Development of a Low-Profile Planar Sensor for the Detection of Normal and Shear Forces

Individuals with balance and mobility problems might benefit by the use of devices that detect small changes in ground reaction forces and potentially be used to assist movement. For maximum effectiveness, such sensors must measure pressure in all three dimensions. Impact and shear plantar force are essential variables in inverse dynamics reconstructions of the human joint force. Various force sensors have been proposed to monitor plantar forces of the human foot. Most of them have a single-axis measurement, and few are intended for monitoring normal and shear stress. This article proposes a low-cost, biocompatible triaxial piezoresistive sensor developed using simple fabrication techniques and inexpensive machinery. The sensor can detect pressures from 0 to 800 kPa with high response and recovery with minimum hysteresis and repeatable results of over than 100 cycles.

Abstract-Individuals with balance and mobility problems might benefit by the use of devices that detect small changes in ground reaction forces and potentially be used to assist movement. For maximum effectiveness, such sensors must measure pressure in all three dimensions. Impact and shear plantar force are essential variables in inverse dynamics reconstructions of the human joint force. Various force sensors have been proposed to monitor plantar forces of the human foot. Most of them have a single-axis measurement, and few are intended for monitoring normal and shear stress. This article proposes a low-cost, biocompatible triaxial piezoresistive sensor developed using simple fabrication techniques and inexpensive machinery. The sensor can detect pressures from 0 to 800 kPa with high response and recovery with minimum hysteresis and repeatable results of over than 100 cycles.
A variety of shear force-sensitive cells have been presented. Chase et al. [14] developed a normal and shear force sensor with a one electrode at the top surface of the sensor and four electrodes at the bottom. The mechanical principle is formed by the deflection and compression forces of the filler layer between the top and bottom electrodes. The shear force and direction were computed using the fractions of the four capacitors. The disadvantage of this sensor is that it only measures a tiny delta in the capacitance, particularly when a shear force is applied.
Lei et al. [15] developed a capacitive pressure sensor for monitoring plantar force. The sensor consists of a top electrode, four bottom electrodes with a "bump" layer, and a PDMS dielectric. Four independent capacitive sensing switches are formed, and values are averaged to enable measurements up to 945 kPa, even in nonuniform loads applied to the dielectric layer. Overall, these sensors have four capacitive elements, which can measure shear and normal forces through selective decoupling of the output signals. Using this approach, in 2013, Dobrzynska and Gijs [16] developed a flexible triaxial force sensor with "E"-shaped design for both the bottom and top electrodes. They consisted of four parallel-plate capacitors with a silicone dielectric. The cell can measure force in each axis up to 14 N (220 kPa), making it suitable for the range of pressure in plantar shear force measurements.
Wattanasarn et al. [17] developed a triaxial force sensor, which is flexible and consists of four structures: a positive profile "bump," measuring coil, spacer, and four excitation coils. When the sensor is not loaded, the same output voltage is present on the four measuring coils. The measuring coil is displaced on the application of load, resulting in differential voltage changes between the excitation coils. These can be selectively decoupled and used to calculate the applied force similar to that used for triaxial capacitive sensors.
In general, these designs feature a certain challenge in measuring shear forces. Substrate integrity and electrode configuration must be arranged to detect shear forces independently. The substrate material implies to the material that contributes to the composite flexibility rather than the charge carrier [18]. The design principle focuses on the structural integrity of the 2768-167X © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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substrate material, where it is reformed to detect normal and shear forces. Finally, Tao et al. [19] developed a paper-based force sensor. Tissue paper was mixed with the graphene oxide (GO) solution to obtain a GO paper. Compared to the previously mentioned force sensors, it has obvious advantages in achieving ultrahigh sensitivity. The fabrication process is relatively easy and cheap to reproduce, and it was used to fabricate and test the initial proof of concept designs of the sensor illustrated in this article. This led to the idea of using the art of folding and cutting paper, kirigami, to form the integrity of the substrate material. By folding paper, a slender material is formed, which can easily bend but not easily stretched, which leads to unique advantages, such as structures designed around stretching are strong and lightweight [20].
The initial sensor concept design has been presented in the 2022 IEEE International Conference on Flexible and Printable Sensors and Systems (FLEPS) and was published in its proceedings [21]. This article provides a detailed analysis of the mechanical and electrical model of the design and, in addition, discusses the data visualization software developed to interpolate the sensor data in an intuitive way to detect forces in 3-D and load distribution in a high-resolution 2-D heatmap.

II. DEVICE DESIGN AND MATERIALS
The design of the proposed device is illustrated in Fig. 1(a). It consists of five different layers. The structure and materials shown as b, i, e top , s, p, and e bot indicate the thickness of the negative bump (silicone elastomer Mold Max 1 10), an insulation layer (Kapton tape), top electrode (copper tape), 3-D printed semiconductive substrate (Ninjatek eel), PDMS (SYLGARD 184) spacer, and bottom copper electrode, respectively. The size of the cell is 10 × 10 mm. One resistor is located on each corner of the substrate in each sensor cell to form a 2 × 2 array. The negative bump has four positive bumps at each corner of the cell and is aligned with the top electrode. The PDMS spacer is found in between the substrate and bottom electrode. The design of the substrate forms four gaps, as shown in Fig. 1(c). The distance between the gaps, dt, on each corner is controlled by the direction of the applied force. The mechanism works like a biplanar seesaw, where torque is generated at the four pivot points shown in Fig. 1(c). Two seesaw mechanisms are formed and respond to the shear force's direction when the moments on each four sides are uneven.
Subsequently, when the device is loaded at the top surface, the substrate is compressed, and the four air gaps between the electrodes decrease identically, as shown in Fig. 1(e). This behavior suggests that the four resistors have an equal resistance change. On the other hand, when the shear load is applied to one direction, the substrate produces a torque, incrementing the gaps for two resistors toward the applied shear force direction, as shown in Fig. 1(f) and (g). As a result, the applied normal and shear force can be sensed differently based on the resistance variation. 1 Tradiational trademark. A 3-D model of the device package was developed in Solidworks. To verify the mechanical principle, the finite element method was used. The material properties were taken from datasheets from all materials forming the device [22], [23], [24]. The analysis was performed using an elastic model since the stress-strain curve of the materials used is almost linear, and the hysteresis is negligible for small deformations. Boundary conditions are applied at the bottom of the model with fixed supports in all directions. Contact surfaces were used between the pivot points referred to Fig. 1(c) and the opposed surface on the top. To simplify the analysis for computation cost with the trade of the compressibility effect, more contact surfaces sets were not used; therefore, the penetration shown cannot be avoided. The scope of the FEA is to show the mechanical principle of the sea-saw mechanism and not to find accurately the displacement induced. Fig. 1(e) presents the application of normal (z) force across the whole top surface of the device illustrated from both side views. Shear pressures were applied in both xand y-directions across the whole top surface of the device. As shown in Fig. 1(f) and (g), the cell deforms as expected for shear pressures on the xand y-axes. Each side of the biplanar see-saw mechanisms responds to the direction of the shear force in a different manner.

III. PIEZORESISTIVE MODEL
The sensor was modeled using a simple approach of four resistors in parallel located at each corner of the sensor to translate the resistance change in the x-, y-, and z-axes. The four resistors in the following equation are the four independent sensing elements located at the top side of the sensor for shear and normal loads detection: The length of each wire connection in the circuit in Fig. 2(a) was equal; therefore, it is assumed that wiring has no influence. Strain present on the xand y-axes is negligible since the force applied to the device is compression, not tension. Therefore, on the z-axis, maximum strain is found. The areas of all four-square electrodes were designed identically with the area A = A1 = A2 = A3 = A4. The theoretical model assumes that the resistivity is equally thick across the entire sensor with a thickness of t when load is not applied and varies independently on each corner according to the load applied. Therefore, the resistivity (2) can be derived for the initial resistance Re as: where ν and ε are the Poisson's ratio and strain, respectively, and ϱ is the material's resistivity A force in the z-direction reduces the distance by dt, and decreasing all four resistors' resistance there Rz is the sum of all resistors as in (3). A force in the x-direction increases the thickness of the resistor R1 by dt and decreases the thickness of R3 to the same extent while not influencing R2 and R4. A subtraction of each pair of resistance indicates the applied shear forces in the xand y-directions, as shown in (4) and (5) A piezoresistive analysis was performed in ANSYS to investigate the effect of displacement induced from load within the substrate versus the electric potential. For simplicity, 2-D analysis was performed by modeling the substrate as a rectangular shape with dimensions of 0.9 mm thick and 10 mm long. The element type used was coupled-field tennode tetrahedron. Positive and negative terminals were set at the rectangle's top and bottom, respectively. The model was fixed from the bottom and loaded from the top with 800 kPa. The elasticity and resistivity of the substrate are isotropic; therefore, a volume resistivity of 15 000 was used. Data for displacement and electric potential were taken from nodes across the vertical side on the right-hand side. The deformed shape behaves elastically up to 12 Mpa pressure, as shown in Fig. 2(b) and (c). The results in Fig. 2(d) and (e) illustrate that electric potential within the substrate media is directly proportional to the load applied to the sensor.

IV. SURFACE TREATMENTS AND PACKAGING
The device comprises of two identical semiconductive substrates in a sandwich-like design, as shown in Fig. 3. The design was done in solidworks, and the material used was thermoplastic polyurethane (TPU) Eel carbon nanotubes fused filament. Ninjatek Eel is a flexible conductive filament, consists of TPU doped with carbon-black, produced by Ninjatek Wet etching was performed to shape the electrodes using copper and Kapton tape. First, the two tapes were adhered together, avoiding any air bubbles in between, as shown in Fig. 3(a). A photosensitive film was applied on copper surface and a mask of the positive profile of the desired electrode location with its connection traces and pads. Then, photolithography penetrated the film, leaving the electrode configuration's negative profile [ Fig. 3(b) and (c)]. A positive developer (NaOH) was used to remove the mask's penetrated traces [ Fig. 3(d)]. The etching process follows, where the PI-Cu laminate was exposed to ferric chloride acid [ Fig. 3(e)]. This results in a 5.5-µm-thick copper electrode with 6.3 µm of insulation. Finally, wires are soldered to the copper pads in the PI-Cu laminate. PDMS spacer was molded by mixing the two parts and degassing them. The uncured silicone was poured on a flat surface and agitated using an orbital shaker to form a thin layer for the spacer. Then, it was placed in a convection oven at 80 • C for approximately 1 h 30 min until the PDMS was completely dry. When cured, the PDMS is cut using squareshaped hole punchers. Silicone MoldMax 10T was used as an encapsulated layer at the top, and by the molding method, the desired design was achieved. Packaging was done manually by stacking part (g) and (f) with the encapsulation on top, as shown in Fig. 3(f)-(i).

V. DATA VISUALIZATIONS
A Python code has been developed for the visualization of real-time data of the pressure sensor. The code consists of importing the data from an Arduino board and using them to create a 3-D schematic representation of the forces that act when pressure is applied. Specifically, the Arduino ports were connected, and numerical/mathematical libraries were imported to aid the analysis. The Rx, Ry, and Rz components of the applied force were imported from an Arduino board, and the values were appended into three lists (one for each dimension). An algorithm has been written for calibration needs that takes the initial x, y, and z values without applying any pressure on the sensor and converts them to zero, so that the force applied is shown as none, which is the actual case. These initial values were then subtracted from every reading to use the real applied force. Once the calibration was done, a white scene with a black box representing the sensor as created, as shown in Fig. 4(b). An arrow was also produced that points to the direction of the applied force in 3-D. Moreover, the size of the arrow scales like the value of the force applied, i.e., for a small, applied force, the arrow appears small, and for a bigger applied force, it appears to be larger. Additionally, using spherical polar coordinates, as shown in Fig. 4(a), the total force magnitude, as well as the theta (θ, angle between the force vector and the normal to the sensor) and phi (ϕ, angle measured clockwise between the force vector and the North) angles have been calculated using Cartesian coordinates, as shown in the following equations [25]: Other than the force projection simulation explained above, the sensor signals can also be used to visualize normal forces in a high-resolution image. The sensor can detect only normal forces when interpolating the results using heatmap visualization. Commercial force-sensitive sensors have a single output, which means single pixel data. Multiple commercial sensors need to be used to form an image of pressure distribution. The proposed sensor can only form up to 64 × 64 pixel image using four analog channels from one sensor. The explanation to interpolate the results, as shown in Fig. 4(c), is as follows.
1) Three arrays have been created: one for each axis (x, y, and z). Each array consists of 50 random points between −30 and 30, representing the coordinate position. 2) A 2-D mesh grid has been created between the maximum and minimum x-y values (i.e., −30 and 30 in this case), using 1000 points. 3) For each coordinate value, (xi, yi, and zi), a Gaussian has been produced, which scales as the force in the z/downward direction, i.e., zi component. This means the Gaussian will appear higher for a larger force and shorter for a smaller force. 4) The following Gaussian equation has been used, where x is the x-component of the force, y is the y-component, z is the z-component, and w is the width of the Gaussian: 5) The width (w) of the Gaussian has been set to change according to the force in the xand y-components, as in the case of the Gaussian's height. 6) For each (xi, yi, and zi), a new figure has been created, so that the simulation updates as the loops iterate. 7) The heatmap's color bar also represents the strength of the downward force. Red corresponds to a large force, green corresponds to a gentle force, and blue corresponds to a weak force. 8) The resulting 3-D plot shows a fixed x-y mesh grid, where the Gaussian updates according to the x, y, and z forces imported from the sensor.

A. Device Performance Characteristics
Device performance characteristics were tested using a universal Mechanical test machine (Zwick Roel). The whole surface of the cell was covered with a rigid indentor and a known force was applied. The cell was supported at the bottom to a silicone slab to simulate the mechanics of plantar forces as the application of the human foot is striking the shoe elastomer and not the ground. Power supply was used at 5-V, 0.3-A dc connected to the bottom electrode of the device and TEKTRONIX 4 channel oscilloscope was used to measure the voltage change on the top electrodes through a voltage divider circuit. First, to find hysteresis, response, recovery, repeatability, and fatigue resistance of voltage change, a cyclic fatigue test was performed. A constant load of 10 N with 300-ms hold was applied for 100 cycles. Second, a creep test was prompted to find the voltage relaxation by holding a constant load of 20 N for 1 h. Third, the sensitivity of the tactile cell was found using a stepwise load test ranging from 1 to 80 N, with increments of 1 N per step. Finally, by supplying a constant current for 1 h, zero drift time was found. Table I summarizes the overall performance of the sensor cell. Fig. 5(a) illustrates the sensitivity of the sensor from the stepwise load test. The sensor appears linear in two regions, one between 0 and 200 kPa with ∼100 Pa/mV and another from 200 to 800 kPa with 375 Pa/mV. Consequently, the cell is almost four times more sensitive to low pressures than to higher pressures. Nevertheless, by tuning the calibration  algorithm in the simulation explained, the force range sensitivity makes the sensor suitable for plantar measurement. Although, the peak pressures of heavy-weight users could be a problem. The force range could be customized upon the task by altering the percentage infill of 3-D printing or the thickness of the substrate materials, which will be explained later. Fig. 5(b) and (c) shows the raw data from the cyclic fatigue test and creep load. It is observed that the bespoke parameters satisfy the needs of plantar measurements. Specifically, the fatigue test showed that for calibration, a "warm-up" of ten cycles must be loaded when the sensor is first connected to obtain repeatable results. It has been observed that after ten cycles, repeatability is within 4%. The deviation percentage of the signal form the 11th cycle to the last was used to derive the repeatability of the sensor. It is important for the sensor to supply repeatable results for a constant load. The creep test illustrates that sensor relaxation has 5% deviation in 30 min of continuous constant load. The PDMS spacer improves hysteresis, allowing the sensor to restore the open circuit when no load is applied. The zero drift time was tested by capturing data from the sensor continuously for 1 h without any load application. This was performed to test the deviation percentage of the signal when current passes through the device for long periods of time.
Another experimental setup was used to apply shear force in four directions to calibrate the relation between voltage and force applied in the planar plane (shear). The set-up consists of three axes linear controlled test rig with a 3-D printed indentor. Deflection of the indentor is measured using commercial implant strain gauges, which are highly sensitive and accurate. They were glued 60-mm away from the point of load application to measure the strain change, while the indentor was applying shear force on the sensor cell. The motion of the end-effector is controlled automatically, moving in each axis from one corner to the other, as shown in Fig. 6(a) and (b), from 0 to 10 mm. Therefore, the total deflection of the beam on the y-axis is 10 mm. Data collected from strain gauges and sensor cells were synchronized and analyzed for comparison. A strain gauges were used to measure the strain within the indentor along each direction and the applied shear force can be found using the formula simple elastic bending beams, where y is the deflection, M is the moment induced, E is the Young modulus, and I is the inertia Initially, the force was applied on the top surface of the cell acting on the z-axis, followed by shear force on the xand y-axes, as shown in Fig. 6(a) and (b). Fig. 6(c) depicts the force calculated using (9) from the data recorded from the strain gauge versus sensor data for the x-axis. The x-axis shear load results show that voltage changes in sensing elements V 1-V 3 are much more significant than V 2-V 4. Also, V 1 and V 3 are out of phase; by taking the difference between them, shear load data can be obtained. Data shown in Fig. 6(c) and (d) are synchronized with the strain gauge data and behaves almost identical. Similarly, the y-axis shear load results in Fig. 6(d) show the same behavior when a shear load is applied. By taking the difference of values in V 2-V 4, the shear load can be obtained from the sensor.

B. Data Visualization Validation Tests
To validate the accuracy of the force projection arrow from the simulation explained earlier, a rigid 2 DOF test rig was assembled carefully. To apply force at an angle, the test rig contains a hinge joint and a linear actuator, as shown in Fig. 7(a). The actuator is controlled with an Arduino, a driver board, and forward, reverse, stop switches. The sensor cell is attached to a rotating platform measured with an analog goniometer. The same tool was used to measure the angle of the hinge joint. Constant load is achieved at various angles, which made it suitable to validate the accuracy of the force projection found from the simulation. Constant load was applied at 10 • , 20 • , 30 • , and 40 • for θ angle and 90, 180, 270, and 360 for ϕ angle. Data were collected using an Arduino, which enables connection to the simulation in Python. Text files of force, angle θ, and ϕ were exported and 20 data points from each dataset were used to perform a one-way ANOVA test. By plotting the variance, the accuracy of the measurements is within a sensible range to deduct accurate reading for inverse kinetic calculations, as shown in Fig. 7(c) and (d). It was observed that the sensitive range of θ and ϕ is within ±45 • and ±180 • , respectively.
The accuracy of the heatmap simulation was validated by applying constant pressure using a 4-mm-diameter spherical indentor at various sensor locations starting from the center. The location of the load application is identical to the heatmap result, as shown in Fig. 8(a)-(f).

C. Scalability Experiments
Further experiments were conducted to explore printing modifications' efficacy for other applications requiring different pressure ranges. The conductivity of the 3-D printed substrate media can be modified to the desired pressure range sensitivity. There are two methods this can be done, first by changing substrate thickness and second by adjusting the percentage printing infill of the 3-D printer. By increasing the thickness of the substrate, the distance between active layers is increased, and due to the elastic properties of the substrate, higher compression forces are susceptible to the structure. Therefore, thicker substrates are sensitive to higher pressures and thinner substrates to lower pressures. In the following, the graphs show a stepwise load test from 0 to 120 N with increments of 4 N each step. Thicker substrates are less conducive since there is a more significant gap between active layers (copper), allowing a higher pressure measuring range. The saturation point is at 5 V, where saturation is the point when maximum strain is induced from high forces within the structure, causing resistance to decrease to the minimum. The sensor behaves as a closedcircuit, hence 5V in = 5V out . At 120 N, the 0.3-mm sensor reads a value at 2.5 V and the 0.7 mm at 1 V as observed in Fig. 9(a). Until saturation point, the 0.7-mm sensor will detect much higher pressures.
In addition, a high percentage of printing infill enables higher conductivity within the substrate, thus sensitive to lower forces, and alternatively, low infill is sensitive to lower forces. Fig. 9(b) shows two sensors with different printing infills injected with 12 V 0.3 A. It can be observed that lower infill has a decreased sensitivity to lower forces and can be sensitive to higher forces since the point of saturation is at 12 V. In contrast, the 100% infill saturates at 12 V when 120 N is applied to the sensor. The images of 100% and 80% printing infill taken from a Keyence VH-Z100R are shown in Fig. 9(c) and (d), respectively.

VII. CONCLUSION
This article has described the design and development of a low-profile planar sensor that can measure shear and normal load (pressure). The goal is to develop an instrumented shoe insole with an array of the sensors to measure ground reaction force and the foot's center of pressure. The desired sensor performance for such an application is within a pressure range of 0-740 kPa for normal forces, 0-140 kPa for shear forces, and sampling rate of 50 Hz during normal walking. As presented in this article, the sensor proposed is able to support the desired performance. While designed primarily for in-shoe application, the device could be used for measuring shear forces between any adjacent surfaces, where a small, lowprofile sensor is needed. This new sensor has many potential applications; in the healthcare sector, it could be integrated in wearables, prosthetics, surgical robot haptics, and artificial pressure-sensitive skins, such as data gloves. It could be used more widely in any industrial applications, such as in load cells of triaxial mechanical test machines or industrial assembly line robots for fine grasp control. A third sector which could benefit is sport industry, for example, collecting data from athletes to analyze their training performance especially in running and football. As mentioned in this article, alterations could be made to fit the requirements of each of these different applications. Overall, the device shows promising results with reliability although part to part reproducibility can be improved by using dual extrusion printing. Printing insulating and semiconductive materials at the same time you can achieve reproducible and complex designs. This method creates self-packaged devices, which will be used in future developments.