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Design Innovation Paper: Design Innovation Papers

# Design and Treadmill Test of a Broadband Energy Harvesting Backpack With a Mechanical Motion RectifierPUBLIC ACCESS

[+] Author and Article Information
Yue Yuan, Mingyi Liu, Wei-Che Tai

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Lei Zuo

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: leizuo@vt.edu

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 4, 2017; final manuscript received April 16, 2018; published online May 23, 2018. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(8), 085001 (May 23, 2018) (8 pages) Paper No: MD-17-1804; doi: 10.1115/1.4040172 History: Received December 04, 2017; Revised April 16, 2018

## Abstract

The energy harvesting backpack that converts the kinetic energy produced by the vertical oscillatory motion of suspended loads to electricity during normal walking is a promising solution to fulfill the ever-rising need of electrical power for the use of electronic devices in civilians and military. An energy harvesting backpack that is based on mechanical motion rectification (MMR) is developed in this paper. Unlike the conventional rack-pinion mechanism used in the conventional energy harvesting backpacks, the rack-pinion mechanism used in the MMR backpack has two pinions that are mounted on a generator shaft via two one-way bearings in a way that the bidirectional oscillatory motion of the suspended load is converted into unidirectional rotation of the generator. Due to engagement and disengagement between the pinions and the generator shaft, the MMR backpack has broader bandwidths than the conventional energy harvesting backpacks; thus, the electrical power generated is less sensitive to change in walking speed. Two male subjects were recruited to test the MMR backpack and its non-MMR counterpart at three different walking speeds. For both subjects, the MMR backpack for most of the time generated more power than the non-MMR counterpart. When compared with literature, the MMR backpack had nearly sixfold improvement in bandwidth. Finally, the MMR backpack generated nearly 3.3 W of electrical power with a 13.6 kg load and showed nearly two- to tenfold increases in specific power when compared with a conventional energy harvesting backpack.

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## Introduction

Over the past decade, humans have become more and more dependent on electronic devices. Civilians are using them to enhance the quality of life [1]. For example, people who participate in outdoor recreation activities, such as multiday camping, backpacking, and sports, are using cameras, global positioning system, smart phones, etc., to enrich the activity experience and sustain their adventure [2]. At the same time, military is using global positioning system, night vision goggles, communication devices, etc., to survive and prevail over electronic warfare. What both of these scenarios have in common is the ever-rising need of electric power. For example, a typical dismounted U.S. Soldier or Marine needs to carry up to 20 lbs. (9.1 kg) of batteries on a 72 h mission [3,4]. One promising solution to address the power requirement is the use of a suspended-load backpack that converts mechanical energy from the vertical movement of suspended loads to electricity during normal walking, e.g., see Refs. [57]. When humans are walking or running while wearing a backpack that is suspended from their torsos, the suspended load oscillates vertically to produce kinetic energy. A conventional suspended-load backpack uses a rack-pinion design to convert the vertical oscillation into rotational motion of a miniature power generator, generating electricity from the kinetic energy.

The first suspended-load energy harvesting backpack was invented by Rome et al. [5]. Their backpack generated electrical power of 7.4 watts with a 38 kg load when walking at 3.5 mph (5.6 km/h). Their experiments also showed that the electrical power increases with increasing load and walking speed. Two other energy harvesting backpacks based on the same principle were developed later. One was by Xie et al. [6], and they reported electrical power of 4.1 watts with a 15 kg load at the same walking speed. The other is the energy harvesting assault pack (EHAP), which was developed by the United States Army Communications-Electronics Research, Development and Engineering Center (U.S. Army CERDEC) [7]. They reported 1.5 W with a 15.9 kg (35 lbs.) load when walking at 3 mph. While energy harvesting backpacks keep having new designs, the fundamental has been remaining the same, i.e., they are all the same as the linear vibration energy harvesting system reported in Ref. [8]. As explained in Ref. [8], such a system (also conventional energy harvesting backpacks) relies on resonance, a phenomenon in which maximum power is achieved when the natural frequency of the system is tuned to match a dominant excitation frequency of the host. To have as large maximum power as is possible, the mechanical damping is kept as low as is possible. Yet, a low damping design has a high-quality factor (Q factor) that results in a very sharp and narrow resonance peak. Consequently, resonance-based energy harvesting is very sensitive to changes in walking speed, stride frequency, and backpack load, which is known as $detuning$. For example, as will be shown later, it is observed that the power of the backpack in Ref. [6] reduced by nearly 60% when the walking speed reduced by only 1 km/h.

In response to this drawback, a fundamentally different energy harvesting backpack that utilizes mechanical motion rectification (MMR) is developed [9,10]. Distinct compared to conventional energy harvesting backpacks (referred to as non-MMR hereinafter), MMR utilizes a mechanism that converts the up and down oscillatory motion of the suspended load into unidirectional rotational motion of the generator. Most importantly, MMR enables $broadband$ energy harvesting, i.e., the power generation is less sensitive to change in excitation frequency of the host, e.g., see Ref. [11]. Applications of MMR energy harvesting can also be found in car suspension and ocean wave energy conversion [12,13].

The rest of this paper is organized as follows: In Sec. 2, the design of the MMR-based power-take-off unit (PTO) will be reported. The working principle of MMR will be briefly reviewed. Next, the design of the suspended-load backpack frame will be presented. In Sec. 3, two numerical simulations will be conducted to compare the MMR-based backpack with its non-MMR counterpart. First, the optimal spring stiffness and electrical resistive load will be predicted. Second, frequency response functions of both backpacks will be computed and compared to examine the bandwidth. In Sec. 4, experimental data collected from two male subjects during treadmill tests, including average electric power and optimal resistive loads, will be reported and studied. In Sec. 5, the performance of the MMR-based backpack will be compared with other designs reported in the literature.

## Mechanical Motion Rectification-Based Power-Take-Off Unit

The principle of MMR is briefly described in this section. Figure 1 shows an electromagnetic generator connected to a MMR mechanism. The MMR mechanism herein employs a rack-pinion design and consists of two racks, two pinions, two one-way bearings (clutches), and an output shaft that is connected to the generator. Unlike the conventional rack-pinion mechanism in the conventional energy harvesting backpacks [57], the pinion gears are mounted on the output shaft via two one-way bearings; see Fig. 1(b). One one-way clutch is mounted to allow its pinion gear to engage the generator shaft when it rotates clockwise while the other is mounted to allow the other pinion gear to engage the shaft when it rotates counterclockwise. Consequently, no matter the racks are moving upward (up stroke) or downward (down stroke), the output shaft and the generator are always driven to rotate in one direction (unidirectional rotation).

When the racks and pinion gears are accelerating, regardless of up or down stroke, the shaft is driven via the one-way clutches. When the pinions are decelerating to an extent that the rotational acceleration of the pinions becomes smaller than that of the generator shaft, both pinions can no longer drive the generator shaft via the one-way clutches, similar to what happens to a bicycle gear when the rotational acceleration of the gear is higher than that of the pedals. The state when neither of the one-way bearings engages the shaft is termed as “disengagement state.” After disengagement occurs, the rotational velocity of the shaft and pinions becomes different. The former is governed by the generator dynamics and the latter is by the motion of the racks. The rotational velocity of the generator gradually slows down because the pinions no longer drive it while its kinetic energy is continuously converted into electricity via an energy harvesting circuit. After the pinions stop decelerating and start accelerating (here cyclic excitations to the racks are assumed), their rotational velocity rises and eventually matches the descending rotational velocity of the generator shaft; instantly, the pinions engage the shaft via the one-way clutches once again. The state when one of the pinions engages the shaft is termed as “engagement state.” Since cyclic excitations are assumed, the MMR switches between disengagement and engagement cyclically too. Mathematical explanation of the switching process and mechanism is provided in detail in Sec. 3.

Figure 2 shows the design of a suspended-load backpack frame, consisting of a fixed board to be fixed to the human body, a moving board suspended from the fixed board by two springs, two linear guides to guide the relative motion between the two boards, and finally the MMR-base PTO installed in a cutout of the moving board. Furthermore, the upper end of the racks is connected to the fixed board such that when the relative motion occurs, the racks will drive the generator via the MMR. The backpack frame has a compact design with thickness being less than 38 mm and weight less than 0.77 kg. The MMR harvester also has a light weight of 0.59 kg.

Finally, the generator is a DC motor used in the reverse mode. The specifications of the generator can be found in Table 1. If an electromagnetic generator is shunted with a resistive electrical load and the inductance is small, the force induced by the back electromotive voltage will be proportional to the electrical current and can be modeled as an ideal viscous damping [8]. The viscous damping coefficient is also known as equivalent electrical damping coefficient, or ce. Furthermore, the rotational inertia of the generator will produce an inertial force proportional to the relative acceleration of the backpack load. In this regard, the rotational inertia of the generator is equivalent to an inerter, a two-node device that generates a force proportional to the relative acceleration between the nodes [14]. The proportionality is known as inertance, or me, which is used as a mechanical analogy with capacitance of ungrounded capacitors in the “force-current” analogy between the mechanical and electrical networks [15], and can be found in several studies that involve inerters, e.g., see Ref. [16]. The equivalent damping coefficient and inertance can be calculated as follows: Display Formula

(1)$ce=ke2ng2(Ri+R)r2;me=Jeng2r2$

where ke is the back EMF constant, ng is the gear ratio, Ri and R are the internal and external resistance of the generator, respectively, and r = 7.94 mm is the radius of the pinion gear. The interested reader is referred to Ref. [11] for details of the derivation of me.

## Numerical Analysis

Figure 3 shows the mathematical model of the MMR-based energy harvesting backpack, consisting of engagement and disengagement state. During engagement state, the generator exerts two resistance forces to the backpack load; one is the electrical damping force $fe=−cez˙$ and the other is the inertance force $fint=−mez¨$, where $z˙$ and $z¨$ are the relative velocity and acceleration between the backpack load m and the base, respectively, and ce and me are the electrical damping coefficient and inertance, respectively, defined in Eq. (1). Note that the negative sign indicates resistance forces. Thus, the equation of motion of the backpack load during engagement state can be derived via Newton's second law as Display Formula

(2)$mz¨+cmenz˙+kz=−my¨+(fe+fint)or(m+me)z¨+(cmen+ce)z˙+kz=−my¨$

where z is the relative displacement, $y¨$ is the base acceleration, k is the spring stiffness, and $cmen$ is the mechanical damping coefficient during engagement state. Note that me and ce are present in Eq. (2) because of the resistance forces exerted by the generator. During disengagement state, the generator and backpack suspension system are separate; thus, me and ce become absent. Together with Eq. (2), the equation of motion of the backpack load in each state can be derived as Display Formula

(3)$Engaged(θ˙g=|θ˙p|): (m+me)z¨+(cmen+ce)z˙+kz=−my¨Disengaged(θ¨g>−|θ¨p|): mz¨+cmdez˙+kz=−my¨$

where $cmde$ is the mechanical damping during disengagement state; $θ˙g, θ˙p, θ¨g$, and $θ¨p$ are the rotational velocity and acceleration of the pinions (subscript p) and generator shaft (subscript g), respectively. Two things worth noting in Eq. (3) are: First, the mechanical damping during disengagement state is different from that during engagement state. Because the generators are disengaged, the mechanical damping of the suspension frame is mostly contributed by the motion linear guides, which is typically much smaller than that by the generator; thus, $cmen>cmde$. Second, the switching conditions between engagement and disengagement state depend on the relations between $θ˙g, θ˙p$, $θ¨g$, and $θ¨p$, which are provided inside the parentheses. The derivation of these relations is explained as follows.

When disengagement occurs, the rotational acceleration of the generator is larger than that of the pinions, i.e., $θ¨g>−|θ¨p|$; see the right diamond block of Fig. 3. Note that the absolute value is used because the rotational motion of the generator is unidirectional while that of the pinions are bidirectional. Afterward, the generator disengages the backpack, leading to two separate subsystems. One is the disengaged backpack system, whose equation of motion is defined in the second equation in Eq. (3).

The other subsystem is the generator shunted by external electrical resistance. Because the generator is separate from the backpack, the pinions no longer drive it. As a result, the rotational velocity of the generator gradually slows down because the rotational energy stored in the generator continues to be converted into electricity, which can be modeled as a first-order system in terms of $θ˙g$. In other words Display Formula

(4)$meθ¨g+(ce+cg)θ˙g=0$

where cg is a parasitic mechanical damping coefficient to describe the energy loss due to internal mechanical damping of the generator. The closed-form solution of Eq. (4) is $θ˙g=θ˙gdee−(t−tde/τ)$, where $θ˙gde$ is the rotational velocity at the instant of disengagement, tde is the instantaneous time of disengagement, and $τ=me/(ce+cg)$ is the time constant of the generator. Note that the larger ce the smaller τ is, and thus the faster the decay rate is, because larger ce indicates that the rotational energy is harvested faster. On other hand, the larger me the slower the decay rate is, because larger me means that more rotational energy needs to be harvested. As the generator slows down, its rotational velocity will eventually match that of the pinions, i.e., $θ˙p=|θ˙g|$; see the left diamond block of Fig. 3. Instantly, the generator engages the backpack again and engagement state is resumed. Due to this unique feature, the MMR backpack is a nonlinear energy harvester.

The power generated by the MMR backpack can be calculated as follows: Display Formula

(5)$Engaged: P=RRi+Rcez˙2Disengaged: P=R(Ri+R)2ke2ng2θ˙g2$

where $z˙$ and $θ˙g$ are the relative velocity of the backpack load and rotational velocity of the generator, respectively, which can be obtained by solving Eq. (3).

In this numerical analysis, the mechanical damping during engagement state is estimated to be $cmen=125$ Ns/m by measuring the mechanical damping coefficient of the backpack with the MMR mechanism being replaced with the conventional rack-pinion mechanism by removing the one-way bearings and one rack. The mechanical damping during disengagement state is estimated to be $cmde=9$ Ns/m by measuring the mechanical damping of the backpack frame without connecting the generator. These two scenarios are chosen to best mimic the backpack's behavior during each state. Furthermore, the parasitic mechanical damping coefficient of the generator is estimated to be cg = 31 Ns/m by curve fitting the measured voltage output of the generator during disengagement state to the solution of Eq. (4). The estimated damping coefficients are used throughout this paper. Note that $cmen$ is typically much larger than $cmde$ because the mechanical damping of a generator and gearbox is much larger than that of motion linear guides. Finally, the backpack load is set to be m = 13.6 kg (30 lbs.), corresponding to the real load used in subsequent treadmill tests.

An in-house fourth-order Runge-Kutta numerical integration scheme is developed to solve Eq. (3) with varied spring stiffness constant k and external resistance R to identify the optimal values that lead to maximum average power. The average power is obtained by averaging the instant power over one period of excitation. The human center of mass (COM) motion is modeled as a sinusoidal base excitation $y=A sin ωt$, where A = 25 mm and $ω=1.97$ Hz. The excitation amplitude is chosen based on the experimental data reported in Ref. [17], which was recorded when the test subjects were walking at 1.33 m/s (2.97 mph) while carrying a fixed-load backpack with a load of 20 kg. The excitation frequency is chosen based on the experimental data reported in Ref. [5]; see Table S4 in online supplement of Ref. [5], which was measured when walking at 5.6 km/h (3.5 mph) while carrying a suspended-load backpack with a load of 29 kg.

Two cases are compared in the numerical analysis. The first is the MMR-based energy harvesting backpack and the second one is the non-MMR counterpart, which uses the conventional rack-pinion design. The average power of the MMR backpack is obtained by numerically integrating Eq. (3) while that of the non-MMR backpack is by integrating the first equation of Eq. (3) for both engagement and disengagement state since the non-MMR backpack always remains engaged. The results are shown in Fig. 4. There are several things worth noting in Fig. 4. First, given the same excitation condition, the MMR and non-MMR backpack generate approximately the same maximum average power. The former has 2.68 W and the latter has 2.59 W. Second, they have very different optimal spring stiffness constants. The simulated MMR backpack's optimal stiffness constant is 3172 N/m and the non-MMR's is 5345 N/m. Third, both backpacks have approximately identical optimal electrical resistance (MMR: 11.24 Ω; non-MMR: 11.24 Ω).

To examine the bandwidth of both MMR and non-MMR backpacks, the frequency response functions of both backpacks are simulated by solving Eq. (3) with varied excitation frequencies ω and mechanical damping coefficients $cmen$. Note that the measured mechanical damping coefficients $cmen=125$, $cmde=9$, and cg = 31 Ns/m and simulated optimal stiffness k = 3172 N/m (MMR) and k = 5345 N/m (non-MMR) are used. Also, the excitation amplitude is 25 mm. Two cases of $cmen$ are considered, namely, $cm,100%en=125$ Ns/m, corresponding to the actual mechanical damping of the backpack and $cm,50%en=62.5$ Ns/m, corresponding to 50% of the actual damping. The results are shown in Fig. 5. There are several things worth noting in Fig. 5. First, for most of excitation frequencies considered, the MMR backpack generates more power than the non-MMR backpack, indicating that the MMR backpack has broader bandwidths. Second, higher the excitation frequency, the more power the MMR backpack can harvest than the non-MMR backpack. For example, at 3 Hz, the MMR backpack generates 8.1 and 10.1 W for $cm,100%en$ and $cm,50%en$, respectively, while the non-MMR backpack can only harvest 4.6 and 3.1 W, equivalent to differences of 3.5 and 7 W. At low excitation frequencies, e.g., $ω<1.5$ Hz, on the other hand, the difference between MMR and non-MMR backpack becomes less distinguishable. This simulation result can be explained as follows. As earlier explained, the MMR nonlinearity is due to engagement and disengagement between the one-way bearings and shaft. Generally speaking, longer the disengagement period, the stronger the nonlinearity is. According to Ref. [8], the disengagement period is proportional to the excitation frequency. In other words, faster the excitation frequency, the more the MMR backpack can outperform the non-MMR backpack. Third, the mechanical damping has a different role in the bandwidth of the MMR and non-MMR backpack. For the non-MMR backpack, smaller damping results in narrower bandwidths. For the MMR backpack, on the other hand, smaller damping actually yields broader bandwidths. In short, the MMR backpack is broadband and less sensitive to change in excitation frequency. A similar broadband effect was observed in a MMR pendulum energy harvester developed in Ref. [11].

## Treadmill Tests

Two male subjects were recruited to participate in the tests. The demographic and anthropometric information of these two subjects can be found in Table 2. The tests were to compare the electrical power output of the MMR-based energy harvesting backpack and the non-MMR counterpart. The MMR backpack used two springs with total spring stiffness of 2286 N/m, which was the closet to the simulated optimal spring constant of 3172 N/m (cf. Fig. 3) among commercially available springs. The non-MMR counterpart was obtained by removing the one-way bearings and one rack from the MMR backpack. It used two springs with total spring stiffness of 5397 N/m, which was chosen by the same principle. Finally, the MMR and non-MMR backpack had an identical dead load of 13.6 kg and the same generator was used. The experimental rig is shown in Fig. 4.

The test protocol is briefly explained as follows. First, before the tests, both subjects were orally briefed on the purpose, risks, and benefits of the study. Second, the subjects were given the opportunity to practice walking on the treadmill while wearing the backpack. At the same time, necessary adjustment was given to the backpack per subject's request until the subjects felt comfortable for the test trials. Third, they were asked to carry either the MMR-based energy harvesting backpack or the non-MMR counterpart to walk on a treadmill at 4.83 km/h (3 mph), with varied electrical resistance. Four values of electrical resistance, including 5, 10, 15, and 20 Ω were tested. For each electrical resistance value, the subjects were asked to conduct three test trials, amounting to 12 test trials (four electrical resistance × three trials) per person. Fourth, in each test trial, the subjects started with a comfortable walking speed and gradually increased the speed by themselves until it reached the targeted speed. They continued on walking at the targeted speed for 30 s, and then a data acquisition system started recording data, including generator voltages and backpack relative displacements, for another 30 s. It follows that the power was averaged over the last 30 s in each trial of each subject, and the results of three trials were averaged to obtain the final average power and error bars for each subject. Fifth, between each test trial, every subject was given at least five minutes of resting time to avoid fatigue as a confounding factor. Finally, all 12 test trials of each subject were completed in the same day to avoid uncertainties of physical conditions (Fig. 6).

The treadmill tests results are shown in Fig. 7. There are several things worth noting in Fig. 7. First, the optimal electrical resistance for both MMR and non-MMR backpack falls within 10–15 Ω for both subjects, which generally matches the simulated value of 11.24 Ω reported in Fig. 4. Second, the MMR backpack generated the maximum power for both subjects, when compared to the non-MMR backpack. The largest maximum paper is 2.82 W, generated by subject A. Third, overall, when the electrical resistance is not optimal, the MMR backpack generally has a slower rate of power decrease, which also qualitatively matches the trend observed in Fig. 4.

The observation that the MMR backpack generated more maximum power than the non-MMR is indeed intriguing. Based on the simulation in Fig. 4, they should have had roughly the same maximum power. To identify the reason of non-MMR's low power, the instant power output of both backpacks is plotted in Fig. 8.

As clearly shown in Fig. 8(b), the non-MMR backpack generated zero power for nontrivial time interval when the power transitioned through minimum values. This transition occurred when the rack changed its direction, from up stroke to down stroke or the other way around. The most likely culprit was the rack's backlash, which caused a lost motion in the non-MMR harvester due to gaps between the gear and rack every time when the shaft changed its direction. The MMR backpack, on the other hand, showed less backlash because the shaft always rotated in the same direction.

Next, average power of each subject was measured at two other walking speeds, 4.02 and 5.63 km/h (or 2.5 and 3.5 mph). The backpack parameters were kept the same as in the 4.83 km/h case. The results are plotted in Fig. 9. There are two things worth noting in Fig. 9. First, the MMR backpack generated higher power than the non-MMR backpack except for one data point (subject B at 4.02 km/h). Second, higher the walking speed (also walking frequency), the more power the MMR backpack generated than the non-MMR backpack. This trend qualitatively matches the simulated frequency response functions shown in Fig. 5.

Finally, the MMR backpack was compared with the work of Rome et al. [5], Xie and Cai [6] and the EHAP [7]. For fair comparison, the power of each work was normalized with respect to each backpack load, i.e., specific power (watts per kg) was considered. The results are plotted in Fig. 10. There are several things worth noting in Fig. 10. First, Rome et al. and the EHAP have approximately the same performance. Both of them have specific power lower than 0.2 W/kg. Second, Xie et al. have higher specific power but a much narrower bandwidth as the dotted-dash line has a steeper slope than the dotted lines and dashed lines. In other words, the backpack of Xie et al. is more sensitive to change in walking speed. Third, the MMR backpack achieved both high specific power and a broad bandwidth due to the MMR nonlinearity. Quantitatively, the MMR backpack's power reduced by approximately 11% when the walking speed reduced by around 1 km/h (0.24 W/kg at 5.63 km/h to 0.22 W/kg at 4.83 km/h). With the same walking speed reduction, an approximate 60% reduction is found in Xie et al. (0.16 watts/kg reduction per km/h. The calculation was interpolated using a linear regression method with a R-squared value R = 0.9998.), indicating nearly sixfold improvement in bandwidth. Finally, the MMR backpack has 0.24 W/kg at 5.63 km/h. When compared with Rome et al., it has nearly two- (176%) to tenfold (953%) increases in specific power; see Table 3.

As a final remark, Xie et al. [6] developed a frequency-tunable energy harvesting backpack based on their work in Ref. [6], which requires one to manually tune the spring stiffness at each walking speed and by doing so they claimed a range of specific powers between 0.20 and 0.353 W/kg using a 30 kg load when walking at 5.5 km/h. Nonetheless, the MMR-based backpack utilizes passive devices and does not rely on any active frequency tuning mechanisms; a direct comparison is not applicable unless the MMR based backpack has a similar frequency tuning capability, which, however, is out the scope of this work.

Another way to assess the backpack performance is to use the normalized power density (NPD) proposed by Beeby et al. [19], which is defined as $NPD=P/(A2M)$, where P is the average power, M is the backpack load, and $A=Yω2$ is the peak acceleration of the COM motion of the human, and Y and ω are the displacement of the COM motion and walking frequency respectively. As we do not have any motion capture equipment to measure the COM motion of the test subjects, we estimate Y using the formula developed by Xu [20], which is defined as Display Formula

(6)$Y=R2(1−1−(0.963πVRω)2)−0.0157R$

where R is the leg length and V is the walking velocity. For subject A, ω and R can be found in Tables 2 and 4, respectively. Consequently, the NPD of subject A with the MMR backpack at different walking speeds is calculated as 0.0127 kg/cm3 (5.63 km/h), 0.0224 kg/cm3 (4.83 km/h), and 0.0301 kg/cm3 (4.02 km/h),which increases as the walking speed decreases. Therefore, NPD is not a good metric to investigate the bandwidth of energy harvesting backpacks. In fact, Beeby et al. [19] also pointed out that NPD metric is not ideal since it ignores important factors such as bandwidth.

## Conclusions

In developing the MMR-based energy harvesting backpack, the following conclusions are made in terms of design, numerical simulations, and treadmill tests.

In terms of design, unlike the conventional energy harvesting backpacks that use conventional rack-pinion designs, the MMR unprecedentedly converts the vertical oscillatory motion of suspended loads into the unidirectional rotation of the generator by using two paired one-way bearings.

From the viewpoint of numerical simulations, the simulated frequency response functions show that the MMR backpack has a broader bandwidth than the non-MMR counterpart. The broadband feature is due to the MMR nonlinearity.

Two male subjects were recruited to participate in the treadmill tests, which were conducted at three different walking speeds: 4.03, 4.83, and 5.63 km/h (or 2.5, 3 and 3.5 mph). The test results showed that the MMR backpack generated higher power than the non-MMR counterpart for both subjects except for one data point. Furthermore, higher the walking speed, the more power the MMR backpack harvested than the non-MMR backpack. When compared with literature, the MMR backpack had nearly sixfold improvement in bandwidth. Furthermore, it generated 3.29 W with a 13.6 kg load and showed nearly two- to tenfold increases in specific power.

## Acknowledgements

This material is based upon work supported by the U.S. Army Communications-Electronics Research, Development and Engineering Center (U.S. Army CERDEC). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of U.S. Army CERDEC.

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Beeby, S. P. , Torah, R. , Tudor, M. , Glynne-Jones, P. , O'donnell, T. , Saha, C. , and Roy, S. , 2007, “ A Micro Electromagnetic Generator for Vibration Energy Harvesting,” J. Micromech. Microengineering, 17(7), p. 1257.
Xu, X. , 2008, “ An Investigation on the Interactivity Between Suspended-Load Backpack and Human Gait,” North Carolina State University, Raleigh, NC.
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Beeby, S. P. , Torah, R. , Tudor, M. , Glynne-Jones, P. , O'donnell, T. , Saha, C. , and Roy, S. , 2007, “ A Micro Electromagnetic Generator for Vibration Energy Harvesting,” J. Micromech. Microengineering, 17(7), p. 1257.
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## Figures

Fig. 1

MMR-based PTO unit: (a) CAD design drawing and (b) working principle of MMR (the mounting bearings are not shown)

Fig. 2

Design of a suspended-load backpack frame: (a) front view and (b) side view

Fig. 3

Mathematical model of MMR-based energy harvesting backpack. Note that the system consists of two states: engagement and disengagement states. During engagement state, the generator engages the backpack. During disengagement state, they are separate.

Fig. 4

Average power versus spring constant and electrical resistance: (a) MMR backpack and (b) Non-MMR backpack. Excitation conditions: base excitation with 25 mm amplitude and 1.96 Hz excitation frequency. Note that the measured mechanical damping coefficients cmen=125, cmde=9 and cg = 31 Ns/m are used.

Fig. 5

Simulated frequency response functions of MMR and non-MMR backpacks show that the former has a broader bandwidth. Note that both backpacks are subjected to sinusoidal excitations of varied excitation frequencies and a constant amplitude of 25 mm. Also note that the measured mechanical damping coefficients cmen=125, cmde=9, and cg = 31 Ns/m and simulated optimal stiffness k = 3172 (MMR) and k = 5345 N/m (non-MMR) are used (cf. Fig. 4). Finally, cm,100%en=125 and cm,50%en=62.5 Ns/m.

Fig. 6

Treadmill test setup: (a) Backpack experimental rig. The PTO is installed in the cutout of the moving board while the racks are fixed to the fixed board. A 13.6 kg dead load is also attached to the moving board. A laser displacement sensor is used to measure the relative displacement of the suspended load. (b) Illustration of treadmill testing.

Fig. 7

Measured average power of two subjects at different electrical resistance. Walking speed: 4.83 km/h. Suspended load: 13.6 kg. The power was averaged over the last 30 s in each test trial. Three test trials were averaged to obtain the final average power and error bars.

Fig. 8

Instant power of MMR and non-MMR backpack for eachsubject: (a) subject A and (b) subject B. Walking speed: 4.83 km/h. The optimal electrical resistance of each subject (cf.Fig. 7) was used.

Fig. 9

Average power of two test subjects at (a) different walking frequencies and (b) different walking speeds: 4.02, 4.83 and 5.63 km/h. Note that the leg length of subject A is shorted than subject B (cf. Table 2); thus, the fundamental frequencies of walking are higher; see Table 3. Three test trials were averaged to obtain the final average power and error bars at each walking speed.

Fig. 10

Comparison of MMR energy harvesting backpack with literature [57]. Note that the dash lines are regeneration of Fig.4 of Ref. [5], where I, II and III represent backpack loads of 20 kg, 29 kg, and 38 kg, receptively. Dash-dotted line is of Fig. 4 of Ref. [5]. Dotted lines are regeneration of Ref. [7], where I and II represent backpack loads of 7.94 kg (17.5 lbs.) and 15.9 kg (35lbs.), respectively.

## Tables

Table 1 Specifications of the generator and the gear-head. EMF: electromotive force
Table 4 Fundamental frequencies of walking of two test subjects at 4.02, 4.83 and 5.63 km/h
Table 2 Demographic and anthropometric information of test subjects. Note that leg lengths were measured following the definition in Ref. [18]
Table 3 Percentage increases of specific power of MMR compared with Rome et al. [5] at different walking speeds

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