社団法人 ஢子情報通信学会
THE INSTITUTE OF ELECTRONICS,INFORMATION AND COMMUNICATION ENGINEERS

信学技報
TECHNICAL REPORT OF IEICE

ダブルコイル機構を用いたリニアアクチュエータ
野間春生

柳田康幸

鉄ૌ信二

ATR メディア情報科学研究所〒619-0288 京ற府京޸奈学研ற市光台 2-2-2
E-mail: {noma,yanagida,tetsutani}@atr.co.jp
あらまし 二重螺旋構造に巻いたコイル間のৌ஢気力を利用したリニアアクチュエータの開発を進めている。提案するアクチュエータはコイル２個を同ࡃに巻き込んだものであり、コイルをコンデンサーの஢極として機能させることで、極間にৌ஢気による吸引力を発生させる。このৌ஢気力とコイルのバネとしての機械的弾性力のバランスによって巻き方向にリニア駆動可能なアクチュエータとして実現することを目指している。この構造により柔ఫなリニアアクチュエータの開発が期待される。本稿では、アクチュエータ自体の実現性を検証するために、஢気的、および、機械的なモデルを検討した。ࠟ作コイルによる実験では機構全体の振動現象が観測されたが、十分な伸縮効果は観測されなかった。また、モデルにスケールファクターを導入し、本提案が有効に機能するスケールについて検討を加えた。
キーワード リニアアクチュエータ、バーチャルリアリティ、ৌ஢気力

Development of the New Linear Actuator Using Double Coil Structure
Haruo NOMA

Yasuyuki YANAGIDA andNobuji TETSUTANIATR Media Information Science Laboratories
2-2-2 Hikari-dai, Keihanna, Science City, 619-0288, Japan
E-mail: {noma, yanagida, tetsutani}@atr.co.jp
Abstract
Double-coil actuators are based on the concept of electromagnetic field-induced deformation between twocompliant electrodes. With the coil configuration, the double-coil actuators can be bended easily, which make them applicable
to use as the wearable actuators. Both electrical and mechanical characteristic of the proposed actuators were investigated byusing the simplified simulation model in order to find the relationship between the applied voltage to the double-coil actuatorand the force and strain response conducted inside the coil. In experiment, even the experimental results were not as same as
the expected results obtained from simulation model, but some strain response can be observed. Further investigation on thescale and mechanical characteristic of the coil should be made to find out the suitable scale for the real application.
Keyword: Linear actuator, Virtual reality, Electrostatic attraction

1. Introduction
During the past few years, various types of actuator weredeveloped to satisfy the demand of the particular applicationsuch as the muscle-like actuators for small robots [Kornbluhet al. 1995]. The double-coil wearable actuators, inparticular, are a type of flexible linear actuators that has
demonstrated the strain response in a short response time.
This unique performance combined with other factors suchas low cost, and simple operational characteristic suggests
many potential applications.
First, the basic background and proposed model of the
double-coil actuators were introduced in chapter 2. The
simplified electrical and mechanical model of the proposed
actuators using in the simulation were discussed,respectively. Next, the shrinkage in distance of double-coildue to the electromechanical force was calculated. Then, theexperimental results were explained in chapter 3, andfollowed by the simulation results for the relationshipbetween the applied voltage and the force and strain
response in chapter 4. Finally, the conclusion and discussion
was stated in chapter 5.

2. Model of a double coil actuator
2.1 Basic BackgroundThe double-coil actuators operate on the simple principle
as shown in Fig.1. When a voltage is applied across thecompliant electrodes, the electromagnetic force (Fe), as
shown in equation (1), is generated and results in shrinkage
in separation between two electrodes. When apply thevoltage across the two compliant electrodes, theelectromagnetic force generated is described by thefollowing equatione AV 2Fe = 0 22d(1)Where,_0: Permittivity of air (Farad/m)
A: Area of Compliant electrode (m2)
d: Distance between
two electrodes (m)†V: Applied Voltage (Volt)e0 (2N -1)AV 2
2d 2(2)

Where,
A: Area of 1 turn coil (m2)
N: Number of turn of each coil†

2.3 Mechanical Model
The simplified mechanical model using in the simulation
was shown in Fig.3.
The total spring constant of the double-coil actuator (k(tot))
from the mechanical simplified model is:

V+d+++(3)Where,
k: equivalent spring constant of each turnfor each coil (N/m)
N: Number of†turn of each coilFm(tot ) = k(tot )Dx(4)
Where,
Dx: shrinkage distance of the double-coil (m)2.4 Shrinkage Distanceof Double-Coil Actuator†In order to investigate the shrinkage distance of thedouble-coil actuator, both electrical and mechanic
characteristic of the coil must be considered. The simplified
model of double-coil, which considers both electrical andmechanical force is shown in Fig.4.
For equilibrium equation under stable condition:

Fe = Fme0 (2N -1)AV 2= k(tot )Dx
2d 2+(5)(6)† that shrinkage distance (Dx) is enoughHere, we supposed
smaller than coil length (Nd).Then, the shrinkage distance ofthe double-coil†
actuator (Dx) is:e0 (2N -1)AV 2
Dx =2k(tot )d 2

Fe-2kNThe derived total electrical force (Fm(tot)) conducted insidethe double-coil actuator based on the above model is:

2.2 Electrical Model
In order to simplify the simulation model, we considered
the electrical and mechanical characteristic of the doublecoil actuator separately.
The simplified electrical model used in the simulation wasshown in Fig. 2.
The derived total electrical force (Fe(tot)) conducted insidethe double-coil actuator based on the above model is:

Fe(tot ) =k(tot ) =(7)3. Experimental Results†----Fig. 1. Electromagnetic force (Fe) conducting
between two compliant electrodes

In order to verify the simulation model, we performed theexperiment using the following configuration.
-Width of the coil: 4 mm.
-Number of turn (N): 35 turns-Area (A) : 4.0212*10-4 m-2-Separation (d) : 1 mm.
-Spring Constant (k) : 58.96 N/mVdVVd(a) Physical Model(b) Physical Simplified Model(c) Electrical Simplified Model
Fig. 2. Electrical simplified model of double-coil wearable actuator2kkk(a) Physical Modelkkk

each spring
constant “k”
represents
one of 1 turnof each coil.

(b) Mechanical Simplified Model

Fig. 3. Electrical simplified model of double-coil actuatora) The simplified model
When the applied voltage is offb) The simplified model with electricaland mechanical force when voltage is onFig.4 The shrinkage distance (Dx) of double-coil actuator causedby the resultance force among electrical and mechanical force.
-Applied Voltage (V): 0-8 kVolts
According to the above configuration, the expectedshrinkage calculated by using the proposed simulation
model is 0.0131 m. Anyway in the real experiment, wecannot obtain the shrinkage as much as we expected. When
we applied high voltage to the experimental coils, thedouble-coil moves suddenly. Even we held the high voltage
for a while, the coil still shaking and not stable enough tomeasure the shrinkage.

4. Simulation in different scale
Since we could not obtain the good experimental results
by using the double-coil actuator prototype, some of thesimulation model considered other scales of the double-coilactuator was constructed. From the derived equation (2);
FromFe(tot ) =e0 (2N -1)AV 2
2d 2(8)Here we consider s times bigger or smaller configuration
than the previous prototype. Area of the coils and gap
between the coils are affected and voltage and permittivity
are userd same†one.

e (2N -1)(s2 A)V 2
Fe(s) = 02(sd) 2(9)Wheres: scale factor of the double-coil actuator
SoFe(s) = Fe †(10)
Or describe in word, the change in scale factor has noeffect on the electrical force conducted in the double-coilactuator.
†Then relationship between the total electrical force (Fe(tot))
and the scale factor of the double-coil actuator can be shownin Fig. 5. In Fig. 5, the scale factor 1 indicates theexperimental coil. When we consider the large scale from
10-100 times larger in size such as in the construction
application, the electrical force applied to the double-coilactuator is so small and not applicable to the large-scale size.
But when we consider the small-scale (micro-scale)application such as in cell technology, the electrical force ishigh compare to its size. So this graph can be indicated thatour proposed double-coil actuator maybe applicable insmall-scale application.

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Fig. 5 Relationship between the total electrical force and thescale factor of the double-coil actuator.

Fig. 7 Rrelationship between the shrinkage (Dx) and the scale
factor of the double-coil actuator.

The plot between the shrinkage in separation of the twocoils and the scale factor is shown in Fig. 7
From Fig. 7, the shrinkage increases as the scale factor
decrease. Anyway due to the limitation of manufacturing
and the spring characteristic, in reality, we cannot
manufacture the spring in very small size (represent by thedash line region) as we shown in the graph. This graphshows the trend that our proposed double-coil actuator gain
some advantage in small scale and may be applicable for thesmall scale technology.

5. Conclusions and Discussion

Fig.6 The inner diameter and outer diameter of the coil
The relation between the shrinkage in separation of thetwo coils (Dx) and the scale factor of the double-coil actuatorcan be derived as in the following:
FromDx =e0 (2N -1)AV 2
2k(tot )d 2(11)When the scale factor of the coil changes, the spring
constant (k) also changes as follows;

Gd 4 †
8ND3G(sd) 4ks =8N(sD) 3

k=(12)(13)So,†
e 0 (2 N - 1)( s 2 A)V 2 Dx(14)Dx s ==s2( sk )( sd ) 2†

Where
D: The outer diameter of the coil (m)d: The inner diameter of the coil (m) as shown in Fig. 6

In order to investigate the characteristic of the newly
proposed double-coil wearable actuator, we constructed thesimplify model concerning the electrical characteristic andmechanical characteristic separately. The experiments using
some double-coil actuator prototypes were performed toverify the simulation model. During the experiment somevibration but not clear shrink could be observed when weapplied the high voltage to the double-coil actuator. Thismay cause by the inappropriate scale of the actuator
prototypes. When consider the characteristic of our proposedactuator by changing scale factor, the simulation results
shown that, our new double-coil wearable actuator may be
applicable for the small-scale application. Further
investigation on the scale and mechanical characteristic of
the coil should be made to find out the suitable scale for thereal application.
Acknowledgment
This research was conducted as part of “Research oninteraction media for the high-speed & intelligent
networking.” With funding from the Telecommunications
Advancement Organization of Japan.
Reference[1] Kornbluh et al. “Electrometric Dielectric Artificial Muscle
Actuators for Small Robots”, Proc. Of Third IASTED International
Conference on Robotics and Manufacturing, pp.1-6, 1995

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