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EAP-based actuator: modeling of snake robot.


In the last decades robotic researchers were interested on rigid linked robot design but the scenarios are changed nowadays. Heavy structured robot is not significant for light weighted robot design. Moreover bio-inspired robots become more attractive to the researchers for the further study of the light weighted mobile robot. In line with this requirement, artificial muscles are now most significant actuator for the robot design. Therefore, Electroactive polymer (EAP) is one of the smart material artificial muscles that change its structure after applying electrical power. EAP actuator is designed for snake robot application is illustrated in this paper. Once the electric power applied on the actuator it performs bending operation due to the ionic actuation [1]. The maximum bending happens based on the particular applied voltages. This ionic EAP is a thin polymer that is wrapped by two electrodes around it. The polarity of the power supply is responsible for the direction of the bending of the EAP actuator. Though it is very flexible for actuation but it generates very low force for the actuation [2]. However, the optimization of the amount of polymer and the design of the actuator will be going to new era of soft robotics in near future.

A compliant actuator model is proposed for performing large deflection and experimentally verified at the first place. In line with the actuator model, an electroactive polymer based actuator fabrication procedure is illustrated in this paper. Finally a set of result is shown for the actuation of the EAP actuator which able to perform large deflection according to the proposed design.

2. Modelling of the Compliant Actuator:

The first behavior about the compliant actuator is that the bending configuration is symmetrical both at small and large deflections. For small deflections of a beam, often a linear relationship between angle, deflection, and force is enough to model the behavior, but with large deflections the problem clearly becomes nonlinear. For such nonlinear systems, finite element analysis is normally conducted. However, in this proposed model the pseudo-rigid-body modeling technique is chosen which was outlined by Howell [3].

A free body diagram is analyzed as shown in figure 1 to determine the loads and moments that are acting on the beam. The free body diagram of the model is shown in Fig. 3. Due to its symmetric nature it will orient the beam sideways so the left side would be symmetric to the right.

The beam, therefore, is undergoing both compressive force as well as a moment. The forces on both sides will be the same, which will be exerted by the tension of the spring, while the moment will also be equivalent on both sides. This moment is determined by multiplying the tension of the cable by the perpendicular distance from the line of force to the end of the beam. The pseudo-rigid-body equivalent model for this configuration therefore is created by attaching three rigid beams with two springs and is shown in figure 2.

The motivation then of using this pseudo-rigid-body is to find the horizontal and vertical deflections of the beam given a desired angle between the two platforms. That is, going back to the original upright diagram, the model should be able to determine the x-y deflection of the center of the upper platform that will result in a desired angular deflection of that same platform. Likewise, the model should also determine the amount of force that shall achieve such a configuration.

To start the analysis, the contributions of moment and force must be separated. Moments cause a uniform circular curvature when applied to a beam, and hence the known moment component will create a particular curvature in the beam. This curvature is then referred to as the initial curvature, and the system is treated as if a force is acting upon an initially curved beam [4]. However, since the breakdown of the moment and force aspects are not known. From this initial guess of the curve, Ko, both guesses for the force and initial positions can be made.

[F.sub.o] = 2[[kappa].sub.o]EI/wlsin [theta]/2 (1)

where l = original length of compliant beam, w = length of the platform, and 9 = desired angular deflection oftlie platform.

[a.sub.i] = 2l/[[kappa].sub.o] sin [[kappa].sub.o]/2 (2)

[b.sub.i] = l/[[kappa].sub.o] (1 - cos [[kappa].sub.o]) (3)

The pseudo-rigid angle associated with the initial curve is then given by

[[THETA].sub.i] = [tan.sup.-1] (2[b.sub.i]/[a.sub.i] - l(1 - [gamma])) (4)

The parameter [gamma] determined by the value of the initial curvature [4], and is used also to determine the characteristic length m.

m = (1 - [gamma])l (5)

The second parameter, [rho], is determined by the initial positions and parameter [gamma], which in turn determines characteristic length s.

[rho] = [{[[[a.sub.i]/l - (1 - [gamma])].sup.2] + [(2[b.sub.i]/l).sup.2]}.sup.1/2] (6)

s = [rho]l (7)

Using these values, the final pseudo-positions are determined.

a = 2l(1 - [gamma] + [rho]cos[THETA]) (8)

b = [rho]l sin[THETA] (9)

As mentioned earlier the pseudo-rigid angle is related to the true angle by a parameter known as c, the parametric angle coefficient [5].

[theta] = c[THETA] (10)

From here we continue to solve the problem using the stiffness coefficient, which is in fact a behavior dependent upon the initial curve [6].

K[THETA] = 2.568 - 0.028[[kappa].sub.o] + 0.137[[kappa].sub.o.sup.2] (11)

The effective spring constants of the two springs are therefore determined from the stiffness coefficient.

K = 2[rho][K.sub.[THETA]] EI/l (12)

Finally, from this, the effective force and the maximum stress are determined.

F = K([THETA] - [[THETA].sub.i])/b (13)

[[sigma].sub.max] = [+ or -] Fbc/I - F/A (14)

In this particular problem with a beam of rectangular cross-section, A would be the cross-sectional area, while c would be half of the cross-sectional beam height.

3. Design and Development of EAP Based Actuator:

The EAP cantilever beam model is developed in this research. The EAP beam is subjected to be deformed by the applied voltage. The designed model is indeed a single actuator model of snake robot. The design process started with different models and architecture. Most of the designs that initially developed seemed too specific; that is, only applicable for the particular task in question. Hence, the developing modular design would provide the building blocks for more complicated structures. In fact, a simpler design is easy to fabricate and mass produce, and hence a more attractive alternative. The design is based on the cross-section of an I-beam as shown in figure 3, where the upper and lower portions of the "I" would be relatively thick to maintain rigidity while the central vertical column would be much thinner to enable compliance. From the upper platform to the lower, an actuator would be added. In the smart material actuator application this could possibly be a perfect selection of actuator design. Furthermore, the single unit of the mechanism can be linked to form a chain to achieve a wider range of motions, especially for snake robot application. The modular units can also be linked in an orthogonal configuration such that two or more units can be put together to traverse a surface.

Two metallic electrodes either platinum or gold are responsible to attached by the two sides of the polymer which is known as Electroactive polymer (EAP). The Nafion polymer membrane substrate is used in the EAP actuator. This substrate will activate once the electrical charge applied on it, the ion will dope to perform the shape changing of the EAP. Several steps are required to fabricate the EAP which is time overwhelming procedures. The general process is depicted in figure 4. The EAP-based actuators are fabricated from 1mm thick Nafion polymer membrane. The thickness is chosen based on the better actuation force and perfect bending operation. There are three divisions for the ionic EAP fabrication procedure. At first the procedure will start by polymer sample cleaning. Then the electrodes will attach with the membrane like a sandwich and keep the EAP actuator in the sulfuric acid solution. Finally clean the EAP and mix it with salt solution for ionic exchange.


In the MATLAB environment, to achieve an error rate of 0.1% only nine iterations were performed to find the simulation of the EAP actuator. The proposed algorithm is used to find the full range of motion of the compliant beam of the actuator. Calculations are done based on the proposed model, where the length of the Though the iterative method for solving the non-linear behavior at high-deflections gave positive results, the results were off for smaller deflections. In figure 5 a comparison of the linear and non-linear solutions is shown for the range of motion. Figure 6 shows the solid model of the EAP that performs the bending in both directions.

An experiment was conducted after successfully simulated the proposed model. The mechanical parameters of the EAP are stated in the Table 1. The alignment of the EAP actuator is fixed at 0, 0 to the x-axis. Room temperature was set for the experiment. Fig. 6 shows the EAP model for the experiment. MATLAB was used to perform the input-output parameters of the EAP actuator. The amplified signal generator controller was used to perform this operation. The EAT actuator's position was monitored by the kinect video system, which allows for 32 frames per second. The operated frequency is shown in Fig. 7 which was used in the controller for large deformation.

In the actuation system of a snake actuator, a 30 mm long, 5mm wide, and 1mm thick EAP is developed for the actuation because the primary concern in the design is actuation and the bending response. However, the actuation system should be able to produce a desired deflecting angle for a successful bending device. A flexible bending actuation system is shown in Fig. 7. Fig. 8 shows the operating frequency of the controller used in the experiment. A simulation result of the EAP deflection is shown in Fig. 9 for 3 seconds in positive direction alone the y axis and the negative direction for another 3 seconds from the origin.

The actuation system is applied to the attached rigid frame system. By attaching the actuator in series configuration, it may perform sinusoidal wave to mimic snake locomotion. Finally a series of implementation and verification of the EAP actuator has been performed for 60 seconds. Fig. 10 shows the bending performance of the EAP where each of the snap is depicted in 0 sec and 3 sec. In the Fig. 10, a large deflection is observed for EAP actuator which is compliant with the snake robot actuation system. Fig. 11 shows the results of EAP's experimental bending application, where the deflection lines are captured using image frame.

Using the image processing system, the bending deflection measurement was conducted for EAP actuator [7]. The displacement they achieved is 20 mm by applying 5V, though they were performed more bending displacement by applying more voltage. As shown in Fig. 11, the maximum of 5V was applied and 23 mm of displacement was achieved. However, the flexible four-bar mechanism with EAP patches was designed [8]. The deflection deviation was found about 1 mm in coupler paths occurred due to backlash in joints of prototype, These devices can be used in the form of prosthetic, skeletal and artificial muscles devices [9-11]. Also, we need to consider the mechanical design issues such as lightweight and small size with flexible behaviour etc [12-13].


A unique method of modelling and designing of an EAP-based actuator has been shown in this research. The results from the simulation and actual experiment validate the efficacy of the proposed method. At first a compliant mechanism has been developed to model a compliant actuator. A detail modelling has been demonstrated to fabricate an EAP actuator. The actuator has shown the large deflection by applying the maximum voltage of 5V. Furthermore, when it comes to the specific EAP actuator design presented in this paper, final studies need to be conducted regarding the structure. Such studies would only truly be conclusive for snake actuator mechanisms. Some of the characteristics that would have to be determined would be the maximum force delivered by the proposed actuator so as to determine the maximum achievable deflection for EAP actuator application. The main contribution is to show that the EAP actuator design enable the simplest way of robot modelling.


Article History:

Received 28 September 2015

Accepted 15 November 2015

Available online 24 November 2015


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(1) Mohiuddin Ahmed and (2) Md. Masum Billah

(1) College of Computer Science, Jazan University, Saudi Arabia

(2) Department of Mechatronics Engineering, International Islamic University Malaysia

Corresponding Author: Mohiuddin Ahmed, College of Computer Science, Jazan University, Saudi Arabia

Tel: +966 545344271 E-mail:

Table 1: Illustration oftlis operating signal.

Parameters               Value

Applying Voltage (V)     5
Maximum Frequency (Hz)   9
Minimum Frequency (Hz)   0.01
Operating tUne (Sec)     60
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Author:Ahmed, Mohiuddin; Billah, Md. Masum
Publication:Advances in Environmental Biology
Article Type:Report
Date:Nov 1, 2015
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