Capacitance characteristics of the 10 mm square sensor
In the X direction (Figure ), the shape could be divided into three types, named convex, increasing, and decreasing types. The convex type had the maximum value at X = 0 mm and was observed in the characteristics of FEC and OEC (AD’, BC’, CB’, DA’). The increasing type increased with increasing X and was observed in the characteristics of OEC (AB’, DC’) and DEC (AC’, DB’). The decreasing type decreased with increasing X and was observed in the characteristics of OEC (BA’, CD’) and DEC (BD’, CA’). The difference of capacitance value in the same type was derived from the difference of initial distance in the combination of upper and lower electrodes. In the point of X = −0.2 mm of FEC (AA’, BB’) (arrow in Figure ), the corrected value was temporarily diminished by a shift of the maximum value to the negative domain. The shift arose from the position gap between silicone gel and the substrate in the process of assembling the sensor.
In the Y direction (Figure ), the types of shape were the same as those in the X direction. The convex type had the maximum value at Y = 0 mm and was observed in the characteristics of FEC and OEC (AB’, BA’, CD’, DC’). The increasing type increased with increasing Y and was observed in the characteristics of OEC (AD’, BC’) and DEC (AC’, BD’). The decreasing type decreased with increasing Y and was observed in the characteristics of OEC (CB’, DA’) and DEC (CA’, DB’). The shape and amount of capacitance in the Y direction (Figure ) were similar to the shape and amount in the X direction (Figure ). The line capacitance which occurred in upper and lower electrode lines was involved in the measured capacitance. The line capacitance in the Y direction was different from the line capacitance in the X direction because the electrode substrate had a different pattern for each axis (Figure ). When displacement Y was applied to the sensor, the line capacitance between the electrode lines corresponding to the combination of upper and lower electrodes varied according to the amount of the displacement Y. At the arrows in Figure , there was a temporary increase in the corrected capacitances for the effect of the line capacitance between the electrode lines. In BD’, the lower electrode and line D’ moved toward the upper electrode and line B with increasing Y. When the distance between lines B and D’ is least in varied Y, the line capacitance has a maximum value.
In the Z direction (Figure ), the capacitances of all combinations of upper and lower electrodes increased exponentially with increasing Z because of the decreasing of d. The corrected value was nearly identical to the theoretical value.
In the ΘZ direction (Figure ), the shape could be divided into four types, named convex, concave, increasing, and decreasing types. The convex and concave types had maximum and minimum values at ΘZ = 0 degrees and were observed in the characteristics of FEC and DEC. The increasing type increased with increasing ΘZ and was observed in the characteristics of OEC (AD’, BA’, CB’, DC’). The decreasing type decreased with increasing ΘZ and was observed in the characteristics of OEC (AB’, BC’, CD’, DA’). The amount of d change generated by the varied ΘZ was the smallest in the amounts of d change generated by all varied displacement components. The combinations of FEC only had an overlap area of paired electrodes. Proximity of paired electrodes occurred in other combinations that had no overlap area of paired electrodes. In the methods for calculation of displacement and the calculation of theoretical capacitance, upper and lower electrodes were assumed to be parallel plate type in distance between center points of the paired electrodes. Therefore, measured value contains small error derived from the supposition. And, main factor causing change of capacitance was the occurrence of overlap area and proximity of paired electrodes. In addition, the overlapping effect of the paired electrode line arose at a small yaw angle in all combinations without FEC. For example, an overlapping effect occurred at yaw angle of approximately 7 degree in AD’. The electrode lines of the 10 mm square sensor were connected in ground G, D (D’), C (C’), B (B’), and A (A’) from the left side. The occurrence of proximity of paired electrodes and overlapping of the paired line was divided into the following four patterns.
(i) Proximity of upper and lower electrodes and proximity of upper and lower electrode lines.
(ii) Proximity of upper and lower electrodes and withdrawal of upper and lower electrode lines.
(iii) Withdrawal of upper and lower electrodes and proximity of upper and lower electrode lines.
(iv) Withdrawal of upper and lower electrodes and withdrawal of upper and lower electrode lines.
Figure shows an example in FEC(AA’), OEC(AB’), DEC(AC’) and OEC (AD’). The lower substrate moved with varying yaw angle in the same measurement condition. The behaviors in positive/negative domains of ΘZ were applicable to (iv)/(iv) in AA’, (iii)/(ii) in AB’, (i)/(ii) in AC’ and (i)/(iv) in AD’. All combinations of paired electrodes coincided with any pattern. Therefore, by the overlapping effect, the measured curve of capacitance had a different tendency than that of the theoretical curve. The measured capacitance was corrected by linear approximation for adjustment of gain and offset. The corrected points in varied X, Y and ΘZ were three points in positive and negative domains, respectively. The amount of line capacitance in each region of displacement is different because of difference in displacement points of maximum line capacitance.
Movement of paired electrodes and lines (10 mm square sensor). A. FEC (AA’). B. OEC (AB’) C. DEC (AC’). D. OEC (AD’).
An overlapping effect of lines occurred in the Y and ΘZ directions. It was thought that capacitance varied in the paired line and the shielded cables connecting the line and LCR meter. Thus, it is important to prevent line capacitance such as the back side ground of the substrate and the shielding of paired electrode lines.
When the measured value includes a nonlinear error, it is necessary for the estimation of displacements in arbitrary points to understand the relation between the displacement and the measured capacitance including the error. In this study, displacements were calculated by the equations of a sphere. However, it is difficult to estimate displacements of arbitrary points by this calculation method because the amount of correction has to be determined for obtaining appropriate capacitance in advance. We have therefore developed an iterative calculation method that can be used to estimate displacements of arbitrary points in the allowable range of the sensor because the relation of capacitance and displacements in arbitrary points without calibration points was interpolated using measured input–output characteristics. Each displacement is estimated in series within 25 steps of iteration.
Calculation of force and torque components of the 10 mm square sensor
The standard force measured by a universal tester and the measured value was converted in E = 25.7 kPa. The standard force was approximately 1.5 N in the condition of Z = 3 mm. E was obtained in a test of silicone gel (“Methods, Sensor design and fabrication”) and it was calculated in the strain of 20%. The calculated normal force FZ in the same condition was also about 1.5 N (Figure ). Therefore, it was thought that the calculated force was appropriate. The FS error was calculated from the absolute error between estimated and theoretical values of force and torque components. FS of force/torque is shown in Table . FS error in Figure was the maximum value in force and torque components of each varied displacement. The range of maximum FS errors was 0.4-10.1%. The FS error increased at the measured point affected by the position gap between the substrates and the overlapping of lines corresponding to the paired electrodes. The error ratios in the force and torque calculation were equal to those in the displacement calculation because the force and torque are proportional to the strain as shown in the section “Sensor theory, Calculation of force and torque components”. In this result, standard normal force was converted in a constant elastic modulus. Actually, however, normal force varies with increasing displacement Z in a nonlinear fashion for change in stiffness. An iterative calculation method for estimation of force enables estimation of force that has a nonlinear characteristic in a manner similar to the iterative calculation method of displacements.
Calculation of force and torque components of the 20 mm square sensor
A new sensor of different size (cross sectional area of 20 mm square) was developed and the capacitance was measured in four DOF displacements. As shown in Figure , we improved the electrode pattern and grounding means of electrode lines in consideration of the overlapping effect in the results obtained for the 10 mm square sensor. The upper and lower electrode lines in the 20 mm square sensor were not facing each other, and the electrode line connected to the ground area was placed in the middle. The electrode lines were connected in D (D’), C (C’), ground G, B (B’), and A (A’) from the left side. The electrode lines were shrouded in pressure-sensitive adhesive tape for electrical insulation (Kempton tape, P-221, Permacel) and a stainless plate connected to ground was located between the upper and lower electrode lines. Figure shows the overlapping effects of AA’ and AD’ in the 10 and 20 mm square sensors. The horizontal axis is the varied yaw angle and the vertical axis is the capacitance change that is differential value at the value of ΘZ = 0 degree. Gaps of peaks in AA’ were derived from the position gap of the upper and lower substrates in the process of the assembling the sensor. In AD’ of the 10 mm square sensor, the capacitance curve in the positive domain of yaw angle was decreased compared to the theoretical value for withdrawal of electrode lines A and D’. The overlapping condition of the lines occurred in approximately 3 degree. In AD’ of the 20 mm square sensor, the line effect was diminished by the improvement. The displacements and forces were calculated in the same way as that for the 10 mm square sensor.
Overlapping effect of paired electrode line in capacitance characteristics.A. AA’ of the 10 mm square sensor. B. AD’ of the 10 mm square sensor. C. AA’ of the 20 mm square sensor. D. AD’ of the 20 mm square sensor.
In estimation in force/torque of four DOF, as shown in Table , maximum FS errors through 625 measured points were 4.1%, 6.3%, 14.1% and 16.4% in X, Y, Z and ΘZ, and average errors were 1.1%, 1.8%, 1.8% and 3.9%. Although the overlapping effect of line capacitance was remedied by improvement of the electrode pattern and grounding means of electrode lines, position gap of upper and lower electrodes occured. Most of the calculated normal forces in the condition of Z = 2 mm were approximately 8.6 N. The standard normal force that was converted in E = 54.1 kPa was 9.4 N in the condition of Z = 2 mm. E was newly measured using silicone gel of 20 mm×20 mm×5 mm and it was calculated in the strain of 25% of silicone gel. In the 20 mm square sensor, stiffness of the silicone gel was greater than that in the 10 mm square sensor. Therefore, the range of detection of yaw angle in the 20 mm square sensor was narrower than that in the 10 mm square sensor. In real measurements for subjects, motion of subjects at high risk for pressure ulcers is decreased by restraint of spontaneous movement. Thus, it is considered that the yaw angle range of the 20 mm square sensor was sufficient to measure rotation applied to skin. Table shows examples in Table . We considered the accuracy to be within an acceptable range.
Sensor configuration and materials for real measurement
The sensor deforms along skin surface of the subject because of flexibility of upper and lower substrates. To prevent the deformation of upper and lower substrates, thin and stiff plates are affixed on the substrates for homogenization of applied force. If one substrate is tilted to the other substrate, the measured value includes the effects of pitch and roll torques. In this situation, upper and lower electrodes are assumed to be parallel plate type in distance between center points of the paired electrodes in the method for calculation of displacement. The developed sensor enables detection of torque components TX and TY. However, because the developed sensor does not have the ability for detection of pitch and roll torques, the measurement in the situation should be avoided. Therefore, it is important to arrange an appropriate surface on a bony prominence and to confine motion of the subject during measurement.
Appropriate selection of materials is important for mitigation of error generated by different materials and consideration for the subject [9
]. The creep of silicone gel was tested to select an appropriate material for measurement of force applied to the skin surface. The selection of silicone gel was determined on the basis of appropriate E
. Double-sided tape was selected on the basis of flatness, thin thickness and adhesion strength. The thickness of the double-sided tape was 0.085 mm. The adhesion strength was good when shear displacements and yaw angle were applied to the sensor. In fact, the developed sensor is different from the theoretical condition for a stacked material (silicone gel, double-sided tape and flexible substrate). We considered that the change in structural stiffness by double-sided tape and substrate is small because these materials were thin. However, the capacitance is affected according to the change in thickness of double-sided tape. And, the developed sensor is covered by a protective material such as a polyurethane film after thin and stiff plates are established in upper and lower substrates. An appropriate protective material needs to have the ability of flexibility for detection of yaw angle. The protection may have an undesirable influence on the detection range of detection of displacements.
An error may be observed by motion artifact during measurement for one condition. It is possible to diminish the effect by averaging of several measured points in the same condition. The signal processing circuit for real measurement is still in the trial phase. Time constant and delay in measurement are determined by the circuit and developed sensor. In the displacement estimation method under development, the number of iterations in a calculation for one condition was 25. It is considered to be a sufficiently short time. However, if several measured points in the same condition are measured for decreasing the effect of motion artifact, the time for total measurement is extended. In real measurement, the sensor is arranged on mattress before the subject take target body position. Then, force/torque is measured in appropriate surface on bony prominence. A sequence of actions may be a heavy work for the subject. And, nonrestraint during measurement is desirable for the subject as indicated by [15
]. However, the motion of the subject is limited during measurement in our sensor.