Design and characterisation of a piezoelectric knee-joint energy harvester with frequency up-conversion through magnetic plucking

Piezoelectric energy harvesting from human motion is challenging because of the low energy conversion efficiency at a low-frequency excitation. Previous studies by the present authors showed that mechanical plucking of a piezoelectric bimorph cantilever was able to provide frequency up-conversion from a few hertz to the resonance frequency of the cantilever, and that a piezoelectric knee-joint energy harvester (KEH) based on this mechanism was able to generate sufficient energy to power a wireless sensor node. However, the direct contact between the bimorph and the plectra leads to reduced longevity and considerable noise. To address these limitations, this paper introduces a magnetic plucking mechanism to replace the mechanical plucking in the KEH, where primary magnets (PM) actuated by knee-joint motion excite the bimorphs through a secondary magnet (SM) fixed on the bimorphs tip and so achieve frequency up-conversion. The key parameters of the new KEH that affect the energy output of a plucked bimorph were investigated. It was found that the bimorph plucked by a repulsive magnetic force produced a higher energy output than an attractive force. The energy output peaked at 32 PMs and increased with a decreasing gap between PM and SM as well as an increasing rotation speed of the PMs. Based on these investigations, a KEH with high energy output was prototyped, which featured 8 piezoelectric bimorphs plucked by 32 PMs through repulsive magnetic forces. The gap between PM and SM was set to 1.5 mm with a consideration on both the energy output and longevity of the bimorphs. When actuated by knee-joint motion of 0.9 Hz, the KEH produced an average power output of 5.8 mW with a life time >7.3 h (about 3.8 × 105 plucking excitations).


Introduction
Implantable and wearable body sensors with wireless communication abilities are increasingly widening their use for applications in athletics, medicine, emergency response and consumer entertainment [1]. These sensors-all of which require power sources-are currently powered by batteries, which have a limited energy storage capacity and thus a limited lifetime. With the batteries being a critical bottleneck for body sensors, wearable energy harvesting has been, in recent years, the subject of a scientific and technological effort worldwide [2], which harvests energy from human activities, such as kinetic and thermal energies, to provide sustainable power supplies for these sensors and so establish a fit-and-forget body sensor technology. Due to the high kinetic energy available in human activities, a significant effort has been devoted to converting kinetic energy into electric power by exploiting various mechanisms for operation, including electromagnetic [3,4], electrostatic [5,6] and piezoelectric [7,8]. Among these operation mechanisms, piezoelectric energy harvesting has attracted considerable interest due to its simple structure, self-contained power generation capability and high energy density [9,10].
The main challenge in piezoelectric wearable energy harvesting is the low frequency of human motion, which is usually much lower than the resonance frequency of a piezoelectric energy harvester (PEH). This frequency mismatch between the excitation and the harvester results in a low energy transduction efficiency. To address this challenge, one of the methods, frequency up-conversion strategy has been recently investigated, which uses low frequency vibrations from ambient environment to excite the resonance of a PEH at higher frequency. As a result, the PEH always vibrates at its resonance frequency, regardless of the input excitation. The most common approach to achieve frequency up-conversion is to induce an initial deflection in the PEH and then let it vibrate freely at its resonance frequency. The initial deflection can be induced by direct impact [11,12], mechanical plucking [13] or magnetic plucking [8,14,15].
In the previous work, frequency-up conversion based on mechanical plucking has been extensively studied by the present authors through finite element modelling [13] and experimental characterisation [16], which used plastic plectra to pluck piezoelectric bimorphs. This mechanism was successfully applied on a knee-joint energy harvester (KEH), which used knee-joint motions to generate the relative movement between the plectra and the bimorphs [17]. The KEH, which generated an average power of 3.5 mW when actuated at knee-joint motions of 0.9 Hz and terminated with an optimal load resistor of 80 kΩ, was able to power a custom-built wireless sensor node for a period of 46 ms period every 1.25 s after an initial charging time of 28.4 s [18]. The KEH could, therefore, be used to power wireless sensors to sense and transmit data at low sampling frequencies. However, limitations were also observed on the KEH: the direct contact during the mechanical plucking decreased the longevity of the piezoelectric bimorph and plectra, and produced considerable noise. This paper will address these limitations by replacing the mechanical plucking with a non-contact magnetic plucking since the direct contact between the piezoelectric bimorph and the plectra can be avoided.
Frequency up-conversion through non-contact magnetic plucking has been previously reported in several studies for different applications. For example, Pillatsch et al [15] developed a simulation model to study the dynamic performance of a piezoelectric beam subject to non-contact magnetic plucking, and later proposed a miniaturised energy harvester for human body applications, where the human body movements actuated an eccentric proof mass to oscillate and a magnet on the proof mass plucked a piezoelectric bimorph through a magnetic force [8]. Tang et al [19] used a nonlinear oscillator carrying a driving magnet and actuated by inertial force to bend a pair of piezoelectric micro-cantilevers through a magnetic force. Both devices generated power output in the range of tens of microwatts. The application of inertial force in both devices to actuate the magnets ensured a simple device structure; however, it was also found that with input excitations being at low accelerations and low frequencies, the driving magnet might get stuck and does not pluck the piezoelectric element effectively. Luong et al [14] used a magnetic force to excite a piezocomposite generating element in a small-scale windmill, which generated an average power output up to 2 mW. However, the power density was much smaller than that in many other windmills using electromagnetic generators.
This work introduces non-contact magnetic plucking for wearable knee-joint energy harvesting application to achieve high electric power output, long life time and low noise level. The KEH features an optimised number of primary magnets (PMs) positioned on an outer ring, which is actuated by the direct force from knee-joint motion to rotate relatively to a central hub with eight piezoelectric bimorphs fixed. Compared with the literature [15,19], the use of an optimised number of PMs can fully exploit the potential of magnetic plucking, thus increasing the power output, while the direct force excitation avoids the stucking of the PMs, which might happen with inertial force excitation. This paper first investigates effects of the design parameters on the energy output of a bimorph subject to magnetic plucking and then reports the performance of a prototyped piezoelectric KEH with optimised parameters. Based on the design parameters study and analysis, the KEH with 8 piezoelectric bimorphs generates an average power as high as 5.8 mW (0.7 mW per bimorph) when actuated by knee-joint motion at 0.9 Hz. The KEH has operated continuously for 7.3 h without any sign of performance decreasing.

Description of the piezoelectric KEH
A schematic of the KEH based on magnetic plucking is shown in figure 1. PMs, which are referred to as PMs here, are equally positioned along the inner side of the outer ring. Eight piezoelectric bimorphs are mounted in the inner hub to form cantilevers, the free ends of which are glued with a secondary magnet (SM). For the knee-joint wearable application, the inner hub is fixed to the shank, whistle the outer ring is fixed to the thigh. During walking, the thigh and the shank rotate around the knee joint, causing the inner hub and the outer ring to rotate relatively to each other. As a result, the PMs pass by the SMs and pluck the bimorphs through the magnetic forces. Figure 2 illustrates the magnetic plucking action when the interactive force between the PM and SM is repulsive by use of one pair of PM and SM. It should be known that the interactive force between the PM and SM can be attractive. As the PM approaches the SM, the bimorph is deflected from its origin up to a limiting position R 1 and then jumps across the approaching PM onto the other side of the origin, reaching R 2 . Following that, the bimorph vibrates freely at its resonance frequency. By using this mechanism, the low frequency rotation of the knee-joint motion is converted to the resonant vibration (high frequency) of the piezoelectric bimorphs, thus achieving high power generation.
The magnetic forces experienced by a SM on a bimorph are illustrated in figure 3, where, for simplification, two PMs and one SM are used to analyse the magnetic plucking force acted on the bimorph, and the situation that PM 1 passes by the SM and PM 2 is away from the SM is considered. PM 1 and PM 2 apply a repulsive magnetic force, F 1 and F 2 to the SM, respectively. The direction of the forces can be changed to be attractive by altering the polarisation direction of the magnets. Each magnet can be regarded as a magnetic dipole, and the magnetic forces between the PMs and SM can be expressed as [20] where the subscript i=1 and 2; q SM and q PM are the magnitudes of magnetic poles; m is the permeability and approximately equal to 1 in air; d i is the gap between the SM and the corresponding PM, and has a minimum value of d. The xand yaxis components of the magnetic forces can be written by exploring the trigonometric relationship as ( ) d ix and d iy are the components of d i in xand y-axis, respectively. When the bimorph tip deflection is much smaller than the bimorph length, as is the case herein, the resultant force in the y-axis F y (magnetic compressive force) compresses the bimorph, and thus induces a compressive stress in the bimorph The resultant force in the x-axis (magnetic plucking force) plucks the bimorph to generate energy output and therefore is of interest in this study. Because F x 1 and F x 2 always opposes each, the plucking force takes the form of Equation (2) suggests that F ix is related to the PM/SM gap, and diminishes to zero when the gap is large enough. Therefore, when the number of the PMs positioned on the outer ring is small, i.e. the distance between PM 1 and PM 2 is  (a) Illustration of the magnetic plucking action when the magnetic force between the PM and SM is repulsive: as the PM rotates from P 0 to P 1 and then P 2 , the bimorph moves from R 0 to R 1 and then R 2 ; (b) the bimorph tip displacement during magnetic plucking. large, the bimorph only experiences F x 1 and F x 2 is negligible. In the extreme case, it represents only one PM installed in the outer ring, which will be studied in sections 3.2.1-3.2.3. When the number of the PMs positioned on the outer ring is large, i.e. the distance between the PM 1 and PM 2 is small, F x 2 cannot be neglected and it reduces the total plucking force, as suggested by equation (4). Therefore, the plucking force is affected by the PM/SM gap and the number of PMs, and so is the energy output of the bimorph. The effects of both parameters on the energy output will be studied experimentally in section 3 to maximise energy output.

Experimental setups and methods
In order to investigate the energy output by a one-off magnetic plucking force and by a continuous magnetic plucking force, two setups were used in the different configurations of the design evaluation, as shown in figure 4. In In both setups, a 3×3×3 mm 3 magnet (F316-N35, Magnet Exert Ltd, Tuxford, UK) was glued to the tip of a PZT-5H bimorph (T215-H4-303X, dimension 38.1×12.7×0.38 mm 3 , Piezo Systems INC. Woburn, US) and served as a SM. The bimorph was mounted with a free length of 26 mm in the inner hub, which was held steady by a bracket. The outer ring, where the PMs (the same as SMs) were fixed, was actuated by a stepping motor to rotate at an adjustable speed. Furthermore, the PZT-5H bimorph was terminated with a load resistor R , m which was chosen at maximising the energy output. The outer ring was actuated to rotate for a full revolution with an angular velocity, w, ranging from 0.1 to 2 revolutions per second (rev s −1 ), which is the variation range of the angular velocity of the knee-joint during normal gaits [16]. The voltage V t ( ) across R m was measured by a NI 9229 data acquisition card (National Instruments, Newbury, UK) to calculate the energy output by equation (5), whereas the displacement at the bimorph tip was monitored by a laser Doppler vibrometer (CLV-2534, Polytec Ltd, Harpenden Hertfordshire, UK).
where Dt is the sampling interval.

Results and discussions
The results in section 3.2.1-3.2.3 were obtained from the setup, shown in figure 3(a), whereas the results presented in section 3.2.4 were measured on the setup, shown in figure 3(b).

Effects of repelling and attracting configurations on
energy output. Initial tests found that the energy output of both repelling and attracting configurations was maximised at R m =40 kΩ. Therefore, this load resistor was used for the design evaluations. Figure 5 shows the bimorph tip displacement (a), velocity (b), voltage (c), and energy output (d) of the bimorph in both repelling and attracting configurations at ω=2 rev s −1 with d=1 mm.
In the repelling configuration, from the beginning to R 1 , the bimorph was deflected away from its origin position by the repelling plucking force from the approaching PM ( figure 5(a)). The deflection of the bimorph reached a limit of −0.8 mm at R 1 , where the bimorph started to snap through to the opposite side of the origin because of the elastic force developed in the bimorph. After R 2 , the bimorph oscillated around its equilibrium position at its resonance frequency. It is noted that the equilibrium position of the bimorph was shifted upward by the repelling magnetic force, as indicated in figure 5(a), and returned back to the origin as the PM moved away.
During snapping through from R 1 to R 2 and with a maximum displacement of 1.6 mm, the repelling configuration generated a voltage up to 60 V ( figure 5(c)) and an energy output of 0.2 mJ ( figure 5(d)), which accounts for 56% of the total energy generated (0.36 mJ). The resonant vibration stage (R 2 onwards) produced an energy output of 0.14 mJ, accounting for 39% of the total energy generated.
In the attracting configuration, the bimorph moved towards the PM because of the attracting plucking force from the approaching PM. Then, from A 1 to A 2 , the bimorph stayed together and oscillated around the travelling PM. At A 2 , the bimorph was released to resonant vibration around its origin position and with decaying amplitude.
During the combined travel stage (A 1 -A 2 ) and with a maximum displacement of 1.6 mm, the attracting configuration generated a voltage up to 20 V and an energy output of 0.028 mJ, accounting for 28% of the total energy produced (0.1 mJ). The energy produced in the free vibration stage (A 2 onwards) was 0.062 mJ, accounting for 62% of the total energy produced.
The results suggest that both repelling and attracting configurations are able to provide frequency up-conversion to the resonance frequency of the bimorph. However, the repelling configuration produced 3.6 times more energy output than the attracting configuration, even though the maximum displacement with both configurations was about the same (1.6 mm). This can be explained by the higher vibration velocity of the bimorph in the repelling configuration caused by the snapping-through stage. A higher vibration velocity leads to a higher strain rate and consequently a higher generated current in the bimorph, since the generated current is analogous to the strain rate [21]. Because the repelling configuration is more efficient in energy generation, it was used for the rest of the studies in this paper.

3.2.2.
Effects of the gap between the PM and the SM on the energy output. Figure 6 compares the performance of the repelling configuration with different values of d. As d increases, decreases are observed in the bimorph displacement, velocity, voltage and energy output. This is mainly because with an increasing d, the plucking force decreases as indicated by equation (5). The decreasing plucking force first of all resulted in a smaller initial deflection and a more gradual release of the bimorph at R 1 . With d=3 mm and displacement being too small at R 2 , there was no resonant oscillation at all. Although the energy output increases with a decreasing d, it should be noted that a higher    energy output is obtained at a higher displacement and thus a higher stress level, which might decrease the longevity of the bimorph, considering the low strength of the piezoelectric materials. The value of d used for the KEH will be determined by taking account of the longevity and will be discussed in section 4.

3.2.3.
Effects of rotation speed ω on energy output. An increase in the energy output is observed with the rotation speed, as shown in figure 7. The energy output increases from 0.08 to 0.42 mJ as the rotation speed increases from 0.2 to 2 rev s −1 . Figure 8 compares the performance of the repelling configuration with ω=0.5, 1 and 2 rev s −1 .
With the three rotation speeds compared in figure 8, the three stages associated with the repelling configuration, described in section 2, can be clearly identified: (1) a deflection stage to R 1 when PM is approaching SM, (2) a snapping-through stage from R 1 to R 2 , and (3) a free vibration stage from R 2 onwards; and in each stage, a higher rotation speed generated a higher energy output. In the deflection stage, the higher energy output can be simply explained by the higher displacement amplitude at R 1 . Although the displacement at R 2 with different w is about the same, this displacement was achieved in a shorter time when w is higher, i.e. the vibration velocity is higher. Consequently, a higher voltage and energy output was produced in the snappingthrough stage with a higher w. It is noticeable that even though the bimorph was released from about the same position (1.6 mm) at R 2 , a higher w still generated a higher energy output in the resonant vibration stage (0.03, 0.08 and 0.14 mJ corresponding to ω=0.5, 1 and 2 rev s −1 , respectively). With a higher w the PM travelled away from the bimorph more quickly, consequently allowing the bimorph to have more time for free vibration at the resonance frequency as little or no magnetic plucking force was acted on the bimorph; and therefore, higher vibration velocity and voltage output were observed.

Effects of the number of PMs on the energy output.
The total energy outputs of the bimorph with different number of PMs, N, are presented in figure 9(a), where the outer ring was actuated to rotate for a full revolution at different speeds. At each rotation speed, the total energy output increases and then decreases with N, with a maximum value at N=32. With each N, a higher energy output is always observed at a higher rotation speed, which agrees with the results in section 3.2.3.
By dividing the total energy output via the corresponding N, the energy output per PM, E PPM can be calculated, shown in figure 9(b), which describes the average energy output of one magnetic plucking, or in other words, the efficiency of energy conversion. With N=1, 4 and 8, E PPM stays constant for all the rotation speeds. Following that, E PPM decreases with N, that is, the efficiency of the energy conversion from mechanical to electric energy decreases with N. With N=16 and 32, the decrease in E PPM is slow, and hence the total energy output still increases with N. With N=64, a sharp decrease in E PPM is observed and consequently, the total energy output decreases significantly.
To investigate the reason behind the dependence of the energy output on N, the displacement and voltage of the bimorph in the first 0.2 s of a full revolution (0.5 s at ω=2 rev s −1 ) are presented in figure 10. With = N 4 and 8, the aforementioned three stages during one magnetic excitation can be clearly identified: a deflection stage (R 1 ) followed by a snapping-through stage (R 1 -R 2 ) and then a resonant vibration stage (R 2 onward). The resonant vibration of the bimorph had fully rung down before a subsequent approaching PM deflected the bimorph again. Therefore, the subsequent PM did not affect the vibration and thus the voltage induced by the previous PM. Consequently, E PPM is the same with = N 4 and 8, as shown figure 9(b). The variations in the initial deflection are caused by the small difference in the positions of the PMs, which lead to variations in PM/SM gap. With = N 16 and 32, the subsequent PM started to deflect the bimorph before the resonant vibration induced by the previous PM had fully rung down, and as a result, the superposition of the oscillation onto the deflection is observed. Because the bimorph had more time to vibrate at resonance with N=16 than N=32, it produced a higher E PPM with N=16. Although the bimorph did not finish the resonant vibration stage, the snapping-through stage was not affected by the subsequent PM, during which the bimorph generated 56% of the energy output as discussed in section 3.2.1; therefore, the decrease in E PPM with N is slow ( figure 9(b)) and the total energy output still increases with N. It is also noted that by increasing N from 1 to 32, the initial deflection remained at about the same level, suggesting that the plucking force keeps constant with these numbers of PMs. With = N 64, a significant drop in displacement was observed in both the initial deflection and snapping-through stages, and there was hardly any resonant vibration. This is because with the distance between the PMs being too small, the plucking force was reduced as discussed in section 2, and also the subsequent PM started to deflect the bimorph even when the latter was still in its snapping-through stage. Because of the low vibration amplitude, the bimorph generated very low voltage, and consequently low E .
PPM The sharp drop in E PPM leads to a significant decrease in the total energy output.
In light of the results, it can be concluded that to maintain the optimal energy conversion efficiency of the bimorph, the maximum number of PMs is 8. However, the energy output with N=8 is not the highest. To get the highest energy output, 32 PMs should be used, although the energy conversion is optimal.

Prototype and characterisation methods
Based on the above evaluation results, a KEH based on magnetic plucking has been prototyped as shown in figure 11. The same 8 piezoelectric bimorphs with a SM glued at the tip of each were mounted in the inner hub, which was held static by a bracket. 32 PMs were equally positioned and fixed on the outer ring, since with this number of the PMs, the bimorph was found to produce the highest energy output although the conversion efficiency per PM was not optimal. The polarisation directions of the magnets were arranged to form a repelling configuration, as it generated a higher energy output than the attracting counterpart. The PM/SM gap between can be adjusted between 1 and 2.5 mm by varying the clamping length of the bimorphs.
The prototype was mounted on a stepping motor, which actuated the outer ring to reproduce the knee-joint motion taken from [17] and presented in figure 12. The knee-joint motion was measured from a human subject during normal walking by a marker-based motion capture system. The angle between the thigh and the shank covers up to 57°during one gait cycle, and the cycle takes 1.1 s, corresponding to a walking frequency of 0.9 Hz.
The characterisation was performed with two steps. In the first step, only one piezoelectric bimorph was installed in the inner hub. The output of the bimorph was connected to a 40 kΩ resistor. This step was performed to examine the dynamic responses of the bimorph and determine a suitable distance d based on the longevity of the bimorph. In the second step, 8 bimorphs were installed, the outputs of which were connected to 8 full-wave rectifiers. The DC outputs from the rectifiers were individually connected in parallel and then terminated with a load resistor. In both steps, the voltage generated across the load resistor was measured by the NI 9229 data acquisition card to calculate the energy output.

Characterisation results and discussion
4.2.1. Energy output of the KEH with one bimorph. Initially, the gap d was set to 1 mm. The KEH generated 2.42±0.4 mJ in one step, corresponding to an average power of 2.2±0.36 mW. However, a crack was developed at the root of the bimorph after operating the KEH continuously for 0.5 h, resulting in a sharp drop of the average power to 0.5 mW. With d=1.5 mm, the KEH generated an energy output of 0.8±0.22 mJ in one step, corresponding to an average power of 0.72±0.2 mW. In this case, the KEH has been able to be operated continuously for 7.3 h (about 2.4×10 4 gait cycles) without any signs of performance decreasing. Therefore, d=1.5 mm was chosen for the KEH, and the responses of the bimorph in one gait cycle are presented in figure 13.
The knee-joint angle is plotted in each figure. Four bursts of displacement peaks (highlighted by dashed circles) are observed in figure 13(a). They all occurred at the time when large knee angles were covered in a short time, i.e. the rotation speed of the outer ring was high. Figure 13(b) shows the details of the tip displacement in the third burst of peaks. The three stages aforementioned can be clearly identified in each excitation cycle with superimposition of the oscillation onto the deflection, which is similar to what has been discussed in 3.2.4 with N=32. Between these bursts of peaks, the outer ring was reversing the rotation directions at low speed, and the bimorph was not effectively deflected by the PM. Four bursts of voltage peaks are observed in figure 13(c), which corresponds to the locations of the displacement peaks. Whenever there is a burst of voltage peaks, a jump in the energy output occurs, as shown in figure 13(d). In one step (1.1 s), the bimorph generated an energy output of 0.59 mJ, corresponding to an average power output of 0.53 mW.
It is worthwhile pointing out that with d=1.5 mm, the bimorph worked at a much higher displacement (about ±0.9-1 mm) than the rated one (±0.51 mm) provided by the supplier. With a displacement of 0.9-1 mm, the maximum bending stress in the piezoelectric material is about 50-56 MPa, calculated by equation (6) [23]. In the case of the KEH, the bimorph experienced 16 plucks in one gait cycle and therefore in the total 2.4×10 4 gait cycles of the longevity test, it was plucked by 3.8×10 5 times without any signs of performance decreasing, which suggests a life time higher than the theoretical value of 10 5 cycles. This may be because the magnetic compressive force (described in section 2) induced an additional compressive stress in the bimorph, which was superimposed to the bending stress. The additional compressive stress decreased the tensile stress and increased the compressive stress in the bending operation. Because the compressive strength of PZT (>517 MPa) is much higher than its tensile strength (∼75.8 MPa) [24], the reduction in tensile stress increased the life time of the bimorphs.

4.2.2.
Energy and power output of the KEH with 8 bimorphs. Figure 14 shows the average output of the KEH across different load resistance with 8 bimorphs installed. At the optimal load resistance of 15 kΩ, the EH generated an average power output of 5.8 mW.
The total voltage and energy output with the optimal load resistance (15 kΩ) are presented in figure 15. The voltage measured across the load resistor is unipolar because of the presence of the rectifiers. Four bursts of voltage peaks are observed, which occurred when the knee-joint rotation speed was high, as discussed in section 4.3.1. At each burst of voltage peaks, a sharp increase in the energy output was observed. In one gait cycle, the EH generated an energy output of 6.4 mJ, corresponding to an average power of 5.8 mW.

Conclusions
A piezoelectric KEH was designed and characterised in this paper, which used non-contact magnetic plucking to achieve frequency up-conversion. The magnetic forces between permanent magnets deflected the piezoelectric bimorphs, which were then released to resonant vibration and thus generated a high energy output. The parameters that affected the energy output of a magnetically plucked piezoelectric bimorph were investigated. While both repelling and attracting configurations were able to provide frequency up-conversion to the resonance frequency of the bimorph, the repelling configuration generated 3.6 times higher energy output than the attracting configuration because of the presence of a snapping-through stage, and therefore was used for the KEH. Reducing the gap between the primary and SMs was found to increase the energy output because of the increasing magnetic plucking force. However, the higher energy output was achieved at a higher stress in the piezoelectric material, which could decrease the longevity of the bimorph. There is certainly a trade-off between the energy output and the life time. The energy output can also be increased by increasing the rotation speed of the PMs. This is partly because at a higher rotation speed, the PM caused a higher initial deflection in the bimorph, and also because the PM moved away from the bimorph more quickly and thus allowing the bimorph to have more time for free vibration at the resonant frequency. The bimorph generated the maximum energy output when 32 PMs were positioned in the outer ring, even though the energy conversion efficiency per PM was not optimal.
A KEH with 8 piezoelectric bimorphs and 32 PMs was prototyped and characterised. With a gap of 1.5 mm between the primary and SMs, the KEH, actuated at knee-joint motion of 0.9 Hz, was able to generate an average power output of 5.8 mW for more than 7.3 h (about 3.85×10 5 plucks) without any signs of performance decreasing possibly due to the compressive stress introduced by the magnetic force. With this magnitude of power level and longevity, the KEH can be used to power body sensors for real applications. Further practical work will develop a wearable prototype with ergonomic design and test its capability to power wireless sensors.