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3
Forces given by the FT−Sensor
60
Fx
force [N]
40
Fy
20
Fz
0
−20
−40
−60
0
100
200
300
400
500
time [s]
600
700
800
900
1000
torques [N*m]
Torques given by the FT−Sensor
3
Tx
2
Ty
1
Tz
0
−1
−2
−3
0
100
200
300
400
500
time [s]
600
700
800
900
1000
Sx
Sy
0.044
Sz
rotx
0
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roty
rotz
800
1000
ž
900
700
600
500
time [s]
400
300
200
100
0
−5
translation [mm] / rotations [rad]
Translations and Rotations. Robot movements
5
Forces given by the FT−Sensor
40
Fx
Fy
20
force [N]
Fz
0
−20
−40
0
100
200
300
400
500
time [s]
600
700
800
900
1000
Torques given by the FT−Sensor
torques [N*m]
Tx
2
Ty
1
Tz
0
−1
−2
0
100
200
300
400
500
time [s]
600
700
800
900
1000
translation [mm] / rotations [rad]
Translations and Rotations. Robot movements
5
Sx
Sy
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Sz
rotx
0
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roty
rotz
−5
0
100
200
300
400
500
time [s]
600
700
800
900
1000
ž
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Stiffness hysteresis in X rotation
1
20
0.5
Tx [N*m]
Fx [N]
Stiffness hysteresis in X translation
40
0
−20
−40
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0
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0
Trans x [mm]
2.5
−1
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5
4
20
2
0
−20
−40
−5
0.05
−2
−2.5
0
Trans y [mm]
2.5
−4
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5
Stiffness hysteresis in Z translation
−0.025
0
Rot y [rad]
0.025
0.05
Stiffness hysteresis in Z rotation
2
50
1
Tz [N*m]
Fz [N]
0.025
0
100
0
−50
−100
−5
0
Rot x [rad]
Stiffness hysteresis in Y rotation
40
Ty [N*m]
Fy [N]
Stiffness hysteresis in Y translation
−0.025
0
−1
−2
−0.05
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Trans z [mm]
2.5
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0
Rot z [rad]
0.025
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Stiffness hysteresis in X rotation
1
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Tx [N*m]
Fx [N]
Stiffness hysteresis in X translation
40
0
−20
−40
−5
0
−0.5
−2.5
0
Trans x [mm]
2.5
−1
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5
4
20
2
0
−20
−40
−5
0.05
−2
−2.5
0
Trans y [mm]
2.5
−4
−0.05
5
−0.025
Stiffness hysteresis in Z translation
0
Rot y [rad]
0.025
0.05
Stiffness hysteresis in Z rotation
2
50
1
Tz [N*m]
Fz [N]
0.025
0
100
0
−50
−100
−5
0
Rot x [rad]
Stiffness hysteresis in Y rotation
40
Ty [N*m]
Fy [N]
Stiffness hysteresis in Y translation
−0.025
0
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−2
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Stiffness parameters (revolute Joints)
120
revJoint[0]
revJoint[1]
revJoint[2]
revJoint[3]
revJoint[4]
revJoint[5]
revJoint[6]
100
60
40
20
Ažž
12
11
10
9
8
6
7
Number of configuration
5
4
3
2
1
0
Stiffness parameter [N*m/rad]
80
Stiffness parameters (prismatic Joints)
11000
prisJoint[0]
prisJoint[1]
prisJoint[2]
prisJoint[3]
prisJoint[4]
prisJoint[5]
10000
9000
Stiffness parameter [N/m]
8000
7000
6000
5000
4000
3000
2
3
4
6
7
Number of configuration
8
9
10
11
5
1
2000
12
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Stiffness parameters (auxiliary Joints) and rigid Links dimensions
0.28
auxJoint[0]
auxJoint[1]
rigLink[0]
rigLink[1]
0.26
Stiffness parameter [N/m] / Dimension rigid Links [m]
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
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12
11
10
9
8
6
7
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5
4
3
2
1
0.08
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Stiffness parameters (revolute Joints)
250
revJoint[0]
revJoint[1]
revJoint[2]
revJoint[3]
revJoint[4]
revJoint[5]
revJoint[6]
Stiffness parameter [N*m/rad]
200
150
100
50
Ež
0.6
0.8
1
2
4
3
Stiffness revJoint[3] "elbow" in [Nm/rad]
5
10
15
0
20
2
x 10
4
Stiffness parameters (prismatic Joints)
prisJoint[0]
prisJoint[1]
prisJoint[2]
prisJoint[3]
prisJoint[4]
prisJoint[5]
1.8
1.6
Stiffness parameter [N/m]
1.4
1.2
1
0.8
0.6
0.4
0.2
0
20
15
10
5
4
3
Stiffness revJoint[3] "elbow" in [Nm/rad]
2
1
0.8
0.6
ŠL¢ž
Stiffness parameters (auxiliary Joints) and rigid Links dimensions
0.26
auxJoint[0]
auxJoint[1]
rigLink[0]
rigLink[1]
0.24
Stiffness parameter [N/m] / Dimension rigid Links [m]
0.22
0.2
0.18
0.16
0.14
0.12
0.1
1
0.8
ž
0.6
2
4
3
Stiffness revJoint[3] "elbow" in [Nm/rad]
5
10
15
0.08
20
ž¢=
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Forces given by the Force−Sensor. Measurement−4
10
5
Force [N]
0
Fx
−5
F
−10
F
−15
y
z
−20
−25
0
50
100
150
200
250
300
350
400
450
500
Moments given by the Force−Sensor. Measurement−4
Moment (N*mm)
2
1
M
x
0
M
−1
Mz
y
−2
−3
0
50
100
150
200
250
300
350
400
450
500
Sx
0.044
0
-0.044
Sy
S
z
rot
z
roty
rotx
−5
500
>
ž
450
400
350
300
250
time [s]
200
150
100
50
0
delta of displacement [mm]
delta of rotation [rad]
Robot−movements (Translations & Rotations). Measurement−4
5
Forces given by the Force−Sensor. Measurement−6
15
10
Force [N]
5
Fx
0
Fy
−5
Fz
−10
−15
−20
0
50
100
150
200
250
300
350
400
450
500
Moments given by the Force−Sensor. Measurement−6
Moment (N*mm)
2
1
Mx
0
My
Mz
−1
−2
−3
0
50
100
150
200
250
300
350
400
450
500
delta of displacement [mm]
delta of rotation [rad]
Robot−movements (Translations & Rotations). Measurement−6
Sx
5
Sy
0.044
0
Sz
rot
-0.044
z
roty
rotx
−5
0
50
100
150
200
250
time [s]
300
350
400
450
500
Šž
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revJoint[0]
expected revJoint[0]
120
Stiffness parameter [N*m/rad]
100
80
60
40
20
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
9
8
6
7
number of configuration
5
10
11
%Šž
4
3
2
1
0
Stiffness parameter [N*m/rad]
revJoint[1]
expected revJoint[1]
40
35
30
25
20
15
10
5
12
revJoint[2]
expected revJoint[2]
140
120
Stiffness parameter [N*m/rad]
100
80
60
40
20
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
Šž
9
8
6
7
number of configuration
5
4
3
2
10
11
X%Šž
1
0
Stiffness parameter [N*m/rad]
revJoint[3] codo
expected revJoint[3]
20
18
16
14
12
10
8
6
4
2
12
revJoint[4]
expected revJoint[4]
80
70
Stiffness parameter [N*m/rad]
60
50
40
30
20
10
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
ŠEŠž
9
8
6
7
number of configuration
5
4
3
2
10
11
%Šž
1
0
Stiffness parameter [N*m/rad]
revJoint[5]
expected revJoint[5]
40
35
30
25
20
15
10
5
12
revJoint[6]
expected revJoint[6]
150
125
Stiffness parameter [N*m/rad]
100
75
50
25
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
=
Šž
prisJoint[0]
expected prisJoint[0]
2
x 10
4
1.8
1.6
1.2
1
0.8
0.6
0.4
0.2
4
5
6
7
number of configuration
8
9
10
11
>
%Šž
12
3
2
1
0
Stiffness parameter [N/m]
1.4
prisJoint[1]
expected prisJoint[1]
8000
7000
Stiffness parameter [N/m]
6000
5000
4000
3000
2000
1000
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
ž
8
9
6
7
number of configuration
5
4
3
2
10
11
Až
ž
1
0
Stiffness parameter [N/m]
prisJoint[2]
expected prisJoint[2]
10000
8000
6000
4000
2000
12
prisJoint[3]
expected prisJoint[3]
x 10
4
2
1.8
Stiffness parameter [N/m]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
Œ ž
8
9
6
7
number of configuration
5
10
11
ž
4
3
2
=
1
0
Stiffness parameter [N/m]
prisJoint[4]
expected prisJoint[4]
12000
10000
8000
6000
4000
2000
12
prisJoint[5]
expected prisJoint[5]
10000
Stiffness parameter [N/m]
8000
6000
4000
2000
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
ž
auxJoint[0]
expected auxJoint[0]
1
0.8
0.6
0.2
0
−0.2
−0.4
−0.6
−0.8
4
5
6
7
number of configuration
8
9
10
11
12
E
ž
3
2
1
−1
Angle of rotation [rad]
0.4
auxJoint[1]
expected auxJoint[1]
1
0.8
0.6
Angle of rotation [rad]
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
ŠLž
8
6
7
number of configuration
5
4
3
9
10
11
ž
2
1
0
Length of the rigid link [m]
rigLink[0]
expected rigLink[0]
0.5
0.4
0.3
0.2
0.1
12
rigLink[1]
expected rigLink[1]
0.5
Length of the rigid link [m]
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
number of configuration
8
9
10
11
12
ž
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PJ>QRosg@fKJDgR
b+;=b+;\I
’
„ Š †
†
mQBoK „ d † ;=b+;rb
y bQiEŠkb „ \b;=b+;\I
„ ^ †
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ †
† ;
jfDklCjYRY@UiEŠ ƒ+„ mQBoK •=<AhgmQBX<+•\I †
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
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jfD?lJjYRY@UifŠ ƒ
„ PJ>QRosg@fKJDgR †
y Š
’zy Dk@Ui
„ mQBoK „ Š †Q† ;
y ^
’zy Dk@Ui
„ mQBoK „ ^ †Q† ;
yAƒ6’zy Dk@Ui
„ mQBoK „rƒX†Q† ;
y 
’zy Dk@Ui
„ <AhgmQBX<
„ Š †Q† ;
y d
’zy Dk@Ui
„ <AhgmQBX<
„ ^ †Q† ;
y Œ
’zy Dk@Ui
„ mQBoK „ c †Q† ;
y bYi ƒ~’Oy Š y ^ yAƒ
y bYiEŠgb
;
’Oy bYi ƒ y  y d y Œ+;
jfD?lUiEŠ ƒ+„ Š G ƒ
•/Š †z’‹y bQiEŠgb
„ GJ•/Š † ;
jfD?lUiEŠ ƒ+„ Š G ƒ
•=^ †z’‹y bQiEŠgb
„ GJ•=^ † ;
jfD?lUiEŠ ƒ+„ Š G ƒ
• ƒE†z’‹y bQiEŠgb
„ GJ• ƒX† ;
jfD?lUiEŠ ƒ+„ Š G ƒ
•\ †z’‹y bQi ƒ „ \b+;=b+;emQBoK „  †
b+;=b+;\I
„ Š †
†
mQBoK „ } † ;=b;=b
† ;
mQBoK „ d † ;=b+;rb
y bQiEŠkb „ \b;=b+;\I
„ ^ †
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ † H`Y`Q`
PJ>QRosg@fKJDgR
'
’
joDklUiEŠ,
„ mQBoK •=<AhgmQBX<+•\I †
jfDklCjYRY@UiEŠ8
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
‰@fK8@XhJZaG
„ PJ>QRosg@fKJDgR †
jfD?lJjYRY@UifŠ,
y Š
’zy Dk@Ui
„ mQBoK „ Š †Q† ;
y ^
’zy Dk@Ui
„ mQBoK „ ^ †Q† ;
yAƒ6’zy Dk@Ui
„ mQBoK „rƒX†Q† ;
y 
’zy Dk@Ui
„ <AhgmQBX< „ Š †Q† ;
y d
’zy Dk@Ui
„ <AhgmQBX< „ ^ †Q† ;
y Œ
’zy Dk@Ui
„ mQBoK „ c †Q† ;
y bYi ƒ~’Oy Š y ^ yAƒ
;
y bYiEŠgb
’Oy bYi ƒ y  y d y Œ+;
jfD?lUiEŠ,
„ Š G ƒ
•/Š †z’‹y bQiEŠgb
„ GJ•/Š † ;
jfD?lUiEŠ,
„ Š G ƒ
•=^ †z’‹y bQiEŠgb
„ GJ•=^ † ;
jfD?lUiEŠ,
„ Š G ƒ
• ƒE†z’‹y bQiEŠgb
„ GJ• ƒX† ;
jfD?lUiEŠ,
„ Š G ƒ
•\ †z’‹y bQi ƒ „ \b+;=b+;emQBoK „  †
b+;=b+;\I
joDklUiEŠgd
†
mQBoK „ } † ;=b;=b
PJ>QRosg@fKJDgR
„ Š †
’
jfDklCjYRY@UiEŠkd
y bQiEŠkb „ \b;=b+;\I
mQBoK „ d † ;=b+;rb
„ ^ †
\b+; mQBLK „ Šgb † ;=b
† ;
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ † `Q`Y`
„ mQBoK •=<AhgmQBX<+•\I †
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
‰@fK8@XhJZaG
jfD?lJjYRY@UifŠgd
„ PJ>QRosg@fKJDgR †
y Š
’zy Dk@Ui
„ mQBoK „ Š †Q† ;
y ^
’zy Dk@Ui
„ mQBoK „ ^ †Q† ;
yAƒ6’zy Dk@Ui
„ mQBoK „rƒX†Q† ;
y 
’zy Dk@Ui
„ <AhgmQBX< „ Š †Q† ;
y d
’zy Dk@Ui
„ <AhgmQBX< „ ^ †Q† ;
y Œ
’zy Dk@Ui
„ mQBoK „ c †Q† ;
y c
’zy Dk@Ui
„ mQBoK „ ŠQŠ †Q† ;
y bYi ƒ~’Oy Š y ^ yAƒ
;
y bYiEŠgb
’Oy bYi ƒ y  y d y Œ+;
y bYiEŠgd
’Oy bYiEŠgb y c;
jfD?lUiEŠgd
„ Š G ƒ
•/Š †z’‹y bQiEŠgd
„ GJ•/Š † ;
jfD?lUiEŠgd
„ Š G ƒ
•=^ †z’‹y Q
b iEŠgd
„ GJ•=^ † ;
jfD?lUiEŠgd
„ Š G ƒ
• ƒE†z’‹y bQiEŠgd
„ GJ• ƒX† ;
jfD?lUiEŠgd
„ Š G ƒ
•\ †z’‹y bQi ƒ „ \b+;=b+;emQBoK „  †
b+;=b+;\I
joDklUiEŠgŒ
†
mQBoK „ } † ;=b;=b
PJ>QRosg@fKJDgR
„ Š †
’
jfDklCjYRY@UiEŠkŒ
y bQiEŠkb „ \b;=b+;\I
mQBoK „ d † ;=b+;rb
„ ^ †
\b+; mQBLK „ g
Š b † =
; b
† ;
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ † `Q`Y`
„ mQBoK •=<AhgmQBX<+•\I †
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
‰@fK8@XhJZaG
„ PJ>QRosg@fKJDgR †
jfD?lJjYRY@UifŠgŒ
y Š
’zy Dk@Ui
„ mQBoK „ Š †Q† ;
y ^
’zy Dk@Ui
„ mQBoK „ ^ †Q† ;
yAƒ6’zy Dk@Ui
„ mQBoK „rƒX†Q† ;
y 
’zy Dk@Ui
„ <AhgmQBX<
„ Š †Q† ;
y d
’zy Dk@Ui
„ <AhgmQBX<
„ ^ †Q† ;
y Œ
’zy Dk@Ui
„ mQBoK „ c †Q† ;
y c
’zy Dk@Ui
„ mQBoK „ ŠQŠ †Q† ;
y _
’zy Dk@Ui
„ mQBoK „ Šg^ †Q† ;
y bYi ƒ~’Oy Š y ^ yAƒ
;
y bYiEŠgb
’Oy bYi ƒ y  y d y Œ+;
y bYiEŠgŒ
’Oy bYiEŠgb y c y _;
jfD?lUiEŠgŒ
„ Š G ƒ
•/Š †z’‹y bQiEŠgŒ
„ GJ•/Š † ;
jfD?lUiEŠgŒ
„ Š G ƒ
•=^ †z’‹y bQiEŠgŒ
„ GJ•=^ † ;
jfD?lUiEŠgŒ
„ Š G ƒ
• ƒE†z’‹y bQiEŠgŒ
„ GJ• ƒX† ;
jfD?lUiEŠgŒ „ Š G ƒ
„ Š †
b+;=b+;\I
†
’
joDklUiEŠ8c
„ ^ †
\b+; mQBLK „ Šgb † ;=b
mQBoK „ d † ;=b+;rb
y bQiEŠkb „ \b;=b+;\I
mQBoK „ } † ;=b;=b
PJ>QRosg@fKJDgR
•\ †z’‹y bQi ƒ „ \b+;=b+;emQBoK „  †
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ † `Q`Y`
† ;
„ mQBoK •=<AhgmQBX<+•\I †
jfDklCjYRY@UiEŠgc
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
‰@fK8@XhJZaG
„ PJ>QRosg@fKJDgR †
jfD?lJjYRY@UifŠ8c
y Š
’zy Dk@Ui
„ mQBoK „ Š †Q† ;
y ^
’zy Dk@Ui
„ mQBoK „ ^ †Q† ;
yAƒ6’zy Dk@Ui
„ mQBoK „rƒX†Q† ;
y 
’zy Dk@Ui
„ <AhgmQBX< „ Š †Q† ;
y d
’zy Dk@Ui
„ <AhgmQBX< „ ^ †Q† ;
y Œ
’zy Dk@Ui
„ mQBoK „ c †Q† ;
y c
’zy Dk@Ui
„ mQBoK „ ŠQŠ †Q† ;
y _
’zy Dk@Ui
„ mQBoK „ Šg^ †Q† ;
y }
’zy Dk@Ui
„ mQBoK „ Š ƒX†Q† ;
y bYi ƒ~’Oy Š y ^ yAƒ
;
y bYiEŠgb
’Oy bYi ƒ y  y d y Œ+;
y bYiEŠ8c
’Oy bYiEŠgb y c y _ y }+;
jfD?lUiEŠ8c
„ Š G ƒ
•/Š †z’‹y bQiEŠ8c
„ GJ•/Š † ;
jfD?lUiEŠ8c
„ Š G ƒ
•=^ †z’‹y Q
b iEŠ8c
„ GJ•=^ † ;
jfD?lUiEŠ8c
„ Š G ƒ
• ƒE†z’‹y bQiEŠ8c
„ GJ• ƒX† ;
jfD?lUiEŠ8c
„ Š G ƒ
•\ †z’‹y bQi ƒ „ \b+;=b+;emQBoK „  †
b+;=b+;\I
PJ>QRosg@fKJDgR
y „ Š †
†
mQBoK „ } † ;=b;=b
y bQiEŠkb „ \b;=b+;\I
mQBoK „ d † ;=b+;rb
„ ^ †
\b+; mQBLK „ Šgb † ;=b
† ;
b+; mQBoK „ Œ † ;=b
\b+;rb+; mQBoK „ _ † `Q`Y`
’zy Dk@Ui
„ mQBoK †
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
'
y D?@Ui
‰@fK8@XhJZaG
„ PJ>QRosg@fKJDgR †
y ’
Šb6b+;
b—sCDYM „ mQBoK †‹ MYK8R
„ mQBoK †
b—MYK,R
y PJ>QRosg@fKJDgR
„ mQBoK † ;
sQDYM „ mQBLK † ];
’zy Dk@Ui
„ mQBoK †
T<?>Y@CBEDSFHG)IJ>oKCMWNA<JFQPU<?R—IA<OVED?FQFAZ
y D?@Ui
‰@fK8@XhJZaG
„ PJ>QRosg@fKJDgR †
y ’
rsQDYM „ mQBLK †
b—MYK,R
b
„ mYBoK † ;
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 MYK,R
PJ>QRosg@fKJDgR
y
„ mQBoK †
;
b—sCDYM „ mYBoK † ];
’zy Dk@Ui
„ mQBoK †
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‰@fK8@XhJZaG
y D?@Ui
„ PJ>QRosg@fKJDgR †
y
’
rsQDYM „ mQBLK †z MYK,R
b
MYK,R
„ mYBoK †
b
„ mQBoK †
b;
sCDYM „ mQBoK †
b;
Š ];