503 72000 2770 0.33
The A flexure hinge group, comprising eight elastic bodies of identical dimensions (length of lA, width of w, and thickness of tA), is horizontally positioned
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with the primary aim of aiding the D mobile platform's translational movement in the y-axis direction. The B flexure hinges have the length (lB), width (w), and thickness (tB) dimensions. Such a design can allow a displacement range for the D platform.
Using rigid bodies in the B group would have the opposite effect, reducing the platform's displacement. Therefore, FHs were employed to construct the B group.
FHs have strain gauges attached to their surfaces in various groups using a suitable adhesive. The positions of the strain gauges were determined through FEA simulation using Ansys software. Through FEA simulation, positions with maximum stress (von Mises stress) and maximum strain are determined. These are the most sensitive positions for the sensor. This implies that strain gauges should be attached at these positions. The strain gauges can be glued to the top surface or bottom surface of a flexure hinge or both. However, the results obtained are the same in value. It means that the strain in the tension state and the strain in the compression state are equal but the strain in the tension state has a positive value and vice versa, the strain in the compression tension state has a negative value (refer to reference [65], [121]). Based on this argument, the A group is bonded with twelve strain gauges numbered S1
through S12, while the B group is fitted with four strain gauges numbered S1B through S4B. The E and F groups have two strain gauges each, labeled as S1E, S2E, and S1F, S2F, respectively (refer to Figure 4. 1a). The platform is secured in place using screws on the fixed holes.
For flexible use in a variety of required situations, the frequency of the platform can be increased. The frequency increase has the following advantages:
Higher accuracy: this is because the higher frequency allows for more accurate measurement of small displacements because the impact of noise and other sources of error is reduced.
Resolution: higher frequency sensors can detect smaller changes in position than lower frequency sensors.
Response time: increasing the frequency of a displacement sensor can improve its response time, allowing it to more accurately track rapid changes in position.
Bandwidth: increasing the frequency of a displacement sensor can improve its
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bandwidth, allowing it to measure over a wider frequency range.
By using the formula for the relationship between stiffness, weight, and frequency (f = sqrt(K/M)/2∗π), As can be observed, there are two ways to raise the frequency of the natural vibration: (i) make the structure more rigid; (ii) make the structure lighter. This means that design parameters need to be changed. However, changing the value of the design parameter can cause a decrease in the deformability of the flexure hinges. Therefore, in this thesis, silicone rubber (a type of elastomer material) with mechanical characteristics as in Table 4. 3 is selected as the reinforcement material when necessary. Moreover, the addition of a silicone rubber pad can help absorb some of the vibrations during operation [99], [160].
Table 4. 3: Mechanical characteristics of Silicone rubber.
Young’s modulus (MPa) Density (kg/m3) Poisson’s ratio
1.35 910 0.49
The SR used in this study had a length of 45 mm, a width of 8 mm, and a thickness of 2 mm, and was utilized to fill the cavities. Figure 4. 2 shows the SR bending deformation. By reinforcing stiffness and increasing frequency, the SR contributes to the platform's enhanced speed since a higher frequency corresponds to a faster platform.
Figure 4. 2: Silicon rubber is reinforced along the contour of the cavity.
4.2.1.2. The working principle of a displacement sensor
The proposed displacement sensor is calculated by using the elastic theory of FHs and the half-Wheatstone bridge circuit as depicted in Figure 3. 6 [58], [159]. In Figure
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3. 6, as the platform is in tension, the R resistance causes an increase R. Nevertheless, as the platform is in compression, the resistance R is in a reduction R.
The strain sensor's gauge factor can be calculated by the following equation:
R , G R
(4. 1)
where the gauge factor is G, R is the variation of gauge resistance, R is a nominal value and is strain.
The following equation describes the relationship between strain () and resulting stress ():
,
E (4. 2)
Equation (4. 3) provides a close approximation of the circuit's output voltage:
1 ,
2 2
o ex ex
V G V R V
R
(4. 3)
where Vo is the circuit output and Vex is the excitation voltage.
The circuit's output voltage may be roughly calculated by substituting Eqs. (4. 1) and (4. 2) into (4. 3):
2 ,
o ex
V G V
E
(4. 4)
According to Eq.(4. 4), the output voltage is proportional to the tension placed on the FHs.
To evaluate the responsiveness of the displacement sensor gauge, Group A is selected for the examination. The linear stiffness of every single A-group FH is computed as follows:
3 3 A,
A A
K Ewt
l (4. 5)
where the stiffness of FH is noted as K.
The force Fy and displacement of an FH is computed as:
y A ,
F K (4. 6)
The force Fy and the stress of the FH are calculated by.
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2
6 y A,
A
F l
wt (4. 7)
The substituting of Eqs. (4. 5), (4. 6), and (4. 7) into (4. 4) leads to:
2
3 ex A ,
o
A
V V Gt
l
(4. 8)
Eq. (4. 8) is equivalent as below:
o ,
V S (4. 9)
where S represents the sensitivity of the strain gauge, and S is calculated by:
2
3 ex A,
A
S V Gt
l (4. 10)
Combining Eqs. (4. 2) and (4. 7), the strain and the geometric parameters of the FH are defined by.
2
6 y A ,
A
F l
Ewt (4. 11)
Through calibrations, it is possible to determine the sensitivity S of the strain gauge. This value can be measured by considering the output displacement of the platform of the displacement sensor and the output voltage. Equation (4. 11) demonstrates the significant effect of the FH's geometric parameters on the strain.
Besides, a few suitable strain gauges should be identified through FEA simulation.