Joysick

1. Proceedings of the 2006 IEEE
International Conference on Information Acquisition
August 20 - 23, 2006, Weihai, Shandong, China
Novel Hall-sensor Joystick Based on Nonlinear
Compensation
Hao Lu, Jiyin Zhao*, Jianpo Li and Zhansheng Wei Hongchul Kim
Department ofCommunication Engineering Department ofElectronic Engineering
Jilin University Pusan National University
Changchun, Jilin Province, China Pusan, Korea
h.lbill@ 126.com
Abstract - A non-contact electronic joystick using a single rheostat; friction will lead to a decline in mechanical
hall-sensor is newly designed, which detects a horizontal vector performance. The dual hall-sensor structure will overcome
in the magnetic field. Furthermore, in this paper, the nonlinear this friction problem, as shown in Fig. 1. However, this dual
character between the output of the hall-sensor and the hall-sensor structure needs a very big support device for the
movement of joystick bar is Illustrated. The dynamic horizontal motion along the X and Y axes. So, a big framework will
vector of the magnetic flux is detected by the hall-sensor while a incase the X instability a is rework to
permanent magnet is rotated with the joystick bar, which has a increase the system's instability and it is required to
two-dimensional detecting area. Using the nonlinear adjustment strengthen the shockproof design.
equations, the output signals of the hall-sensor have been Fig. 2 illustrates another type of hall-sensor structure called
linearized to give higher accuracy in two-dimensional movement. the single hall-sensor structure. This structure can solve the
Finally, through real experiments, it is shown that the single nonlinear problem [9]. Magnetic field lines come from the
hall-sensor structure mechanism is superior to the dual sensor permanent magnet which is on the bottom of the joystick bar
structure in sensing two-dimensional motion without offset. pointing to the hall-sensor. If the joystick bar rotates within
Index Terms - Magnetic Sensors, Least Mean Square (LMS) ±300 apart from the vertical axis of hall-sensor plane, the
Method, Nonlinear Compensation, Joystick output signal shows good linear characteristics.
I. INTRODUCTION Revolved
_3net Rmlvsled
Recently, the non-contact electronic joystick, based on .....t_ W i axis
magnetic technology, has been widely developed and
manufactured by many corporations [1, 2]. On account of its
high precision, it can be used to control the position and
velocity accurately in many kinds of industrial environments.
Furthermore, since the mechanical abrasion is limited to the
negligible lever in this design, the non-contact joystick is Fig. 2 Structure of single hall-sensor joystick with the revolved body
much more durable, reliable and precise than the
mechanical-contacted joystick. In industrial control However, it is regretfully that this single hall-sensor
applications, most non-contact electronic joysticks have a structure also needs a big and delicate framework, since the
dual hall-sensor structure. This structure is very convenient revolved body needs to be supported around the hall-sensor.
for detecting the rotation of the magnetic field and improving Also the relation between the output signal and the motion of
the accuracy of the signal measurement. Since there is no the joystick bar is linear only when the magnetic field lines
need for signal processing and a complicated compensation point to the centre of the revolved body. So it requires both a
algorithm, non-contact electronic joysticks offer a real-time very high design-precision and a very high
response during the control process [3]. machining-precision. When it has been used for a long time,
some offsets come from the friction between the revolved axis
and the framework, which causes the magnetic field lines to
Device tafion deviate from the centre of the revolved body Because of this
ogle m ement offset uncertainty, uniform compensation is impossible [3, 4].
As this paper will show, in order to overcome the above
problem, a joystick with a new-structure single hall-sensor
structure that has linear characteristics and a simple
mechanical
fSteroamwor isprOpsed.In this singlehal-. sns
m
Fi.1 Dual sensor structure joystick whc is th-oainai ftejytc a.Temi
Fig.
i~~~~~~~~~~mprovement in this design is that the rotation centre of the
Mechanical-contacted joysticks mostly use a high accuracy permanent magnet is located in the middle of the joystick bar
* CorrespondingAuthor instead of located at the bottom of the joystick bar. This
1-4244-0529-7/06/$20.OO ©2006 IEEE
1132

2. simple structure also can solve the problem of performance along with the obliquity. It will decrease when the obliquity is
degradation by the framework friction. Furthermore, it is very big and reaches out of the linear region. Magnetic field lines
convenient for a malfunction to occur in the diagnosis. It also within the permanent magnet-bar are parallel with each other
simplifies the manufacturing process, and improves the and the intensity reaches the maximum based on the Gauss
productive efficiency. theorem [4]. The magnetic field lines out of the hall-sensor
However, this new single hall-sensor [6] structure still run from the N-pole to the S-pole making a European football
shows the nonlinear characteristics it had before shape. In other words, the directions of the magnetic field
compensation. These nonlinear characteristics can be lines inside and outside ofthe magnet-bar are opposite.
described in detail by using three parameters: linear region, The nonlinear characteristics are affected by the geometric
signal amplitude and the linearity of the linear region. When shape, especially the length L of the permanent magnet, and
the shape of the permanent magnet and the intensity of the also affected by the vertical distance D between the
magnetic field are fixed, the output of the hall-sensor will permanent magnet-bar tip and hall-sensor. The intrinsic
change according to the motion of the joystick bar based on magnetic flux intensity B ofthe permanent magnet is assumed
the complex nonlinear characteristics. to be constant. To model these characteristics, as the first step
The nonlinear characteristics of sensor output may come we define the nonlinear function X(O) as follows:
from density distribution of the magnetic field and the ,(0) 1 (2)
physical characteristics of the hall component. In general, the I + (kO)n
modeling of the nonlinear characteristics is very complicated where n is the linearity relationship between the sine function
and unpractical. As we will illustrate, steady of a complicated of obliquity, sin(O) and the output of the hall-sensor, k is a
theoretical joystick model derivation; a new linear constant which relates to the geometric shape of the
compensation algorithm is proposed using the three magnet-bar and the design specification ofjoystick frame.
parameters of linear region, signal amplitude and linearity in The relation between the outputs ofthe hall-sensor (Vx, Vy)
the linear region. and the magnetic flux intensity (By, By) is linear, which is
II. NONLINEAR ANALYSIS OF THE JOYSTICK SYSTEM WITH described as follows:
UNIVERSAL JOINT Vx = cBx cos(cx)=c0)Bcos(Cu)
=
cB~
cos(D)2-(3)
A. Nonlinear characteristics and nonlinear compensation ck(0)Bsin(o)
V = cBy sin(u) - D 2
Z I 0
where c is amplification factor of the signal transformation
Uhivesal ot '
Universal jont circuit, a is the rotation angle ofthe joystick bar.
After amplification, low-pass filtering and offset
elimination, the output of the hall-sensor will be calculated in
the DSP core. Solving simultaneous equations (1), (2), (3), the
- Haerllor equation (4) is defined as follows:
sensor ADx ~~~~~~~~~~~sin(O)ncsa
BX =1+ (kO) (4)
Bh *==Wif* AD sin(O) sin(a )
B,! Y
1+(kO)n
where 4 is the amplification factor of the A/D converter,
Fig. 3 Mechanical structure ofthe proposedjoystick the rotation angle a on the X-Y plane is obtained from the
There is a universal joint in the rotation centre of the A/D converter. AD, and ADY are proportional to the magnetic
joystick bar that is the most important characteristic in our flux intensity, B , and the resolution of the A/D converter,
new structural design. It is different from the previous and they are inversely proportional to the reference voltage of
designs, as shown in Fig. 3. When the permanent magnet is the A/D converter, Vref, and squared vertical distance, D2 [7].
slanted by the universal joint with 0 , magnetic flux intensity In the universal joint joystick bar structure, the movement
of the joystick bar links to the two-dimensional vector on the
B will project to the plane of the hall-sensor. This horizontal hall-sensor plane, which is transformed by the hall-sensor into
vector of the magnetic flux intensity B h is resolved along the Cartesian coordinate position ofvalues ADX and ADY. But,
the X and Y axes with a quadrate phase and measured by the in the AID converter a value produced by the hall-sensor is
hall-sensor. The relation between B and B h is described not proportional to sin(0) owing to the magnetic interferences.
as: In other words, the relation between outputs of A/D converter
Bh = 240)Bsin(O) (1) and the movement of the joystick bar is nonlinear. If we want
where )B(O) is a nonlinear function between the distribution to use the A/D value to express the movement of the joystick
characteristics ofthe magnetic field lines and the obliquity of bar, a nonlinear compensation processing should be
the joystick bar. When the magnetic flux density is evenly performed before. From equation (4), the composed value of
distributed and the magnetic field lines are parallel, )(O)equals A/D converter on the hall-sensor plane is given as:
to 1. But, the horizontal vector B h does not always increase
1133

3. ADt = + AD2 +AD2 s
i__n_( derivative of the equation (5) w. r. t. 0 ,the relation between
ADout x Y + (kO) (5) the k and O is defined as:
Linearizing this nonlinear equation is one of major 1
contributions of this paper, which is illuminated by the k O )OI (7)
similarity between the frequency response of the low pass n tan( C)_On
filter and the simulation results based on the equation (5), as Why the linear region 0O is only relevant to these three
shown in Fig. 4. According to the properties of the low pass parameters such as the vertical distance, the length of the bar
filter, in the linear region, the curve is mainly determined by magnet and the area of the bar magnet's tip. In this paper, the
the sin(O). On the contrary, out of the linear region, the curve five assumptions or hypotheses are given as follows: 1. The
mainly determined by the (kO)', which shows the coincidence structure of the permanent magnet is symmetrical. 2.
with the previous nonlinear characteristics analysis. >
Although the magnetic flux intensityB is variable according
y 1500 7 k y ooo
1_ y2500 to the material, the distribution of the magnetic field lines is
1000 -----------2 800 ___----------_------_-- -J 20 invariable. Only the density of magnetic field lines may
3 o ool
2500l; ; ; 4 ~ 1500
1 0 0 r
change. 3. When the area ofthe magnet-bar tip is larger, the
500 ---------4----3000-
500 2
/SH 400 lb 4000 150o /' magnetic field lines are more parallel, and tend to have an
--6
2 0- _ ideal distribution. 4. If the length of the permanent magnet, L,
200 is much longer than the vertical distance between the
500 400 ---------------------
1000 --,-4 A magnet-bar tip and hall-sensor, D, it can be assumed that the
-1000 --------- ----------- -------------------------------10
m
agnetic field lines which distributes the side of the
1~
-800 F-
c -.--permanent magnet-bar as shown in Fig.4 are exactly parallel
-1600 -1000 -2600an
-150005 ° °5 -05 ° °5 -005 ° 0 5 and the magnetic lines from the N-pole to the hall-sensor
(a) 9=5OOO, n=2 X (b) k=3, n=2 X (c) k=2, =6OOO x
4a) ~=000, n2 x () k=3,n=2 x c) k=, 1~1~6000
plane are also parallel. It will cause the variety of ADout and
Fig. 4 Nonlinear characteristics ofA/D values for a specific k, 4 and n
linear region, which is sensitive to the minute movement of
In Fig.4, the X-axis represents sin(0) and the Y-axis the joystick bar. In other words, the linear region is very
Inpresentsthe composed value of the A/D converter. Figure small. 5. If the length of the permanent magnet, L, is not as
represents the composed value of the A/D converter. Figure long as the vertical distance between the magnet-bar tip and
5(a) shows that the linear region is reduce when k increases, the hall-sensor, D, the hall-sensor plane is mainly surrounded
so k can be considered as a parameter to determine the linear b. t
region. Figure 5(b) shows that 4 modifies the A/D values by the magnetic field lines from N-pole, which iS the main
which correspond to with the signal output of the hall-sensor, region becomes insensitive to the extensive movement of the
and it does not change the linear region. Figure 5(c) shows the region becomes ns tothe extensiv ement ofth
strength of the linearity with the increase of n. When n jtickear. It mr
* . . . . ~~~~~~~~~~~~~the
increase ofD.
increases, in a certain linear region, the experiment results
tend to be a straight line. TABLE I
B. The variety ofthe linear region with the design specific
RELATIONSHIP BETWEEN VERTICAL DISTANCE, D, AND LINEAR REGION, 0.
Through the experiments, it is recognized that the linear Vertical distance, D (cm) 0.3 0.8 1.3 1.8
region ofthe joystick system is changed according to the ratio (degree) 7_8 19_3 30_2 41_5
between distance D and length L of the permanent Measured angle 0c (degree) 7.8 19.3 30.2 41.5
magnet-bar. The maximum of obliquity processed by A/D Theoretical value Oc (degree) 8.2 20.3 30.6 39.4
converter is defined as 0,. When the L is constant, 0, will
increase with the increase of D, and the linear region will Table.1 shows the real measured and theoretical values of
extend. On the contrary, when the D is constant, 0, will 0, according to the change ofD under the condition S=0.8cm2,
decrease with the increase of L, and the linear region will be Lcmu
reduced. If L and D are both constant, the area S of the L=2.Scm;
magnet-bar tip will change the linear region too. When S is C. Physical analyzing for the amplification factor of A/D
enlarged, the area where the N-pole magnetic field lines come converter
from will be enlarged, so as to extend the linear region. The output ofthe hall-sensor has been pre-processed in the
According to equation (5), (k=0, 0, =2/2) is the extreme ofthe transformation circuit, such as the amplification, the low-pass
linear region. From the observations and analysis of the filtering and the offset elimination, and then it is converted to
system structure, 0, is represented as: the digital values in the DSP core. So, 4 represents the
L ~[I - exp(-S D (6) amplification factor of the A/D converter, which is directly
c2 L affected by the magnetic flux intensity,s~, and the vertical
which explains that the linear region0c is related to the distance, D. Amplification factor, c, is proportional to the
distribution of the magnetic field lines. Furthermore, the resolution n of the A/D converter. Then, according to the
distribution of the magnetic field lines relate only to the equations (3), and(4), thefollowingrelations arederived:
geometrical structure of the permanent magnet. Other Vr V, cB Vef (8)
physical parameters do not change the linear region. From the ADX ADy ;D2 2N -1
1134

4. Then, 4 can be calculated as follows: master and using this information, sin(O) is computed with the
c(2N -1)B (9) geometrical mechanism. Finally, the master MPU sends those
- 2v to the computer to form the nonlinear experimental curve. In
D ef the Fig. 6, (a) is a curve of 10th order polynomial based on
In the actual experiments, O is increased by augmenting the LMS, (b) is the experimental curve from the DC motors and
ratio of the vertical distance to the length of the magnet-bar. A/D converter, and (c) represents the error between 10th order
In this situation, the output of signal transformation circuit polynomial and experimental data.
usually decreases a little, which comes from the augmentation
of noise interferences, so as to decrease the precision of the 05
joystick motion measurement. In the case of an established
design specification, to solve this problem, the amplification O 0 _ J -
factor c of the signal transformation circuit is increased to a _
proper level according to the equation (9). 0 -5
-400 -300 -200 -100 th 00 200 300 ADE 400
III. VERIFICATION OF THE NONLINEAR COMPENSATION 0.°5 (a Curve of 10 order polynomial out
This section explains another major contribution of this
paper, which is to prove the effectiveness of the proposed . 0- --
nonlinear compensations by comparing them to the curve
fitting results. -o M__ -400 -300 -200 -100 0 100 200 300 AD 400
(b) Curve of experimental data out
A. Obtaining experimental data and curve fitting based on 0.02
0.0K
Interpolating polynomial based on the Lagrange °
o
-- v
interpolation or the Newton interpolation can be exactly 001oh -- ------
derived from the experimental points. But, these points -o o2 0 2 0 1 2 3 A
^ ~~~~~~~-400
-300 -200 -100 0 100 200
300 ADlW 400
include the system errors and random errors [10]. So, it is (C) Error between sin(e) and Pl0 out
better to get a function which represents the characteristics of Fig. 6 Curve fitting based on least mean square method
the whole experimental points. In order to obtain the B. Numerical Method ofnonlinear compensation
above-mentioned function, the curve fitting based on LMS [5, As the first step for the compensation the Newton Method
6] is adopted in this research. is used to obtain 0, and then sin(0) is calculated. With the
sin(l), the horizontal vector of the magnetic flux intensity
lU 1 - f :Bh Can be easily obtained, since there is a linear relationship
between sin(0) and B' h. hin the actual application, the obliquity
is usually limited to± 3O', where sin(0) has a unique solution.
Among many solutions for nonlinear equations, the Newton
Method has been widely used on account of its ease in
processing and rapid convergence speed.
If the function f(x) has continuous derivatives, the
tangential equation of y = f(x) can be calculated. The
numerical solution of the nonlinear equation can be solved by
Fig. 5 Experimental environment means of the point of intersection between tangent and
X-axis, and this method is called as the Newton Method, It is
In the actual applications, we must performance the described as follows:
operations that linearize sin(0) corresponding to horizontal f(Xm) (10)
vector ofmagnetic flux intensity using A/D values. As shown xm+1 =Xm f((Xm)
in Fig. 6, the vertical axis represents measured sin(0), and the
horizontal axis represents the composed A/D values with axis where m=O, 1 , A.
X and Y on the hall-sensor plane. Figure 5 illustrates the According to 2nd order astringency of the Newton Method
experimental environment for curve fitting. In the figure, the [2, 5], the difference between a current value and the last
DC motors with encoder sensors are set at the spin axes X and value in the certain region can be represented as g1under the
Y to measure the obliquity respectively and then its angle assumption off(x) = 0. That is,
displacement pulse signals are fed to the input of slave MPUs. Ixm+ - Xm <1 £ (I 1)
The output signal of the hall-sensor after amplification and
filtering is fed to the input of master MPU and compute the where cl represents a setting error. The numerical method of
compsedA/Dalus, wichisA = ±AD2+ AD lav the nonlinear compensation equation now can be defined as
~out 0 _ADoutk°m+
[kn;sn0)2knAO<
]° sn0
A and B and master MPUs are connected by the CAN 'm+l m [knQCOS(Om)]Om[nnQi 0m] -+4COS(Om)
structure for the information exchange. In this paper, slave A (12)
and B MPUs gathers the pulse numbers, which are sent to the Frti eusv aclto,g sdfnda
1135

5. Om
-Om < £, (13) Fig. 8 Comparison of modeling and the Newton Method curves
After this recursive process, to obtain 0, sin(O) and Fig. 8 shows the comparison result between the modeling
real B h can be calculated through the nonlinear compensation, curve and the Newton Method curve, that express the
the real position of the joystick motion can be obtained. nonlinear characteristics between the output of signal
C. Analyzing of correctness for nonlinear adjustment transformation circuit and motion of joystick bar. From
equations Fig. 10, it found that the modeling result is accurately tracking
The choice of parameters k and 4 has a great effect on the the Newton Method curve, viz. the real experiment curve.
performance of the joystick system. When k and 4 are On account of several interferences coming from the
determined by equations (7) and (9) respectively under the system errors and the random errors in the actual experiments,
given designed specific and which is just coincidence with the there are some errors existing in the experimental curve, after
parameters, which the numerical solution of the nonlinear all. But, from the results of Fig. 7 and Fig. 8, it can be
equation is closely consistent with the 10th order polynomial calculated that nonlinear compensation equations can
based on LMS. This proves the correctness of the nonlinear precisely reflect the nonlinear characteristics of the joystick
model. system.
____ ____ _________________ IV. PERFORMANCE VERIFICATION WITH THE SENSOR
°_ 1 F T STRUCTURE AND SIMULATION
sin(e)
A. Structure ofjoystick
The horizontal vector of the magnetic flux intensity'g h on
the hall-sensor plane is produced by the motion of the
_0_ _ _ ___ __ __ __ universal joint. As shown in Fig. 9, the hall-sensor module is
-400 -300 -200 -100 0 100 200 300 400
(a) Nonlinear curve with the 10oth order ADout located under the joystick structure. The linear region can be
o.5
o polynomial and Newton method
adjusted by changing the height ofthe magnet-bar.
0.006 U-- --- --e-- -a l-- - --t-- --
-0.016
-400 -300 -200 -100 0 100 200 300 AD400
(b) Comparison error Out
Fig. 7 Correctness of curve fitting adjustment
(a) Top view (b) Bottom view (c) Sensormodule
Fig. 7 illustrates the experimental results of the numerical Fig. 9 Configuration ofsingle hall-sensorjoystick
solutions based on the Newton Method and the 10th order B. Stability analysis ofthejoystick structure
polynomial based on LMS. The parameters k = 1.3570, q=
1065 are determined by using the MATLAB to match the
Newton Method curve and the 10th order polynomial result. It -0
is optimized on the condition of n=2, D=1.3cm, L=2.5cm,
S=O0.8cm2, c=25.68, B=3500Gauss, N=10, Vref=5.It shows = 30°
5 Iso
O
4
0o
that k =1.3570, 4= 1065 are the optimal parameters in the real
experimental environment. On the same experimental
environment, k = 1.3653 also can be obtain from equation (7),
and 4 =1089 from equation (9), which is previous modeled in 9O +0
this paper.
40
Curve of Newton Method
Modeling curve
Toaxis
200- hail senjsor 1
:K=1.3570, 1065 I +-
100 - ' . . 4 . ' ' _ Fig.10 Sensing mechanism ofconventional single hall-sensor
<c /------ Fig. 10 represents the conventional single hall-sensor
-100 structure [7], when the centre-line of the magnet-bar exactly
f ~~~~~~~~matchesto the centre of the hall-sensor plane, the joystick
-200 mayhave ahigh linearity.
-300~
~ ~
i .4w-' '21n63-1i---- The nonlinear phenomena also exist in the output of the
. - ~~~~~~ ~~~
hall-sensor in the joystick with the universal joint. However,
-4000 8OlE
014012 0 12 014 lA 0 8afternonlinear compensation processing, the structural defect,
Nlonlinearcharacteristics sinOe which causes the problem of resolution reduction is
1136

6. completely resolved in the proposed design. Moreover, this V. CONCLUSIONS
structure is robust against the external interferences. A single hall-sensor joystick with a universal joint structure
C. Simulation result has been designed based on the model of magnetic fields. In
Finally, the analysis for nonlinear characteristics in section order to resolve the nonlinear characteristics of the
2 is utilized to show the performance ofjoystick systems. As hall-sensor, the nonlinear compensation system is derived.
shown in Fig.11, the horizontal axis represents sin(O) and the The coherence between the compensation results and the real
vertical axis represents the value ofthe A/D converter and the motion of the joystick bar has been achieved experimentally.
simulation results are obtained under the conditions of: n = 2, It is clarified that the newly designed joystick has high
B = 1OOOGauss, N = lO,Vref= 5 and c = 90. From Fig.11, it is reliability to be used for industrial applications. For the
noted that the appropriate choice of parameters for the compensation ofthe nonlinear characteristics, two DC motors
geometrical modeling ofthe joystick is very important to cope are designed to get the real positions of the joystick bar
with the nonlinearity and linear region. movements, along with X-axis and Y-axis. The output data are
used to fit the curve function based on the LMS. Through the
quoo6cm2 * quoo D
= O
Newton Polynomial Interpolation Method, the parameters for
1.:6cm CInolea
500 --;------l----100C-----
---o O nonlinear compensation algorithms are obtained, and then
o L t 1-2Cm20 0
2 ° Ln 1 icm 2 obtained with the sin(O), which is linear with A/D values
l 8cm 2 4
tm. within± 30 .
In the linear region ofthe proposed design, error
-5o0 i 0 = t
0 -oo0 t X 1 could be limited to 1%, so as to overcome the structural
(a)oo -looo >>i defects ofthe conventional joystick friction and vibration.
a)
D-1
-0.2c5 l0 0.5cill ~ 2
1 b1 S-0. Ocm2 L=_ 1cil The mathematical modeling proposed in this paper not only
D
.2cm,
L=2. cm (b) $ 1 0cm2 L=2.5 m
compensates for the nonlinear characteristics of the joystick
lO C - _ __ _ __ _ __ _ 400
o 0. cm 4 0 5cm system, but is also easily obtained. This scheme gives
500- --, !I;Oc -l - 200 .- 0,&cffL ,-assistance in selecting the specifications of joystick design.
o ---------
--------- 0 ---------------
1- - A Using this method of modeling based on mathematical
2
:-5cn* ' -2 1 7cm hypothesis, the performance of total control systems can be
-500 -voo 1enhanced.
-lOOC - __________________- -400 VEnlarging the obliquity ofthe joystick bar may improve the
-1 -o.E 0 0.o 1 -1 -0.o 0 0.o 1 robustness, which can be achieved by increasing D under the
(C) S=0.8cm2 D=1 .5cm (d) S=0.5cm2, (D+L)=4.Ocm condition that a permanent magnet has been fixed by
Fig. 11 Variety of nonlinear characteristics with the choice of design designers. However, a larger D may increase the interference
specifications of noise. Obtaining and adjusting the optimal D is left for
Fig. 12 describes the variety of characteristics of the signal future research.
transformation circuit output at the linear region O that is REFERENCES
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1137