The pizzicato knee-joint energy harvester: characterization with biomechanical data and the effect of backpack load

The knee-joint piezoelectric energy harvester is fixed to the outside of the knee by braces (figure 1). As the wearer walks, the inner hub and the outer ring rotate relatively to each other with reciprocating motion, so that the four bimorphs (mounted on the hub) are forced to pass in front of the plectra (embedded in the outer ring). In this way, the plectra pluck the four bimorphs. The prototype of the EH (figure 2) was realized based on this design. For testing, the prototype was mounted on a knee-joint simulator (figure 2), which uses a stepper motor to reproduce the kinematics of the knee-joint of a human subject. The main advantage of testing the device on a simulator rather than directly on a human subject is the reproducibility of the tests as the motor will accurately reproduce the recorded gait at every run whereas the real gait cycle changes slightly from one step to the next. This reproducibility is important as it allowed us to carry out statistical analysis and isolate the contribution of the harvester alone. The electrical outputs produced by the bimorphs were rectified, dissipated across resistors, and the corresponding voltage drops were recorded. Data reported in this paper were taken during 18 experimental runs, where each load-specific gait cycle (0, 12 and 24 kg, as specified later) was run three times for each direction of motion. Reversing the direction of motion means mounting the device on the other leg or, alternatively, swapping the links to thigh and shank. This is relevant because the objective of the plectra's design was to increase energy production (and resistance to motion) during the swing extension phase of gait and minimize it during the stance phase, making it asymmetric. The asymmetry is beneficial as the muscles of the leg perform negative work during the swing extension phase [3]: the device would harvest energy which otherwise must be dissipated by the muscles.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The EH features four bimorphs mounted on the inner hub and 74 active plectra mounted on the outer ring. The piezoelectric bimorphs, referred to as B1 to B4 in this paper, are of type T215-H4-303X and produced by Piezo Systems Co.; more details are found in figure 1(b). The main selection criteria for the bimorph were commercial availability and appropriate dimensions to give a combination of compact size and good energy output.The bimorphs were mounted within copper-clad mechanical fixtures doubling up as pick-off electrodes. The plectra were cut out of a 125 μm-thick Kapton^® polyimide film. The typical distance between plectra is 3.5 ± 0.5 mm, although there are two gaps of about 8–9 mm along the circumference, due to manufacturing issues. The prototype harvester occupies a volume of 226 cm³ and has an approximate mass of 235 g.

During testing, the hub was held steady by a bracket, while the ring was rotated by a stepper motor (M60STH88 from Motion Control Products Ltd) controlled by a micro-stepper driver (MSD880, same supplier), which received low-level control signals from a computer via a D/A card and current amplifiers. The controller requires two TTL-level signals: pulse and direction. A micro-step is generated by the controller at every rising edge of the pulse signal, whereas the high or low level of the direction signal controls the clockwise or counter-clockwise rotation. The controller was set for 20 000 micro-steps per revolution and the pulse signal was generated with a sampling period of 8 μs, so as to ensure the necessary frequency of low-to-high transitions even at the highest speeds. Pulse and direction control files were prepared in MATLAB by an algorithm which calculated the time interval between two rising edges based on the instantaneous speed given by the biomechanical data. As all gait cycles were periodic, at the start of each experiment the relative position of hub and ring was the same, as verified by direct visual observation.

To measure the power generation performance, four electrical loads (55.9 kΩ resistors) were connected to the bimorphs via individual full-bridge rectifiers (MULTICOMP-DBLS103G). The voltage drops across the four loads were simultaneously sampled with a NI-9229 A/D card. The instantaneous power was then calculated as P(t) = V²(t)/R, where V(t) is the measured voltage and R is the equivalent resistor from the parallel combination between the electrical load and the internal impedance of the acquisition card, i.e. R = 55.9 kΩ ∥ 1 MΩ = 52.9 kΩ. The vibration of the bimorph was measured with a Laser Doppler Vibrometer (LDV, Polytec CLV-2534); as it was not possible to shine the laser beam parallel to the direction of vibration, it was placed at a small angle (approximately 15°) and the resulting systematic error accounted for in the processing of the data. During the experiments reported here, the laser was shone on the tip of bimorph B4 (lower left in the photograph). The sampled velocity was numerically time-integrated to yield displacement and a base line was removed to account for the jitter of the hub caused by variable friction with the outer ring.

Kinematic data derived from marker-based motion capture systems is the gold standard method for the accurate characterization of human biomechanics. For this investigation, one healthy male subject was recruited. The trials were conducted at an unforced manner, at a speed self-determined by the subject. A six camera Qualisys Proreflex MCU240 motion-analysis system capturing at 100 Hz was used. Reflective markers were attached to the subject's lower limbs at the anterior superior iliac spine, posterior superior iliac spine, iliac crest, greater trochanter, fibula head, tibial tubercle, medial condyles, lateral condyles, calcaneus, lateral malleolus, medial malleolus. The markers form the basis of anatomical reference frames and centres of rotations of the joints. Five rigid plates, each consisting of four non-collinear markers, were also secured on the antero-frontal aspect of the leg, thigh and around the pelvis (figure 3). The calibrated anatomical systems technique (CAST) [10] was employed to determine the movement of these segments during the walking trials. The subject undertook five repeated trials with three backpack load conditions of 0, 12 and 24 kg; the backpack loads were evenly distributed to avoid bias and all of the markers remained attached to minimize positional inconsistencies in re-attachment. The selection of backpack loads was dictated by the initial motivations of the project, sponsored within the Battery-free Soldier initiative of the MoD of the UK.

Zoom In Zoom Out Reset image size

The knee-joint angle displacement was extracted from the main kinematics dataset. The joint kinematics was calculated using an X–Y–Z Euler rotation sequence in which the centre of the knee-joint is defined as the midpoint between the medial and lateral condyles markers [11]. The angle between the thigh and shank in the sagittal plane is used in the knee-joint simulator, where a naturally standing extension is calibrated to 0° and all higher angular displacements represent flexion (figure 4), whereas further extension is possible beyond the natural standing position, giving negative angles. The angular displacement during each time interval of 0.01 s was averaged over all trials, giving a mean angular displacement sampled at 100 Hz. No temporal normalization into one gait cycle was done in order to preserve the time values in seconds that are needed to measure the average power generation.

Zoom In Zoom Out Reset image size

Biomechanical data collected from a human subject carrying a selection of backpack loads confirm that the load influences the gait (figure 5). The first peak in all three curves, reaching approximately 20°, is the flexion of the knee-joint immediately following heel-strike, when the leg is loaded with the body weight; the second peak, over 50°, is associated with lift-off, when the leg has lost contact with the ground and is carried forward in preparation for the following heel-strike. Whereas the gait cycles for 0 and 12 kg loads are very similar, the highest load of 24 kg forces the subject into a significantly different gait pattern, which also lasts approximately 0.1 s more, lowering the step frequency from an average of 0.95 to 0.88 Hz.

Zoom In Zoom Out Reset image size

We now focus on time-domain results from bimorph B4 tested with the kinematic data for a 0 kg backpack load to present the typical behaviour of a bimorph in the harvester. In the first 0.5 s of motion (figure 6) the speed is low and the bimorph experiences only a few well-spaced plucking actions, so that the ring-down following release can be clearly seen (although the 300 Hz resonance vibration of the bimorph cannot be discerned well at this scale). The peak centred at about 0.4 s is very wide, suggesting that the contact plectrum–bimorph was held for a long time; in fact in this case the plectrum did not effectively pluck the bimorph, rather it deflected it and then re-accompanied to the rest position as the direction of rotation was reversed. There are two bursts of peaks in the second half of the cycle, where large angles are covered in a short time. Here the peaks are so close together that the bimorph vibrates continuously. More details on the different response of the bimorph at high plucking frequency versus low plucking frequency can be found in [9].

Zoom In Zoom Out Reset image size

Similar features are seen also in the voltage and power signals (figure 7): well spaced and not so high peaks in the first half of the gait cycle and two quick sequences of higher peaks in the second half of it. The wide displacement peak highlighted above (near 0.4 s) yields only very small voltage peaks at its beginning and end, and negligible power, because the deflection is very slow. This further clarifies that plucking can produce much more power than a quasi-static deflection of the bimorph: while the charges produced in open circuit conditions may be the same in the two cases, the corresponding current is higher if the deflection is faster. The response of the harvester in the second half of the gait cycle exemplifies the high power and voltages that can be achieved with plucking: in this area the voltage exceeds 20 V and the instantaneous power reaches 15 mW.

Zoom In Zoom Out Reset image size

The build-up of energy versus time, E(t), during the gait cycle is calculated from the instantaneous power, P(t), by numerical integration via the trapezoidal method, approximating:

$$\begin{eqnarray*} &&E(t)=\int \nolimits _{0}^{t}P(t)\hspace{0.167em} \mathrm{d}t. \end{eqnarray*}$$

The resulting energy versus time data are plotted in figure 8 for all four bimorphs for one of the runs. The energy curves confirm that a small fraction (less than 20%) of the energy is produced in the first half cycle, with the second half contributing substantially more to the overall energy generation.

Zoom In Zoom Out Reset image size

There are clearly some differences in the energy generated by the four bimorphs (figure 8), which in the main can be ascribed to the variability in the plectra they encounter.

As the plectra were cut by hand, their tips do not have exactly the same shape and they do not protrude from the outer ring by the same distance. As a result, some plectra produce more modest final deflections of the bimorphs than others; more importantly, most of the plectra do not release the bimorphs sharply enough, leading to an 'unclean' release. These issues are described in great detail in a previous paper [9], where it was also concluded, from statistical analyses, that the performance would increase by about 60–90% if all plectra were made like the seven best-performing plectra in the current harvester.

The final energy produced by the end of the gait cycle by each bimorph is plotted in figure 9 for all the experimental runs discussed in this paper. First, three successive runs were performed for each of the three gait cycles, i.e. for the subject carrying 0, 12 and 24 kg. After these nine measurements, the direction of the motion was reversed, as if the device was mounted on the other leg or connections to inner hub–shank and outer ring–thigh were reversed, and a similar set of nine measurements performed. The four traces in the lower part of the plot, one for each of the individual bimorphs making the prototype, show that there is a significant difference in the energy produced by each bimorph, with bimorph B3 producing on average 30% more energy than bimorph B2 in the first nine runs, whereas both B1 and B4 generate an amount of energy almost equal (within 3%) to the average of B3 and B2 in the same experiments. Upon direction reversal, bimorph B4 produces 33% more energy than B3, whereas B1 and B2 produce the same energy (within 3%), and again close to the average of the other two (within 4%). The fact that the energy generation for the same bimorph can change drastically with direction, suggests that the cause of the variability is not the bimorph itself, rather the exact shape of the plectra and the angle with which they emerge from their mounting. In fact, most plectra are not normal to the outer ring, i.e. they are not exactly radially oriented. If this was correctly controlled, it would lead to higher energy production during the swing extension phase of gait and reduced resistance to joint rotation during the stance phase, as originally intended at the design stage. Coincidentally, the effects on the four bimorphs almost exactly balance themselves, so that the overall average energy production is a statistically not significant 0.7% higher in the first nine runs than in those following direction reversal. In other words, the energy generated by the harvester presented here is not affected by what leg it is mounted on or, alternatively, whether the hub is fixed to the shank or the thigh.

Zoom In Zoom Out Reset image size

For each experimental run, the end-of-gait energies produced by the four bimorphs were added together to represent the total energy produced by the harvester in one walking step (upper trace with open circles in figure 9):

$$\begin{eqnarray} &&{E}_{\mathrm{tot}}={E}_{\mathrm{B1}}+{E}_{\mathrm{B2}}+{E}_{\mathrm{B3}}+{E}_{\mathrm{B4}}. \end{eqnarray} \tag{ 1 }$$

The horizontal line at 2.21 mJ represents the mean of the total energy in the 18 experiments.

The total energy produced by the harvester (figure 9) was statistically analysed (table 1). The three experimental runs available for each combination of gait/direction were analysed together. Data in the last row were calculated from the original dataset of 18 runs. The uncertainties were estimated as the 90% confidence level of the t-Student distribution. The total energy produced by the harvester is independent of the direction (table 1). It is possible to notice a moderate dependence on the specific gait, with the 24 kg load cycle yielding less energy than the others. As the total angle travelled is 166°, 168° and 170° for loads of 0, 12 and 24 kg, respectively, the gait with 24 kg load may actually trigger more plucking actions than the others, and could therefore produce more energy. The reason for the slightly lower energy production in the 24 kg gait is the lower average speed observed in this case (149° s⁻¹ for 24 kg, 157° s⁻¹ for 12 kg and 161° s⁻¹ for 0 kg): it was shown earlier [9] that the energy generation of a plucked harvester increases as the plucking actions become quicker. At any rate, the difference is very close to the experimental uncertainty, and hence of moderate statistical significance.

The average power produced during each gait cycle was simply calculated as the ratio between average energy and corresponding gait duration. Its mean and uncertainty were then calculated within the three runs of equal conditions and within all the 18 runs (last two columns of table 1), as described above for the energy. The seven mean values are in the region of 2 mW, with the overall mean at 2.06 ± 0.3 mW. The data in the table show that the power is significantly affected, in a statistical sense, by the specific gait cycle. The power output when the subject carries 24 kg is 10% below the mean of all loads. This is a combined effect of the lower energy production just discussed and a longer time during which this energy is generated, as the gait is slower with the highest load. However, in a practical sense, the reduced power generation observed when the subject is carrying a very large load is likely to be of limited importance.