2.1.2. Analysis

To predict the energy performances of the EM-generator designs, the dynamic models of the two electro-mechanical systems, shown in Figure 2, were developed using MATLAB®/Simulink. Figure 3a,b show the physical models corresponding to the two systems in Figure 2a,b, respectively. In Figure 3a, the system consists of the elements of rack, pinion and gear on the mechanical side, and the DC generator (with its own resistance, *RG*, and inductance, *L*) connected to the load *RL* on the electrical side. Contrastively, the elements of rack, pinion and gear are replaced by the nut, lead screw, and bevel gears for the system in Figure 3b. The footstep force *F*(*t*) is modeled as the arbitrary function reported in [9] and presented in Figure 4. The spring with a maximum compression of 15–20 mm provides the restoring force *Fs* to restore the floor-tile back to the equilibrium position. The dynamic equations governing the electro-mechanical models of both designs are formulated as follows.

**Figure 3.** Physical models: (**a**) Rack and Pinion Model; (**b**) Lead-Screw Model.

**Figure 4.** Input Footstep Force.

For the electrical side in Figure 3, Kirchhoff's voltage law yields

$$V\_L + V\_{RG} + V\_{RL} - V\_G = 0,\tag{1}$$

where *VG* is the back emf of the generator; i.e., *VG* = *Kt*ω*<sup>G</sup>* where *Kt* is the back emf (torque) constant. In addition, *VL*, *VRG* and *VRL* are the voltages across the generator's inductor, generator's resistor and load's resistor, respectively. With the voltage-current relations, (1) becomes

$$\dot{i} + \left(\frac{R\_G + R\_L}{L}\right)\dot{i} - \left(\frac{K\_t}{L}\right)\omega\_G = 0,\tag{2}$$

where *i* is the current, *Kt* is the back emf (torque) constant, ω*<sup>G</sup>* is the generator rotational speed, *L* is the inductance of the generator, *RG* is the resistance of the generator and *RL* is the resistance of the load. Equation (2) is the differential equation governing the armature winding of the generator.

From the free body diagram (FBD) of the mechanical system with the rack and pinion in Figure 5, Newton's second law and the law of angular momentum describe the translation of the rack, and the rotations of the pinion and the generator rotor, respectively, as

$$m\ddot{\mathbf{x}} = F(t) - F\_r - F\_{s\nu} \tag{3}$$

$$J\_p \dot{\omega}\_p = J\_p \frac{\ddot{\mathbf{x}}}{r\_2} = (F\_r - f\_r) r\_{2,r} \tag{4}$$

$$J\_G \dot{\omega}\_G = J\_G \frac{\ddot{\mathbf{x}}}{r\_1} = (f\_r - \tau\_G) r\_{1\prime} \tag{5}$$

where *m* is the mass of the plate and rack, and *Jp* and *JG* are the moments of inertia of the pinion and the gear. *x* is the displacement of the rack, ω*<sup>p</sup>* is the angular velocity of the pinion, ω*<sup>G</sup>* is the angular velocity of the gear. In (3)–(5), *F*(*t*) is the input force, *Fs* is the restoring spring and damper force, *Fr* is the friction force between the rack and pinion, *fr* is the friction force between the pinion and gear. In addition, τ*<sup>G</sup>* is the electromagnetic torque of the DC generator, where τ*<sup>G</sup>* = *Kti*, and *r*<sup>1</sup> and *r*<sup>2</sup> are the radius of the gear and pinion, respectively.

**Figure 5.** Rack and Pinion Free Body Diagram.

Eliminating *Fr* and *fr* from (3)–(5), the differential equation governing dynamics of the mechanical system with the rack and pinion is obtained as

$$M\ddot{\mathbf{x}} + \frac{\mathbf{K}\_t}{r\_1}\dot{\mathbf{i}} + F\_\mathbf{s} = F(t),\tag{6}$$

where *M* = *<sup>m</sup>* + *Jp r*2 2 + *JG r*2 1 . Then the governing equations of the electro-mechanical system from combining (2) and (6) are

$$
\begin{bmatrix}
\dot{i} \\
\dot{\chi} \\
\ddot{\chi}
\end{bmatrix} = \begin{bmatrix}
0 & 0 & 1 \\
\end{bmatrix} \begin{bmatrix}
i \\
x \\
\dot{x}
\end{bmatrix} + \begin{bmatrix}
0 \\
0 \\
\frac{F(t) - F\_s}{M}
\end{bmatrix} \tag{7}
$$

Similarly, from the FBD of the mechanical system with lead and screw as shown in Figure 6, the equations govern the translation of the nut and the rotations of the lead screw and the generator rotor, respectively, are

$$
\dot{m}\ddot{\mathbf{x}} = F(t) - F\_a - F\_{sr} \tag{8}
$$

$$J\_1 \ddot{\theta}\_1 = \frac{2\pi J\_1}{l} \ddot{\mathbf{x}} = \boldsymbol{\Gamma} - T\_{B\prime} \tag{9}$$

$$J\_G \ddot{\theta}\_2 = \frac{2\pi I\_G}{l} \ddot{\mathbf{x}} = T\_B - \tau\_{G\prime} \tag{10}$$

where *m* is the mass of the floor-tile and the nut, *J*<sup>1</sup> is the moment of inertia of the lead screw and *JG* is the moment of inertia of the bevel gear. *l* is the pitch of the lead screw, *x* is the displacement of the plate and nut, θ<sup>1</sup> is the angular position of the lead screw and θ<sup>2</sup> is the angular position of the bevel gear. In addition, *F*(*t*) is the applied force from the footstep, *Fs* is the restoring spring and damper forces, *Fa* is the friction force between nut and lead screw, *TB* is the friction torque of the bevel gear, τ*<sup>G</sup>* is the electromagnetic torque of the DC generator; where τ*<sup>G</sup>* = *Kti*. Note that Γ in (9) is the transmitted torque from the nut to the lead screw which is proportional to *Fa* as

$$\Gamma = \Delta F\_{a\nu}$$

where <sup>Δ</sup> <sup>=</sup> *<sup>l</sup>* <sup>2</sup>πη*thread*η*thrust* , with <sup>η</sup>*thread* and <sup>η</sup>*thrust* are the efficiencies of the *thread* and the *thrust* bearing, respectively.

$$\begin{array}{c|c} \hline & F(t) \\ \hline \hline \text{1\\_X} & \text{1\\_f} \\ \hline \text{1\\_X} & \text{1\\_f} \\ \hline & F\_\alpha \text{ }^\uparrow F\_\alpha \\ & \text{1\\_Z} \\ & \text{1\\_Z} \\ & \text{1\\_Z} \\ \hline \end{array} \qquad \begin{array}{c|c} F(t) \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \end{array} \qquad \begin{array}{c|c} \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \text{1\\_Z} & \text{1\\_Z} \\ \hline \end{array}$$

$$m\ddot{x} = F(t) - F\_a - F\_\sharp \qquad f\_1 \ddot{\theta}\_1 = \frac{2\pi f\_1}{l} \\ \ddot{x} = \Gamma - T\_B \qquad f\_G \ddot{\theta}\_2 = \frac{2\pi f\_2}{l} \\ \dddot{x} = T\_B - \tau\_G$$

**Figure 6.** Lead-Screw Free Body Diagram.

By rearranging (8)–(10), the equations become

$$J\_{\alpha\dot{\eta}}\ddot{\partial}\_1 + \frac{\mathcal{K}\_t}{\Delta}\dot{t} + F\_s = F(t),\tag{11}$$

$$\frac{2\pi l\_{eq}}{l}\ddot{\mathbf{x}} + \frac{\mathbf{K}\_t}{\Delta}\dot{\mathbf{t}} + F\_s = F(t),\tag{12}$$

where *Jeq* = *ml* <sup>2</sup><sup>π</sup> <sup>+</sup> (*J*1+*JG*) <sup>Δ</sup> is the equivalent moment of inertia corresponding to the mass of the plate and nut *m*, and the mass moments of inertia of the lead screw and bevel gear *J*<sup>1</sup> and *JG*, respectively. ⎡ ⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

By combining (2) and (11)–(12), the equations governing the electro-mechanical system with the lead and screw design are obtained as

$$
\begin{bmatrix}
\dot{i} \\
\dot{\theta}\_1 \\
\ddot{\theta}\_1
\end{bmatrix} = \begin{bmatrix}
0 & 0 & 1 \\
\end{bmatrix} \begin{bmatrix}
\dot{i} \\
\dot{\theta}\_1 \\
\dot{\theta}\_1
\end{bmatrix} + \begin{bmatrix}
0 \\
0 \\
\frac{F(t) - F\_s}{I\_{\rm eff}}
\end{bmatrix} \tag{13}
$$

or

$$
\begin{bmatrix}
\dot{i} \\
\dot{\chi} \\
\ddot{\chi}
\end{bmatrix} = \begin{bmatrix}
0 & 0 & 1 \\
\end{bmatrix} \begin{bmatrix}
i \\
x \\
\dot{x}
\end{bmatrix} + \begin{bmatrix}
0 \\
0 \\
\frac{I(F(t) - F\_s)}{2\pi I\_{\rm eff}}
\end{bmatrix} \tag{14}
$$

The MATLAB®/Simulink models corresponding to (7) and (14) were developed to predict the voltages and currents for various load resistance *RL* that both the EM generator systems with rack pinion and lead screw could generate. The Simulink model of the system with lead screw is presented in Figure 7. With the selected parameters shown in Tables 1 and 2, the simulation results were compared to the corresponding test results as illustrated in Figures 8 and 9 (The test procedure will be described in Section 2.1.4.). Figures 8 and 9 show that the analytical models accurately predict the magnitudes of the voltages and currents generated by the EM generator. The voltage and current signals in Figures 8 and 9 can be divided into two stages according to the movement, i.e., forward and return stages. In the forward stage, ~0.2–0.8 s, the floor-tile moves downwards when the footstep-force applied, causing the generator to rotate in one direction and hence induce negative voltage and current as shown in Figures 8 and 9. During 0.2–0.8 s, the floor-tile might reach the lowest position, causing the generator to stop the rotation and induce no voltage and current before the return stage begins. In the return stage, ~0.8–1.4 s, the floor-tile moves upwards to the equilibrium position according to the restoring spring forces and drives the generator to rotate backward and induce positive voltage and current as seen in Figures 8 and 9. Note that in Figure 9, there exists the small humps of the predicted voltage and current during 0.6–0.8 s. These signals correspond to the applied force at the same interval when the floor-tile is moving downwards. The discrepancy of this analytical prediction and the test result might be because of the difference between the actual force and the force function in Figure 4.

**Figure 7.** Simulink model for the electromagnetic (EM) generator with lead-screw design.


**Table 1.** Rack-Pinion Parameters.

**Table 2.** Lead-Screw Parameters.


**Figure 8.** Voltage and Current of Rack-Pinion Model from Experiment and Simulation. (**a**) Voltage of Rack-Pinion Model. (**b**) Current of Rack-Pinion Model.

**Figure 9.** Voltage and Current of Lead-Screw Model from Experiment and Simulation. (**a**) Voltage of Lead-Screw Model. (**b**) Current of Lead-Screw Model.

In summary, the induced voltages and currents for both EM-generator designs predicted by the analytical models were compared in Figure 10. Then the performances of the two EM-generators were predicted and summarized in Table 3. The results mainly show that the designed systems generate an averaged 216–886 mJ of electrical energy per footstep, or the averaged power of 216–590 mW. It is sufficient to power electronic devices with low power consumption in the vicinity, such as sensors and communication instruments. This finding assures the possibility of building both of Genpath's prototypes. Moreover, the verified analytical models were used in the parametric design as presented in Section 2.1.3.

**Figure 10.** Simulation of Rack-Pinion and Lead-Screw Model. (**a**) Voltage of Rack-Pinion and Lead-Screw Model. (**b**) Current of Rack-Pinion and Lead-Screw Model.



#### 2.1.3. Design of Elements

The critical elements of the EM generator systems in Figures 2 and 3 were decided with the use of the analytical models to tune for the optimized parameters. Design of the elements such as the rack pinion and lead screw, the springs, the transmitted gears and the DC generator is summarized as follows.

The rack pinion and lead screw shown in Figures 2 and 3 are used to change the translation to rotation. A mechanism of the rack-pinion was first adopted in the first prototype [16] because of its availability and economy cost. The drawback of the rack-pinion mechanism arises from its coarse tolerance, resulting in large friction loss. In addition, only the rough-pitch models were found. Thus, for the rack's allowable displacement of 15 mm, the angular displacement of the pinion is very limited. Therefore, the EM generator system using the rack and pinion is inefficient for harvesting energy from the footstep with limited displacement. To improve the design of the movement converter, the rack-pinion mechanism is replaced by the lead screw in the second prototype. The lead screw has more variety in dimensions for the selection. With finer pitch or smaller lead angles, the angular displacement of the lead can be extended with the limited stroke of the nut. Two sets of the lead angles, i.e., 45◦ and 60◦, were selected and installed to the 24-V-DC-generator system for the comparison. Table 4 presents the energy produced by the generator, when connected to 49-Ω resistance load, for three different designs of the movement converters: the rack pinion, the lead screw with 60◦ lead angles and the lead screw with 45◦ lead angles. It was found that the EM generator system with the 45◦ lead screw produces the highest level of energy among the three designs. With the smaller value of the lead angles, the lead proceeds to larger angular displacement within the same limited stroke of 15 mm, resulting in the greater period for the generator to spin. Therefore, the accumulative energy the generator provides is higher.

**Table 4.** Comparison of Rach-Pinion, Lead-Screw (60◦ lead angles) and Lead-Screw (45◦ lead angles) Average Energy.


The spring and transmitted gears are also the parts critical to harvest the energy. The softer spring is preferable in the design. For the explanation, Figure 11 shows the predicted voltages and currents for the two EM-generator systems varying in the stiffness coefficients. The softer spring, with less value of stiffness coefficient, results in the higher levels of the voltage and current in the forward stage, and hence yields the greater power in harvesting. The softer spring inserts less restoring forces and causes the floor-tile to move down with higher speed that is converted to a higher rotational speed of the generator. With more speed, the generator can produce more power. Although the softer springs are theoretically desirable, they should be sufficiently hard enough to restore the system back to equilibrium due to the friction of the system. To satisfy such conditions, the optimized springs with the wire diameter of 2.2 mm or the stiffness of 40 kN/m were selected.

**Figure 11.** Simulation of Lead-Screw Model with Soft and Hard Springs. (**a**) Voltage of Lead-Screw Model with Soft and Hard Springs. (**b**) Current of Lead-Screw Model with Soft and Hard Springs.

Moreover, the sets of gear train and bevel gears in Figures 2 and 3, respectively, are used to transmit the rotation from the movement converters to the generator's rotor. The gear ratio larger than 1:1 can help increase the speed of the generator. However, the increase of the gear ratio is limited by the amount of the resistance force in the system. The increase of the gear ratio leads to the greater frictions and the greater resistance torque provided by the generator. If the resistance force exceeds the applied force from the footstep, the floor-tile will not move. Consequently, the maximum gear ratio of 4:1 is designed for the rack-pinion system and originated from a pinion's 6 cm diameter and transmitted to a gear's 1.5 cm diameter as shown in Figure 2. In addition, the maximum gear ratio of the bevel gears in Figure 3 for the lead-screw system is set to 1:1.

The DC generator was used in the design for simplicity. In order to generate at least 3.3 V for operating the micro-controller, the typical 12-V or 24-V-DC-motor generator was selected to ensure such criteria. To choose a proper DC generator's speed, the kinematic relation of the transmission system was analyzed. With the maximum value of 20 mm displacement for safely walking, the maximum value of the angular velocity is obtained at 210 rpm. Hence, the model of a motor generator with a 300 rpm rated speed was selected. Two types of the DC generators, 12 V and 24 V with the properties shown in Table 5, were installed in the second prototype of Genpath for comparison of their performance. The induced voltage and current for both types of the DC generators are compared in Figure 12. The energy per footstep produced by the DC generators for various rated load resistances are shown in Table 6. The 12-V motor provides the energy as much as 2.5 times that of the 24-V motor because of the resistance during the transience.


**Table 5.** Comparison of 12- and 24-V-DC-Generator Parameters.

**Figure 12.** Comparison Voltage and Current of Lead-Screw Model with 12– and 24–V-DC Generator. (**a**) Voltage of Lead-Screw Model. (**b**) Current of Lead-Screw Model.

**Table 6.** Energy per footstep produced by the DC generators for various rated load resistances.


In conclusion, the analytical models developed in the previous section were utilized to obtain the best-fit design. First, the simulation results show that both the rack-pinion and lead-screw models yield about the same maximum power, according to the same levels of both voltage and current magnitudes as seen in Figure 10. However, the simulation results in Figure 10 also indicate that the lead screw provides the longer time in movement and yields the larger angular displacement of the rotor within the limited stroke. This results in more time for the generator in the lead-screw design to generate power. It was also found that the lead-screw design with the finer pitch or, i.e., 45◦ lead angles, provides the highest energy per step. Second, although the simulation results show that the softer spring could provide higher power in the forward stage, the harder spring with the optimum stiffness value of 40 kN/m was selected to enable to restore the system back to equilibrium. Finally, the 12-V-DC generator, compared to the 24-V-DC generator, gives a better performance probably because of the lower resistance during the transient, as the properties show in Table 5.

#### 2.1.4. Development of the Prototypes

Figures 13 and 14 show the two prototypes of Genpath built with the key components as listed in Table 7. Prototype-I [16] was installed with the 24-V-DC generator and uses the rack pinion for the movement converter. Prototype II is the improved prototype built with the lead screw for the movement converter and the 12-V-DC generator. The experiment was then performed to test the prototypes' performances as shown in Figure 15. First, each prototype was connected to the rated resistor *RL* to provide the maximum power output. Then the voltage across *RL*, the current *i* and the corresponding electrical power when a normal footstep is applied were measured using an oscilloscope and a current probe. The test results are shown in Figure 16 and summarized in Table 8. Genpath prototype-II with 12-V-DC generator and lead-screw mechanism was significantly improved when compared to the prototype-I [16]. It stated in Table 8 that the latest Genpath prototype produces an average energy of 702 mJ (or average power of 520 mW), the maximum voltage of 9.5 V and the maximum current of 285 mA per footstep in the duration of 1.35 s. The energy provided by the EM-generator in Genpath's prototype-II was increased by approximately 184% when compared to that of the prototype-I [16]. The efficiency of the EM-generator system is 26% based on the power generation from the heel strike of a human's walk of 2 W per step. This amount of energy could sufficiently power typical low-power electrical devices, as previously described.

**Figure 13.** Photograph of Rack and Pinion Prototype.

**Figure 14.** Photograph of Lead-Screw Prototype.


**Table 7.** Components of rack and pinion and lead-screw prototypes.

**Figure 15.** Test Set up Diagram for the Prototypes.

**Figure 16.** Comparison Voltage and Current of Prototype I and Prototype II. (**a**) Voltage of Prototype I and Prototype II. (**b**) Current of Prototype I and Prototype II.


**Table 8.** Performances of Genpath prototypes I and II.

#### *2.2. The system of Power Management and Storage Circuit*

The power management and storage (PMS) circuit was designed to convert and store electrical energy at the same time. Figure 17 shows the circuit diagram and the real-world circuit is depicted in Figure 18. From the performance test of Genpath as shown in Figure 16, it is clearly seen that the generated voltage and current waveform are AC signals. Negative portions occur when a footstep is applied, causing the generator to rotate in one direction. Positive portions occur during the restoration period, resulting in the opposite direction of the generator's rotation.

**Figure 17.** Circuit Diagram of Power Management and Storage System.

**Figure 18.** Real-World Circuit of Power Management and Storage System.

The energy from the generator is stored to a 6-V, 4.5-Ah battery through a two-stage power converter. First, the active bridge rectifier converts the AC voltage to the DC voltage. Since the metal–oxide–semiconductor field-effect transistors (MOSFETs) used in the rectifier have extremely low turn-on resistances and junction voltage drops, this kind of rectifier can perform with high efficiency. Second, the buck-boost converter helps convert the variable DC voltage from the rectifier to the battery. This buck-boost converter is operated in accordance with a matching-impedance control scheme which paves the way for the maximum power transfer. In this scheme, the reactance term by inductance is assumed to be small and is neglected from the calculated impedance. This assumption is valid by investigating the value of inductance in Table 5 and the low-frequency AC voltage exhibited in Figure 19b. (Figure 19a shows the output voltage and current without power management and a storage circuit.) The reactance is, therefore, insignificant in comparison with the resistance and

it is neglected in the impedance-matching control scheme for the sake of simplicity. This control scheme is implemented with the microcontroller PIC16F1776 which includes the extreme low-power consumption feature. (Note: the input force to the prototype II in this section is different from the previous section due to the environment setup.)

**Figure 19.** Experimental result showing the operation of power management and storage circuit; *vt* and *it* are outputs of generator; *vi* and *ii* are outputs of the rectifier circuit; *vo* and *io* are outputs of the buck-boost circuit.

The experiment is conducted to evaluate the performance of the two-stage converter. The AC voltage is efficiently rectified; the efficiency of active bridge rectifier is about 95.78%. Figures 19b and 20b show the operation of the buck-boost converter along with the impedance matching control scheme. The converter helps charge the power into the battery and the control scheme can match the impedance to achieve the maximum power transfer. The power management system is capable of gaining the averaged power of 280 mW from each footstep and storing the accumulative energy of 302 mJ into the battery at the output stage. The efficiency of the buck-boost converter is about 78.00%, thus the overall efficiency of the power management system is 74.72%. Table 9 gives the detailed performances of power management and storage system for each footstep. If comparing the Genpath prototype II with the commercial product such as the Pavegen's system, the Pavegen's system which has three generators per tile can generate the energy approximately 2 J per step and the Genpath prototype II which has one generator per tile can generate the energy approximately 0.3 J per step. The Genpath prototype II generates the energy approximately 6 times less than that of the Pavegen's system. Even though it cannot generate as much energy as the commercial one, the Genpath prototype II is developed based on open hardware which is easy to access and build. The mathematical model of the system exists. Thus, it is possible to develop Genpath's system in any community to generate more energy in the future.

(**a**) Power and Energy without Power and Storage Management Circuit.

Storage Circuit

**Figure 20.** Experimental result showing the operation of the power management system regarding the process of power conversion and energy storage; *Pt* and *Et* are power and energy outputs of the generator; *Pi* is power output of the rectifier circuit; *Po* and *Eo* are power and energy outputs of the buck-boost circuit.


**Table 9.** Performances of power management and storage circuit with Genpath prototypes II and 12-V-DC generator.
