Printed Electronics Research Center, KIMM, Jangdong 171, Yuseong-gu, Daejeon 305-343, South KoreaNano-Opto-Mechatronics Laboratory, Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea
r t i c l e i n f o
rticle history:eceived 21 March 2013eceived in revised form 20 August 2013ccepted 20 August 2013vailable online 29 August 2013
eywords:pherical actuator
a b s t r a c t
In this article, we describe the design of and an experiment with a new type of spherical voice coil actu-ator. The designed actuator has a large tilt angle of ±40◦, high tilt torque, and a uniform and decoupledtorque constant for each coil within a compact diameter of 100 mm. The designed actuator is composedof a rotor, a gimbal guide mechanism, and a stator. In order to decouple the tilt torque generated byeach coil, the rotor has two pairs of coils. One pair of coils is circular, and the other is rectangular. Forthat reason, each axis of the gimbal guide mechanism coincides with each axis of the tilt torque gener-ated by each corresponding pair of coils. In addition, because the principle of the proposed actuator is
based on the Lorentz force, the tilt torque generated by each coil is directly proportional to the drivingcurrent. Therefore, the proposed actuator is easy to control. We carried out optimization of the pro-posed actuator to maximize the tilt torque with a limited size. To verify the results of the optimal designprocess of the actuator, an FEM simulation was carried out. We realized and tested the designed actu-ator to verify the torque performance. The realized actuator has an X and Y′-axis tilt torque constantof 0.35 Nm/A.
As the need for multiple-degree-of-freedom rotational jointsncreases, many studies on single-unit spherical actuators haveeen performed. The spherical actuator is an electric machinehat is able to tilt its shaft on multiple degrees of freedom usinglectromagnetic force. A spherical actuator has the advantages ofompact size, high motion precision, fast response, directly drivenechanism, and high efficiency [1–3]. Their applications can be
ound largely in robotic manipulators, medical and welfare appa-atuses, and positioning devices. Various types of spherical motorsave been developed. The first induction actuator was proposedy Williams et al. [4] and Lee et al. [5–8] devised variable reluc-ance spherical actuators. They researched the design, sensing, andontrol of spherical actuators. Yan et al. [9,10] developed a spheri-al actuator similar to Lee’s but with synchronous drive principles.omoaki et al. [11–13] studied and developed a wide range of
ultiple-degree-of-freedom drive systems. Kim et al. [14] designed
nd analyzed of a rotational VCA (voice coil actuator) in their efforto develop a new type of multiple-degree-of-freedom rotational
∗ Corresponding author at: Printed Electronics Research Center, KIMM, Jangdong71, Yuseong-gu, Daejeon 305-343, South Korea. Tel.: +82 42 868 7403;ax: +82 42 868 7176.
actuator. A three-dimensional magnetic field analysis of spheri-cally polarized permanent magnets in the stator of the actuatorwas obtained.
In previous studies, various types of spherical actuators weredeveloped. They are commonly designed based on the principles ofa synchronous motor. These types of spherical actuators have highnon-linearity of the torque constant with respect to the rotationalposition of the rotor and low tilt with a large overall size of theactuators. Furthermore, synchronous-type spherical actuators arecomplexity and difficult to control when high precision is required,as to control and drive the actuators, calculations of the flux densityof each driving part according to the rotational angle are required.Therefore, an accurate analytic model of the flux density is needed.
A large tilt angle, a large tilt torque value, and easy control ofthe spherical actuator are important factors related to performanceand successful applications. In this paper, a new type of sphericalactuator using the principle of a VCA is proposed and optimallydesigned. We focused on a large working space and high tilt torquewith a compact diameter of 100 mm. A voice coil actuator (VCA)is used due to its ability to generate force with high accelerationand high accuracy over a limited travel range. It is a direct-drivedevice based on a permanent magnetic field and current-carrying
coil windings, producing force that is directly proportional to theapplied current. Based on these novelties, the proposed spher-ical actuator has high tilt torque and is easy to apply andcontrol.
182 H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188
new t
2
2
tc
ABCDE
ehsrtom
2
o
Fa
Fig. 1. Schematics of the proposed
. Concept of the spherical voice coil actuator
.1. Design considerations
In order to achieve a large angle of the tilt motion, high tiltorque, easy control, and good dynamic performance, the followingharacteristics are considered:
. A compact size within a diameter of 100 mm.
. A large tilt angle of ±40◦.
. A high tilt torque constant.
. A uniform torque constant.
. Decoupled tilt torque caused by each coil.
As mentioned above, to apply the proposed spherical actuatorffectively, the spherical actuator should have a large tilt angle andigh tilt torque with a compact size. The dynamic torque constantshould be independent with respect to the rotational angle of theotor and directly proportional to the driving current for easy con-rol. In addition, the axes of the driving torques caused by each setf coils should be decoupled and matched to the axes of the guideechanism.
.2. Conceptual design
In this section, the basic configuration of the proposed new typef spherical voice coil actuator is described.
ig. 2. Schematic figure and cross-sections of the stator. (For interpretation of the refererticle.)
ype of spherical voice coil actuator.
Fig. 1 shows the conceptual design of the proposed new type ofspherical voice coil actuator. It is composed of a stator and a mov-ing coil type rotor. The stator of the actuator has eight permanentmagnets and a steel yoke for a high uniform magnetic flux density.The rotor is composed of a 2-DOF (degree of freedom) gimbal guidemechanism and four coils to drive the tilt motions.
The stator part is fixed to the base frame. As shown in Fig. 2, thestator is composed of four permanent magnet pairs (eight perma-nent magnets), an outer steel yoke, an inner steel yoke, and a fixedshaft. The magnets shown in red are polarized along the radiallyoutward direction, and those shown in blue are polarized along theradially inward direction. The blue arrows represent the flow of themagnetic flux of the stator. A high and uniform magnetic flux den-sity is formed at the air gap between the permanent magnets andthe outer steel yoke. There is an empty internal space in which toinsert the gimbal guide mechanism for two-degree-of-freedom tiltmotion and a rotational motor.
Fig. 3 shows the gimbal guide mechanism. It consists of an X-axistilt guide part and a Y′-axis tilt guide part. The X-axis tilt guide part isfixed on bearings that are inserted at the inner stator. It only allowsX-axis rotational motion on the global coordinate. The Y′-axis isthe Y-axis of the local coordinate which is caused by rotation alongthe X-axis. The Y′-axis tilt guide part is fixed on bearings that are
inserted at the X-axis tilt guide part. It only allows Y′-axis rotationalmotion.
As shown in Fig. 4, two pairs of differently shaped coils are usedto drive the X and Y′-axis tilt motions. The circular coils generate the
nces to color in this figure legend, the reader is referred to the web version of the
H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188 183
Fig. 3. Schematic figure and cross-sections of the gimbal guide mechanism and the inner stator.
Fig. 4. Schematic figures of th
XtT
tfitlcateiocd
3
c
block magnet using a charge model [14,15]. In the stator, there areeight permanent magnets which are all identical. Therefore, thetotal magnetic field density can be obtained by the superpositionof the magnetic field density of each cylindrical block magnet.
Fig. 5. Actuation principle of the proposed spherical voice coil actuator.
-axis tilt torque and the rectangular coils generate the Y′-axis tiltorque. These coils are moved with the gimbal guide mechanism.he coil jig is fixed on the shaft of the gimbal guide mechanism.
Fig. 5 shows the principle of the generation of the X and Y′-axisilt torques. The generation of the tilt torque is based on the Lorentzorce. Uniform magnetic flux exists at the air gap. The coils carry-ng the current generate tangential directional forces that causehe tilt torques. The features of the circular coils and the rectangu-ar coils are represented in Figs. 6 and 7, respectively. The circularoils always generate the X-axis tilt torque, and the rectangular coilslways generate the Y′-axis tilt torque at arbitrary points. Therefore,he X-axis tilt torque and the Y′-axis tilt torque generated by theach coil pair are decoupled and directly proportional to the driv-ng current which flows through the coils. In addition, each axisf the tilt torque generated by each coil pair coincides with eachorresponding axis of the gimbal guide mechanism. Therefore, theesigned actuator is easy to control.
. Modeling
The magnetic flux distribution in the air gap must be modeled toalculate the force and the torque. In order to model the magnetic
e coil part of the rotor.
field density generated by the permanent magnets and the steelyokes of the stator, we obtained an analytical model of a cylindrical
Fig. 6. Direction of the tilt torque generated by the circular coil at an arbitraryposition.
184 H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188
Fp
aeid
→
tTfl
→
B
B
ig. 7. Direction of the tilt torque generated by the rectangular coil at an arbitraryosition.
Fig. 8 shows a schematic diagram of one part of the stator. Therrows in the magnets are the magnetization directions. The gov-rning equation of the charge model is derived in Eq. (1), where Ms the magnetization of the permanent magnet and �0 = 4� × 10−7
enotes the magnetic permeability of the air.
B (x) = �0
4�
∫V
∇(
∇′ · M(x′)|x − x′|
)dv′ − �0
4�
∮s
∇(
M(x′) · n|x − x′|
)ds′ (1)
In order to obtain the magnetic flux density in the radial direc-ion, the Cartesian coordinate changes to the cylindrical coordinate.hen, the governing equation of the charge model and the magneticux density is derived as following equations:
B(r, �, z) = �0
4�
∫V
∇
(Ms√
r2 + r ′2 − 2rr ′ cos(� − �′) + (z − z′)2
)dr ′d�′dz′
− �0
4�
∫s
∇
(Ms√
r2 + r ′2 − 2rr ′ cos(� − �′) + (z − z′)2
)r ′d�′dz′ (2)
r(r, �, z) = −�0Ms
4�
∫V
[r − r′ cos(� − �′)
]g3 · dr′d�′dz′
+�0MsR
4�
∫s
[r − R cos(� − �′)
]g3 · d�′dz′]R2
R1(3)
� M∫ [ ]
�(r, �, z) = − 0 s
4�V
r′ sin(� − �′) g3 · dr′d�′dz′
+ �0MsR2
4�·∫
s
[sin(� − �′)g3 · d�′dz′]R2
R1(4)
Fig. 8. Schematic diagram of the magnet and the yoke of the stator for the modelingof the magnetic flux density.
B is the magnetic flux density, and r, �, and z are the externalposition in the air gap between the magnets and the outer yoke.R1 and R2 are the inner radius and the outer radius of the mag-nets, respectively. To calculate the torque generated by the currentflowing in the coil, we only need the radial directional magneticflux density of the air gap, as shown in Fig. 8. If the dimensions ofthe magnets are identical to those shown in Fig. 9(a), the magneticflux density distribution in the air gap can be modeled as shown inFig. 9(b).
The effective volume of each coil and the direction of the cur-rent flowing in the coils are represented in Fig. 10(a). These valuesare necessary to obtain the tangential Lorentz force. The dynamictangential force FT of the actuator is given as
FT = −∫ ∫ ∫
V
J × BrdV = −∫ ∫
A
⎛⎝ I
A
l∫0
dy × Br
⎞⎠dA, (7)
where A is the cross-sectional area of the coil, I is the current flowingthrough the coil, and l is the effective length of the coil. As shownin Fig. 10(b), the torque generated by one coil is proportional to theradius from the center of the actuator to the effective volume of thecoil as in the following equation:
T =∫ ∫ ∫
V
r × J × Brdv =∫ ∫
A
⎛⎝ I
A
l∫0
r × dy × Br
⎞⎠dA. (8)
4. Design optimization
In order to achieve high tilt torque in the proposed actuator,a design optimization step is required. The objective of the opti-
mization process is to maximize each tilt torque of the actuator.Before the optimization process, the design parameters must bedetermined. Fig. 11 and Table 1 show the design parameters ofthe proposed actuator and the geometric constraints of the design
H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188 185
Fig. 9. Radial directional magnetic flux density of the magnets of stator.
ig. 10. (a) Effective volume for calculation of the force and direction of the current;nd (b) effective torque radius of the coils.
arameters. With these factors, the equation of the objective func-ion is determined as follows:
(tm, ta, dcX, dcY′) = min imize
(1
T2X
+ 1
T2Y′
). (9)
There are a number of fixed parameters and constraints relatedo the optimization. As mentioned above, the geometrical con-traints of the design parameters are shown in Table 1. Theifference between the X-axis tilt torque and the Y′-axis tilt torque
able 1esign parameters used for the optimization process.
Design parameters Geometric constraints (mm)
Thickness of magnet, tm 6 ≤ tm ≤ 12Thickness of air gap, ta 4 ≤ ta ≤ 8Diameter of X-axis tilt coil, dcX 0.2 ≤ dcX ≤ 0.5Diameter of Y′-axis tilt coil, dcY′ 0.2 ≤ dcY′ ≤ 0.5
tm + ta ≤ 15
Fig. 11. Design parameters for design optimization.
is less than the 2% of the larger tilt torque. To test the proposedspherical actuator, we used current amplifiers, in this case theTA105 (Trust Automation) model. These models can generate a con-tinuous current of 1.0 A. Then, the coil current is considered to beequal to 1.0 A. Therefore, heat generation caused by the currentand the resistance of one X-axis tilt coil and one Y′-axis tilt coilis considered. To prevent a failure of the system by heat, we seta temperature limitation of the coils when 1.0 A of current flowscontinuously. To calculate the temperature of the coils, the heatconsumption of the system is modeled as shown in Fig. 12 and asexpressed by Eq. (10). The fixed parameters and the constraints aresummarized in Table 2.
Fig. 12. Heat consumption model of the spherical actuator.
186 H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188
of th
g(t
TF
Fig. 13. Convergence
To optimize the design parameters, a sequential quadratic pro-ramming (SQP) method and the MATLAB optimization toolboxMathWorks, USA) were used. Fig. 13 shows the convergence ofhe objective function and the design parameters used during the
able 2ixed parameters and constraints for the optimization process.
Value
Fixed parameters Diameter of the stator 100 mmThickness of the outer yoke 4 mmThickness of the inner yoke 6 mmWidth of the permanent magnet 20 mm
Constraints Torque difference between TX and TY′ ≤2%Current flowing in each coil 1 ATemperature of the coils ≤80 ◦C
e design parameters.
optimization of the proposed spherical voice coil actuator. Theresults of the design optimization are summarized in Table 3. Toverify the optimization result, a FEM electromagnetic simulationis carried out and compared with results as shown in the last tworows of Table 3.
5. Realization and experiment
To verify its performance, the optimally designed actuator wasmanufactured as shown in Fig. 14. The realized actuator has a tiltangle of ±40◦ and a rotation angle of 360◦. A torque measurement
system was designed and manufactured to measure the X and Y′-axes tilt torque constants. Fig. 15 shows the setup of the tilt torquetest. To evaluate the torque constant characteristics of the actua-tor, a load cell (MAS333, CAS®) is used. X and Y′-axes tilt coils are
H. Kim et al. / Sensors and Actuators A 203 (2013) 181– 188 187
Table 3Optimization results and final design parameters.
Optimal design Final design
Design parameters Thickness of the magnet, tm 9.0069 9.0 mmThickness of the air gap, ta 5.9931 6.0 mmDiameter of the X-axis tilt coil, dcX 0.3183 0.3 mmDiameter of the Y′-axis tilt coil, dcY′ 0.2786 0.25 mm
Dependent parameters Number of turns of the X-axis tilt coil 309.1 300Number of turns of the Y′-axis tilt coil 288.5 300Resistance of the X-axis tilt coil 8.9 10.3 �Resistance of the Y′-axis tilt coil 16.1 20.6 �X-axis tilt torque constant 0.321 0.327 Nm/A (FEM)Y′-axis tilt torque constant 0.315 0.334 Nm/A (FEM)
e designed spherical actuator.
ccvprwI
adlTt
Fa
Fig. 14. Realization of th
onnected to the current amplifiers (TA105, Trust Automation). Toontrol the current amplifiers and monitor the measured torquealue, a real-time controller (DS1103, dSPACE) was used. In theerformance test, a current of 1.0 A is applied to the coil of theotor. The tilt torque was measured at various rotation angles whichere measured by the rotary encoder (GPI R120S, Gurley Precision
nstruments).The results of the torque constants according to the rotation
ngles are shown in Fig. 16. As shown in Fig. 16, solid lines (blue)enote the tilt torque constants from the experiment and dashed
ines (red) are the tilt torque constants from the FEM simulation.he graphs of the experimental result are similar to the graphs ofhe FEM simulation result. In addition, the torque constants at 20◦
ig. 15. Test setup for evaluating the torque constant characteristics of the realizedctuator.
Fig. 16. Each tilt torque constants of the actuator: (a) X-axis tilt torque constant, and(b) Y-axis tilt torque constant according to rotation angles. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthe article.)
1 ctuato
atT
6
dd±obutdsds
A
D
R
[
[
[
[
[
[
88 H. Kim et al. / Sensors and A
re nearly identical to design optimization results. In this actuator,he torque constants differ slightly according to the rotation angle.herefore, this system is easy to control.
. Conclusion
In this research, a new type of spherical voice coil actuator wasesigned and tested. We developed a new decoupled multiple-egree-of-freedom rotational actuator with a large tilt angle of40◦, high tilt torque, and a compact diameter of 100 mm basedn the principle of a VCA. In addition, the developed actuator cane controlled easily. The results of the optimization were verifiedsing a FEM simulation. This optimized spherical voice coil actua-or can easily be implemented into applications requiring multipleegrees of freedom of the tilt motion as well as high torque and highpeed capability. Furthermore, we manufactured and assessed theesigned actuator to verify its performance. The realized actuatorhowed an X and Y′-axes tilt torque constant of 0.35 Nm/A.
cknowledgement
This research was supported by a grant from the Agency forefense Development (ADD) funded by the Korean government.
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Biographies
Hyunchang Kim received his B.S., M.S., and Ph.D. degrees in mechanical engineeringfrom the KAIST, in 2007, 2009, and 2013. He is now a post-doc researcher in KIMM.His research focuses on the fields of precision stage, planar motor, and sphericalactuator.
Hyoyoung Kim received his B.S. degree in mechanical engineering from theHanyang University, in 2007, and M.S. and Ph.D. degrees in mechanical engineeringfrom the KAIST, in 2009 and 2013. His research focuses on the fields of precisionstage and spherical actuator.
Dahoon Ahn received his B.S. degrees in mechanical engineering from the KAIST, in2006. He is currently pursuing the Ph.D. degree in mechanical engineering at KAIST.His research focuses on the fields of planar motor and spherical actuator.
Daegab Gweon received his B.S. degree in mechanical engineering from the Hanyang
University, in 1975, and M.S. degree in mechanical engineering from the KAIST,in 1977. He then received his Ph.D. degree from Stuttgart University, Germany,in 1987. Since 1990, he has been a Professor of mechanical engineering at theKAIST. His research interests focus on precision positioning system and opticssystem.
