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Smart Mater. Struct. 20 (2011) 105020 (7pp) doi:10.1088/0964-1726/20/10/105020

An earthworm-like actuator usingsegmented solenoids

Bu Hyun Shin1, Seung-Wook Choi1, Young-Bong Bang2 andSeung-Yop Lee1,3

1 Department of Mechanical Engineering, Sogang University, 1 Shinsu-dong, Mapo-gu,Seoul 121-742, Korea2 Advanced Institutes of Convergence Technology, Seoul National University 864-1, Iui-dong,Suwon-si, Gyeonggi-do 443-270, Korea

E-mail: sylee@sogang.ac.kr

Received 22 December 2010, in final form 21 June 2011Published 31 August 2011Online at stacks.iop.org/SMS/20/105020

AbstractA biomimetic actuator is developed using four segmented solenoids mimicking earthwormlocomotion. The proposed actuator not only has a simple structure composed of cores and coils,but also enables bi-directional actuation and high speed locomotion regardless of frictionconditions. We have implemented theoretical analysis to design the optimal profiles of inputcurrent signal for maximum speed and predict the output force and stroke. Experiments using aprototype show that the earthworm-like actuator travels with a speed above 60 mm s−1regardless of friction conditions.

S Online supplementary data available from stacks.iop.org/SMS/20/105020/mmedia

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Recently, there has been increasing research on worm-likelocomotion mechanisms for medical endoscopes, rescue robotsand industrial inspection systems [1, 2]. Various segmentedlocomotion designs have been adopted in order to mimicthe crawling mechanism of soft-bodied creatures includingearthworms and inchworms [3].

There have been many attempts to develop worm-like locomotion mechanisms by adopting various types ofactuators. In general, piezoelectric materials, shape memoryalloy (SMA), magnetostrictive materials, electromagneticactuators and electroactive polymers are used. Variouspiezoelectric actuators using earthworm locomotion show fastresponse and large output force [4, 5]. However, they requirehigh voltage to implement satisfactory performance. Shapememory alloy (SMA) has an advantage in the aspect ofsimple structure, but low speed and slow response are itsdrawbacks [6]. Menciassi et al [7] have developed an SMAactuated segmented micro-robot, and experiments with a bodylength of 3 cm show that the maximum speed is 2.5 mm s−1.

3 Author to whom any correspondence should be addressed.

Dielectric elastomers have been used for the biomimetic softactuations [8–10], but the polymer based actuators producesmall output forces. Magnetostrictive materials have been alsoadopted for worm-like linear and rotary actuations [11, 12].

Electromagnetic actuators have many advantages suchas fast response, simple control law and low manufacturingcost. Crawling locomotion by an electromagnetic actuator usesimpact-driven force or stick–slip motion. An impact-drivenmechanisms using a coil and a permanent magnet has fastmoving speed and bi-directional motion [12–14]. However,the moving speed by the impact-driven mechanism becomesslower for higher friction. Stick–slip based locomotion usesa solenoid and a permanent magnet and travel is based onattractive and friction forces rather than impulse [15]. Stick–slip locomotion has also been developed using a slotlesstubular linear motor [16]. However, bi-directional actuationis impossible in the worm-like locomotion mechanism.

In this paper, a new earthworm-like locomotion mech-anism is proposed using four segmented solenoids. Theproposed actuator has a simple structure composed of coresand coils, but it enables bi-directional, high speed locomotionregardless of friction conditions. We have implementedtheoretical analysis to design the optimal profiles of input

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Figure 1. Schematic diagram of an earthworm-like locomotionmechanism using segmented solenoids.

current signal for maximum speed and predict the output forceand displacement. A prototype of four segmented solenoidswith a length of 48 mm is manufactured to verify the theoreticalpredictions.

2. Theoretical analysis

2.1. Locomotive mechanism

The objective of this research is to develop an artificialactuator mimicking the locomotion of an earthworm with asegmented body. Figure 1 shows a schematic diagram of a newearthworm-like locomotion mechanism with four segmentedsolenoids. The strongest advantage of using a solenoid as anactuator is that both the direction and the magnitude of theelectromagnetic force can be easily controlled by changing theinput current to the solenoid.

The proposed actuator with four segmented solenoids hasfour steps to complete a cycle of earthworm-like locomotion.The ends of each solenoid act like south and north poles. Thepoles of the four solenoids at each step of a cycle are shownin figure 1. At step 1, there is a repulsive magnetic forcebetween the first and second segments and there are attractivemagnetic forces between the others. If the repulsive force islarger than the friction force at the first segment, it moves to theleft only. The other three segments work as one body combinedby the attractive forces between them. If the total repulsiveforce of the three segments is smaller than the friction force,the segments remain still. At step 2, the first segment hasan attractive force because of the pole change in the secondsolenoid. If the attractive force is smaller than the friction forcein the first segment, it is stalled. The second segment has anattractive force with the first segment but a repulsive one withthe third segment with the same direction. If the total magneticforce of the second segment is larger than the friction force, thesegment moves left. The other two segments work as one bodyby the attractive force between them. If the repulsive magneticforce of the two segments is smaller than the friction force, thesegments remain stationary. At step 3, the third part moves

left and the others keep still. The other force distributions aresimilar to those in step 2. At step 4, the last segment movesleft, and one cycle of locomotion finishes.

2.2. Dynamic model

Three different forces, namely attractive, repulsive and frictionforces are applied in the segmented actuator mimickingearthworm locomotion. The electromagnetic attractive andrepulsive forces depend on the gap between each segment.The friction force is assumed to be constant during motion.According to the free body diagram shown in figure 1, theequation of motion by Newton’s second law is (1)

md2x

dt2= Fma(x, t) + Fmr(x, t) − Ff (1)

where m is the mass and x is the displacement of eachsolenoid. Fma and Fmr are the electromagnetic attractive andrepulsive forces, respectively. Previous works assume thatthe electromagnetic forces are constant [15]. However, theelectromagnetic forces Fma and Fmr depend on the distancesbetween solenoids. The friction force Ff depends on thevelocity of the actuator segment as (2)

Ff =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

Fm if v = 0 and Fm < μsmgμsmg if v = 0 and Fm = μsmgμkmg if v > 0

−μkmg if v < 0.(2)

Here v is the velocity of the solenoid. Fm = Fma + Fmr is thetotal electromagnetic force. μs and μk are the static and kineticfriction coefficients. Generally, the kinetic friction coefficientis about 0.7 times of the static one. In order to solve thenonlinear differential equation (1) directly, we use the principleof work and energy as (3)

12 mv

21 +

∫ x2

x1

{Fm(x) − Ff} dx = 12 mv22. (3)

Here v1 and v2 are the velocities at the positions x1 and x2 ofthe solenoid. In (3), the velocity and the electromagnetic forceare functions of the solenoid position. In order to maximize thelocomotion speed, we choose the optimal profile of the inputcurrent to each solenoid to meet the force conditions. Whena collision between solenoids occurs at the end of each stepof locomotion, it is assumed to be totally inelastic with therestitution coefficient of zero, causing the backward or reboundmotion to vanish.

2.3. Prototype design

A cross sectional view of the proposed actuator design is shownin figure 2(a). The outer diameter and length of a segmentcore are 10 mm and 12 mm, respectively. The total bodylength is 48 mm. The mass of a segment is 5 g and the totalmass is 22 g. The material used for the yoke is carbon steel(JIS S45C). The stroke of a solenoid segment is 5 mm; thatis the maximum gap between segments, because a larger gapdoes not guarantee a sufficient attractive force to cause the

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Figure 2. Design of the earthworm-like locomotion mechanismusing segmented solenoids: (a) cross sectional view, (b) prototypewithout adhesive tape cover and (c) prototype with adhesive tapecover.

next stroke. The prototype of the earthworm-like locomotionmechanism using segmented solenoids is shown in figure 2(b)and the prototype with its cover in figure 2(c). The cover isgreen fluorescent adhesive tape made by Shurtape Company.The coil diameter and the number of coil turns are chosen fromsimulation results. The coil is wound around the yoke to make480 turns.

2.4. Simulation and optimal design

For a segmented stick–slip mechanism considering friction, thetotal electromagnetic force must be within the following range:

μsmg < Fm < 3μsmg. (4)

In order to determine the appropriate electromagnetic forceat each step of locomotion, a finite element analysis of theactuator motion was conducted using the commercial softwareANSYS Workbench. The electromagnetic force depends onboth the input current and the gap between segments. First ofall, we determine the constant value of input current appliedto each solenoid at state 1 to satisfy the force range (4). Thesimulation result on the magnetic flux density at step 1 is shownin figure 3 when the input voltage and current are 5 V and0.75 A. The total electromagnetic force must less than theupper limitation (3μsmg = 147 mN, μs = 1) in (4). Asshown in figure 4(a), we choose the constant input currentto the first solenoid as 0.75 A at state 1 in order to haveFm = 150 mN. The input currents applied to the other solenoid

Figure 3. Flux density result using ANSYS Workbench at step 1 atan input voltage of 5 V.

Figure 4. Design parameters of the first solenoid at step 1: (a) inputcurrent, (b) electromagnetic force and (c) velocity.

segments are determined to meet the following two conditions.One is that the electromagnetic force of the first segment isequal to the total repulsive force of other three solenoids. Theother is that small attractive forces exist between solenoids2 and 3 as well as between solenoids 3 and 4, in order toavoid unwanted separation of solenoids 2, 3 and 4 after impactbetween solenoids 1 and 2.

Then the total electromagnetic force, depending on theposition of the first solenoid, is calculated and it is shownin figure 4(b). In order to obtain the approximated value ofthe position-dependent electromagnetic force at step 1, weimplement a curve fitting using force data at six differentspatial points to obtain the following third-order polynomialequation:

Fm = 577 638.8x3 − 2421.1x2 − 19.4x + 0.2. (5)By substituting (5) into (3), we obtain the duration and thevelocity of the first solenoid at step 1. We use a finite differenceanalysis for (3):

v2n(2) = v2n(1) + {Fm(x) − Ff}�x . (6)

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Table 1. Theoretical time steps at various friction conditions.

Frictioncoefficient

Duration atstep 1 (s)

Duration atstep 2 (s)

Duration atstep 3 (s)

Duration atstep 4 (s)

Duration of1 cycle (s)

Speed(mm s−1)

0.35 0.020 0.018 0.013 0.017 0.068 73.50.5 0.021 0.019 0.013 0.017 0.070 71.40.75 0.024 0.020 0.014 0.018 0.076 65.8

Figure 5. Profiles of input currents applied to each solenoid from thesimulation.

The first segment starts from rest and we divide the first strokeof 5 mm into 500 steps using the spatial distance �x =0.01 mm. We assume that the velocity is constant during eachspatial distance. The calculated velocity of the first solenoidsegment at state 1 is shown in figure 4(c), when the frictioncoefficient is kept at 0.75 uniformly. Finally we can determinethe duration of state 1 depending on the frictional conditionsfrom the velocity. We repeat a similar procedure to choose theinput current applied to each solenoid at other states in orderto calculate the resultant forces and durations of the solenoids.The duration of each step and the average velocity at variousfriction conditions are shown in table 1.

The time profiles of the input currents applied to allsolenoids over one cycle are shown in figure 5. The currentprofiles based on the duration of each step are slightly modifiedto maximize the locomotion speed in the experiment. Theelectromagnetic forces at six spatial points and the associatedcurve fitting results of third-order polynomials are shown infigure 6. The curve fitting results are (7) at step 2, (8) at step 3and (9) at step 4.

Fm = 6 880 033.5x3 − 32 134.1x2 + 22.2x + 0.163 (7)Fm = 25 194 796.8x3 − 130 336.1x2 + 206.5x + 0.245 (8)Fm = 17 759 999.7x3 − 84 870.5x2 + 165.9x + 0.123. (9)

Figure 7 shows the displacement of the first segment overone cycle using the current profiles in figure 5. In order toevaluate the effect of the position-dependent electromagneticforce on the locomotion speed, we compare it with the motioninduced by the constant electromagnetic force. We calculate

the averages of the electromagnetic forces applied to allsolenoids over one cycle in order to obtain the displacement ofthe first solenoid. Figure 7 shows that the discrepancy betweenthe two locomotion speeds is not negligible, meaning that theposition-dependent electromagnetic force must be consideredin the theoretical analysis of the locomotion.

3. Experiments

3.1. Experimental setup

We construct an experimental setup to measure the frictionforces of various materials using a load cell (CASTM PW4MC3), as shown in figure 8(a). Three friction conditions werechosen to test the earthworm-like locomotion mechanism usingsegmented solenoids. It was found from the experiment thatthe friction coefficients of the cellophane holder, fabric mousepad and fine sand paper are 0.35, 0.5 and 0.75, respectively.We use a laser displacement sensor (KeyenceTM LB 081) witha resolution of 0.008 mm to measure the displacement of theprototype in the experiments, as shown in figure 8(b).

The time interval of each step and the current switchingare manipulated by a microprocessor 8051 and a DAC. Usingan OP-Amp L272, the maximum current output allowed perport is 1 A. The supply voltage is ±5 V. The resistance of eachsolenoid coil is 6.4 � and the maximum current applied to eachcoil is 0.78 A.

3.2. Experimental results

Firstly, we measured the electromagnetic force of the firstsolenoid induced by the input current at step 1 as illustratedin figure 5. In figure 9, the experimental electromagneticforces depending on the gap are compared to the simulatedones in figure 6(a). Based on the similarity between thetheoretical and simulated results of the position-dependentelectromagnetic forces, the theoretical electromagnetic forcesshown in figures 6(b)–(d) can be reasonably applied to theother solenoids.

The input current applied to each solenoid and the timeintervals of four steps over one cycle are based on thetheoretical results in section 2.4. In the experiments, theoptimized time intervals are slightly altered to maximize thelocomotion speed based on the theoretical time intervals. It isnoted that the optimal profile of the input current can maximizethe moving speed regardless of the friction conditions. Thetime intervals are 0.022 at step 1, 0.020 s at step 2, 0.014 s atstep 3 and 0.019 s at step 4. The total duration of one cycle is0.075 s and the resultant stroke is 5 mm.

The experiments were conducted in three frictionconditions using the surfaces of a cellophane holder, a fabric

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Figure 6. Theoretical electromagnetic force depending on the gap: (a) first, (b) second, (c) third and (d) fourth solenoid.

Figure 7. Theoretically analyzed motion of the first solenoid at theμk = 0.75 condition.

mouse pad and #2000cw fine sand paper. We comparethe experimental results on the motions of the segmentedsolenoids with theoretical predictions using a high speedcamera capturing 600 frames per second. The captured imagesat each step are shown in figure 10. The difference between theduration of the input signal and the measured one is less than 1frame.

The experimental results on the motion of the first solenoidover five cycles at three friction conditions are shown infigure 11. The theoretically predicted stroke and velocity

Table 2. Experimental results on the average stroke and velocityover five cycles using theoretical time steps.

Frictioncoefficient(μk)

Averagestroke(mm)

Standarddeviationof stroke

Averagevelocity(mm s−1)

Standarddeviationof velocity

0.35 5.0 0.19 66.7 2.60.5 4.7 0.27 60.0 3.60.75 4.8 0.58 63.3 7.8

are 5 mm and 66 mm s−1 at all friction conditions. Theaverage strokes and velocities of the actuator over five cyclesusing both the theoretical and the optimized time intervals aresummarized in tables 2 and 3. The experimental strokes andvelocities are similar to the theoretical ones. In the case ofμk = 0.75, the stroke over a cycle is almost the same as thetheoretical prediction of 5 mm. However, for the other frictionconditions, the experimental strokes and velocities have smalldiscrepancies with the theoretical ones for higher cycles. It wasdue to this that we set the electromagnetic force in the rangeof (4) to meet a high friction condition in the design of thesolenoids. It is noted that the measured velocity is higher thanthe theoretical one at μk = 0.35. This is because the repulsivemagnetic force is larger than the friction force at each step. Theredundant repulsive force pushes the front segments forward.In the case of μk = 0.5, the measured velocity is smallerthan the theoretical one. Here the attractive magnetic force is

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Figure 8. Experimental setup to measure (a) the friction force and(b) the displacement of the first segment.

larger than the friction force at each step, and then backwardmotion occurs. For accurate positioning during locomotion, itis necessary to set the magnetic force and duration of each stepin an appropriate range of friction force. For high locomotionspeed, it is necessary to use a higher repulsive magnetic forcethan the friction force to cause the additional motion by impact.

Figure 9. Experimental result for the electromagnetic force of thefirst segment at step 1.

Table 3. Experimental results on the average stroke and velocityover five cycles using optimized time steps.

Frictioncoefficient(μk)

Averagestroke(mm)

Standarddeviationof stroke

Averagevelocity(mm s−1)

Standarddeviationof velocity

0.35 5.6 0.32 73.2 4.30.5 4.7 0.27 63.4 3.60.75 5.2 0.65 69.8 8.6

It is simple to change the locomotion direction of thesegmented solenoids for backward motion. The experi-mental result for bi-directional motion of the prototype isshown in figure 12 where forward and backward motionsof four cycles are implemented (see also supplementaryvideos for one-way and bi-directional motions, available atstacks.iop.org/SMS/20/105020/mmedia). From the experi-ments, it is confirmed that the earthworm-like locomotion

Figure 10. Captured images of the segmented solenoids using a high speed camera at μk = 0.35: (a) t = 0, (b) t = 0.021 s, (c) t = 0.041 s,(d) t = 0.057 s, and (e) 0.077 s.

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Smart Mater. Struct. 20 (2011) 105020 B H Shin et al

Figure 11. Experimental results on the displacement of the firstsolenoid at three friction conditions and comparison with theoreticalpredictions.

Figure 12. Bi-directional movement of the prototype in the μk = 0.5condition.

mechanism using segmented solenoids guarantees bi-directional,high speed actuation at any friction conditions.

4. Conclusion

The proposed inchworm-like actuator using segmentedsolenoids enables bi-directional, high speed locomotionregardless of friction conditions. Optimal selection of theelectromagnetic force and duration at each locomotion stepguarantees good positioning and velocity performance atany friction conditions. A prototype with a body lengthof 48 mm travels with a maximum speed of 73 mm s−1.The proposed earthworm-like locomotion mechanism usingsegmented solenoids is useful for micro-mobile robots formedical and industrial purposes.

Acknowledgments

This research was supported by the National ResearchFoundation of Korea funded by the Ministry of Education,Science and Technology (Grant No. 2010-0014718)

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1. Introduction2. Theoretical analysis2.1. Locomotive mechanism2.2. Dynamic model2.3. Prototype design2.4. Simulation and optimal design

3. Experiments3.1. Experimental setup3.2. Experimental results

4. ConclusionAcknowledgmentsReferences