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SS
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6
.
(
T
h
e
p
ictu
r
e
b
elo
n
g
s
t
o
R
o
b
o
tic
ar
m
,
p
r
o
d
u
ct
o
f
KU
KA
C
o
m
p
a
n
y
)
I
n
t
h
is
ar
ticle,
w
e
d
escr
ib
e
o
u
r
s
u
cc
e
s
s
f
u
l
m
ec
h
an
i
s
m
d
esi
g
n
a
n
d
k
in
e
m
atic
s
i
m
u
latio
n
to
cr
ea
te
s
i
x
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
f
o
r
m
o
ti
o
n
in
a
r
o
b
o
tic
ar
m
,
w
h
ich
a
llo
w
ed
u
s
to
ef
f
ec
ti
v
el
y
co
n
t
r
o
l
i
ts
m
o
tio
n
.
T
h
e
f
u
n
ctio
n
alit
y
o
f
t
h
i
s
s
y
s
te
m
i
s
b
ased
o
n
p
ar
allel
m
ec
h
an
is
m
s
[
1
7
,
1
8
]
.
I
n
th
i
s
m
ec
h
an
i
s
m
w
e
h
a
v
e
u
s
ed
s
p
ec
iall
y
f
r
o
m
estab
lis
h
m
en
t
o
f
s
o
m
e
4
-
b
ar
lin
k
ag
e
m
ec
h
a
n
is
m
s
i
n
a
p
ar
allel
co
m
b
in
a
ti
o
n
.
B
y
s
o
d
o
in
g
,
w
e
w
er
e
ab
le
to
tr
an
s
m
it
t
h
e
r
o
tat
io
n
al
m
o
t
io
n
o
f
th
e
m
o
to
r
s
o
f
j
o
in
ts
3
,
4
,
5
,
an
d
6
(
all
o
f
w
h
ich
w
er
e
p
lace
d
in
th
e
R
o
b
o
t’
s
b
ase
a
n
d
in
t
h
e
li
n
k
1
)
to
its
o
w
n
m
ain
r
o
tatio
n
al
ax
i
s
f
o
r
j
o
in
t
3
a
n
d
to
t
h
e
r
ec
tif
ier
m
ec
h
an
is
m
f
o
r
th
e
o
th
er
j
o
in
ts
.
W
e
s
h
o
u
ld
n
o
tice
to
th
is
i
s
s
u
e
th
a
t
th
e
h
ig
h
r
ig
id
it
y
o
f
p
ar
allel
r
o
b
o
ts
(
an
d
p
ar
allel
m
ec
h
a
n
i
s
m
s
)
i
s
o
n
e
o
f
t
h
e
c
h
ar
ac
ter
is
tics
f
o
r
w
h
ich
th
e
y
ar
e
s
elec
ted
f
o
r
s
o
m
e
ap
p
licatio
n
s
[
1
8
]
.
T
h
e
m
ai
n
r
ea
s
o
n
f
o
r
s
elec
tio
n
o
f
a
p
ar
allel
li
n
k
a
g
e
m
ec
h
a
n
i
s
m
b
y
u
s
,
w
a
s
to
ass
is
t
t
h
e
r
o
b
o
t
in
b
ein
g
r
i
g
id
ag
a
in
s
t
u
n
w
an
ted
m
o
v
e
m
en
t,
w
h
ich
i
s
v
er
y
i
m
p
o
r
ta
n
t
in
ter
m
s
o
f
r
o
b
o
t’
s
v
ib
r
atio
n
an
d
co
n
tr
o
l
o
f
its
m
o
tio
n
.
I
n
f
ac
t,
th
e
lo
ca
tio
n
a
n
d
p
er
f
o
r
m
an
c
e
o
f
th
e
m
o
to
r
s
o
f
j
o
in
ts
1
an
d
2
w
er
e
th
e
s
a
m
e
a
s
th
e
y
ar
e
in
t
h
e
u
s
u
a
l
m
ec
h
a
n
i
s
m
s
f
o
r
s
u
ch
r
o
b
o
ts
,
s
in
ce
ch
a
n
g
in
g
th
e
p
o
s
itio
n
o
f
t
h
e
m
o
to
r
o
f
j
o
in
t
1
is
im
p
o
s
s
i
b
le,
an
d
,
in
jo
in
t
2
,
tan
g
ib
le
ch
a
n
g
e
i
n
t
h
e
a
m
o
u
n
t
o
f
i
m
p
o
r
ted
to
r
q
u
e
o
n
th
e
m
o
t
o
r
o
f
jo
in
t 1
is
in
e
f
f
ec
tiv
e.
I
n
s
ec
tio
n
t
w
o
o
f
t
h
is
ar
ticle,
w
e
s
h
o
w
th
e
d
esi
g
n
m
et
h
o
d
o
f
th
is
m
o
tio
n
tr
a
n
s
f
er
m
ec
h
an
is
m
,
w
e
d
esig
n
ed
a
C
A
D
m
o
d
el
f
o
r
an
o
p
er
atio
n
al
6
DOF
r
o
b
o
ti
c
ar
m
b
ased
o
n
t
h
i
s
m
ec
h
a
n
i
s
m
,
a
n
d
at
la
s
t
w
e
p
r
o
v
id
e
th
e
k
i
n
e
m
a
tic
r
elatio
n
s
h
ip
s
b
et
w
ee
n
th
e
ac
t
u
ato
r
s
s
p
ac
e
an
d
th
e
j
o
in
ts
s
p
ac
e
o
f
th
e
r
o
b
o
t
w
ith
t
h
i
s
m
ec
h
a
n
i
s
m
.
I
n
t
h
ir
d
s
ec
tio
n
,
an
o
p
en
-
lo
o
p
co
n
tr
o
l
m
et
h
o
d
u
s
ed
in
k
i
n
e
m
atic
s
i
m
u
la
ti
o
n
w
as
r
e
v
ie
w
ed
.
Mo
r
eo
v
er
,
th
e
k
in
e
m
at
ic
s
p
ec
if
icatio
n
s
o
f
t
h
e
s
i
m
u
lated
r
o
b
o
t,
s
i
m
u
latio
n
p
a
y
lo
ad
,
an
d
f
i
n
all
y
,
t
h
e
d
esi
g
n
o
f
a
s
i
m
u
latio
n
p
at
h
an
d
i
m
p
le
m
en
tatio
n
ap
p
r
o
ac
h
,
w
er
e
d
o
n
e
in
M
A
T
L
A
B
Si
m
Me
c
h
a
n
ics
s
o
f
t
w
ar
e
w
er
e
r
ev
ie
w
ed
.
I
n
th
e
s
ec
tio
n
f
o
u
r
,
w
e
p
r
o
v
id
e
t
h
e
r
esu
lts
o
f
k
i
n
e
m
atic
s
i
m
u
lat
io
n
o
f
th
e
r
o
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o
tic
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m
’
s
f
u
n
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n
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L
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m
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h
a
n
ics
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o
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t
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ar
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n
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ap
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o
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n
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t
h
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lts
o
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t
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e
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i
m
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la
tio
n
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d
i
n
t
h
e
las
t
s
ec
tio
n
w
e
w
il
l e
x
p
r
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t
h
e
co
n
clu
s
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n
s
o
b
tain
ed
f
r
o
m
t
h
e
s
i
m
u
latio
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r
es
u
lt
s
.
2.
MEC
H
A
N
ISM DE
SIG
N
O
F
M
O
T
I
O
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T
R
A
N
SF
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T
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asis
o
f
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n
ctio
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o
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m
ec
h
a
n
is
m
p
r
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n
te
d
h
er
e
w
as
e
s
tab
lis
h
ed
o
n
t
h
e
p
ar
allel
co
m
b
i
n
atio
n
o
f
s
o
m
e
o
f
4
-
b
ar
lin
k
ag
e
m
ec
h
a
n
i
s
m
s
.
T
h
e
p
r
o
ce
s
s
o
f
tr
a
n
s
f
er
r
in
g
r
o
tatio
n
al
m
o
tio
n
b
y
th
e
4
-
b
ar
lin
k
ag
e
m
ec
h
an
i
s
m
(
C
-
C
)
[
C
r
an
k
–
C
r
a
n
k
]
i
s
illu
s
tr
ated
in
F
ig
u
r
e
2.
I
n
F
i
g
u
r
e
2
,
w
e
ca
n
s
ee
tr
an
s
m
is
s
io
n
o
f
r
o
tar
y
m
o
tio
n
f
r
o
m
t
h
e
ac
t
u
ato
r
m
o
to
r
(
P
o
in
t O
1
)
to
th
e
f
o
llo
w
er
lin
k
’
s
ce
n
ter
o
f
r
o
tatio
n
(
P
o
in
t
O2
)
.
Fu
r
th
er
,
th
e
D
lin
k
is
r
o
tated
b
y
th
e
m
o
to
r
,
b
ec
au
s
e
th
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p
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r
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m
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m
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i
s
m
an
d
t
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e
F l
in
k
w
il
l t
u
r
n
ac
co
r
d
in
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to
its
ce
n
ter
o
f
r
o
tatio
n
.
So
th
e
D
a
n
d
F lin
k
s
al
w
a
y
s
w
il
l b
e
p
ar
allel.
Fig
u
r
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3
s
h
o
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s
t
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icac
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a
n
d
i
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IJ
RA
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A
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ew 6
DOF
R
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b
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tic
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r
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w
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tio
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Mech
a
n
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m
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ct
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...
(
Mo
h
s
en
S
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37
Fig
u
r
e
2.
R
i
g
h
t:
T
r
an
s
itio
n
p
r
o
ce
d
u
r
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o
f
r
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al
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b
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th
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k
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g
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m
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h
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(
C
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a
n
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–
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r
an
k
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.
L
e
f
t:
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eq
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v
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n
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ig
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d
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r
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o
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r
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R
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P
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o
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j
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4
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6
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3
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3
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r
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L
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An
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38
I
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F
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4
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g
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4
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:
Th
e
fir
s
t
co
n
d
itio
n
:
T
h
e
m
o
t
o
r
o
f
jo
in
t
3
is
in
t
h
e
in
itial
s
tate
an
d
is
n
o
t
r
o
tatin
g
;
j
o
in
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2
h
as
+α
d
eg
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s
r
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s
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m
i
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g
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at
th
e
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ir
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o
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n
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m
al
v
ec
to
r
o
f
r
o
tatio
n
is
in
w
ar
d
th
e
p
late)
.
No
w
,
w
e
ca
n
s
ee
th
at
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e
ar
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o
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in
t 3
h
as d
ev
iated
–
α
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s
f
r
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m
lin
k
No
.
2
,
th
er
ef
o
r
e
w
e
h
a
v
e:
3
2
3
3
2
3
0
(
)
m
a
a
a
a
m
(
1
)
*
m
: r
o
tatio
n
r
elate
d
to
th
e
m
o
to
r
o
f
jo
in
t;
a
: r
o
tatio
n
r
elate
d
to
th
e
j
o
in
t.
Th
e
s
ec
o
n
d
co
n
d
itio
n
:
T
h
e
m
o
to
r
o
f
j
o
in
t
3
h
as
b
ee
n
r
o
tate
d
+α
d
e
g
r
ee
s
,
a
n
d
j
o
in
t
2
al
s
o
h
a
s
+
α
d
eg
r
ee
s
o
f
r
o
tatio
n
.
No
w
,
w
e
ca
n
s
ee
th
at
lin
k
s
No
.
3
an
d
No
.
2
ar
e
in
t
h
e
s
a
m
e
d
ir
ec
tio
n
.
T
h
er
ef
o
r
e
w
e
h
av
e:
3
2
3
3
2
3
(
)
(
)
0
m
a
a
a
a
m
(
2
)
Th
e
th
ir
d
co
n
d
itio
n
:
T
h
e
m
o
t
o
r
o
f
j
o
in
t
3
is
r
o
tated
+
(
α
+β)
d
eg
r
ee
s
,
an
d
j
o
in
t
2
is
r
o
tated
+α
d
eg
r
ee
s
.
No
w
,
w
e
ca
n
s
ee
t
h
at
th
e
ar
m
o
f
j
o
in
t 3
h
as d
ev
iated
+β d
eg
r
ee
s
f
r
o
m
t
h
e
ar
m
o
f
j
o
in
t 2
.
T
h
er
ef
o
r
e
w
e
h
a
v
e:
3
2
3
3
2
3
(
)
(
)
m
a
a
a
a
m
(
3
)
No
w
,
w
e
h
a
v
e
d
is
c
u
s
s
ed
th
e
co
n
d
itio
n
s
o
f
t
h
e
r
elatio
n
s
h
ip
s
o
f
m
o
t
io
n
b
et
w
ee
n
t
h
e
r
o
tati
o
n
o
f
j
o
in
t
3
,
r
o
tatio
n
o
f
j
o
in
t
2
,
an
d
r
o
tat
io
n
o
f
t
h
e
m
o
to
r
o
f
j
o
in
t
3
i
n
a
ll t
h
r
ee
co
n
d
itio
n
s
.
Af
ter
ca
lcu
latin
g
t
h
e
eq
u
atio
n
cr
ea
tin
g
th
e
s
e
co
n
d
itio
n
s
,
if
w
e
w
an
t
to
d
is
tr
ib
u
te
t
h
is
r
ela
tio
n
s
h
ip
to
li
n
k
ag
e
m
ec
h
a
n
is
m
s
o
f
j
o
in
t
s
No
.
4
,
5
an
d
6
,
b
ec
au
s
e
th
e
lin
k
a
g
e
m
e
ch
an
i
s
m
s
o
f
th
e
s
e
j
o
in
ts
f
r
o
m
th
e
b
ase
o
f
th
e
r
o
b
o
t
u
p
to
th
e
jo
in
t
3
ar
e
s
i
m
ilar
to
lin
k
ag
e
m
ec
h
a
n
is
m
o
f
j
o
in
t
3
,
f
o
r
all
o
f
t
h
e
li
n
k
ag
e
m
e
c
h
an
i
s
m
s
o
f
t
h
ese
f
o
u
r
j
o
in
ts
(
3
,
4
,
5
an
d
6
)
,
w
e
h
av
e
a
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
m
o
tio
n
o
f
li
n
k
ag
e
m
ec
h
an
i
s
m
s
a
n
d
th
e
r
o
tatio
n
s
o
f
j
o
in
ts
No
.
2
an
d
3
.
32
aa
(
4
)
T
h
is
eq
u
atio
n
(
No
.
4
)
is
eq
u
al
to
3
m
(
r
eq
u
ir
ed
r
o
tatio
n
f
o
r
m
o
t
o
r
o
f
j
o
in
t
3
)
f
o
r
j
o
in
t
3
’
s
r
o
tatio
n
p
r
o
ce
d
u
r
e,
an
d
eq
u
al
to
th
e
af
f
ec
ted
an
g
le
o
n
t
h
e
li
n
k
a
g
e
m
o
t
io
n
m
ec
h
an
is
m
s
o
f
j
o
in
ts
No
.
4
,
5
an
d
6
f
r
o
m
r
o
tatio
n
s
o
f
j
o
in
ts
No
.
2
an
d
3
.
W
e
m
u
s
t
b
ea
r
in
m
i
n
d
th
at
t
h
e
r
o
tatio
n
o
f
j
o
in
t
No
.
1
h
as
n
o
in
f
l
u
en
ce
o
n
t
h
e
m
o
tio
n
o
f
t
h
e
co
n
n
ec
to
r
s
o
f
t
h
e
4
-
b
ar
lin
k
a
g
e
m
ec
h
a
n
is
m
s
.
Up
to
th
is
s
tep
,
w
e
h
av
e
d
is
cu
s
s
ed
h
o
w
th
e
r
o
tatio
n
o
f
j
o
in
ts
1
,
2
,
an
d
3
o
cc
u
r
s
,
an
d
,
also
,
th
e
d
ep
en
d
en
c
y
o
f
t
h
e
m
o
tio
n
o
f
j
o
in
t
3
to
j
o
in
t
2
w
a
s
ex
p
la
in
ed
.
Fo
r
o
th
er
lin
k
s
(
4
,
5
,
a
n
d
6
)
,
w
e
tr
a
n
s
f
er
r
o
tatio
n
al
m
o
tio
n
b
y
m
ea
n
s
o
f
a
lin
k
a
g
e
m
ec
h
a
n
i
s
m
f
r
o
m
t
h
eir
m
o
to
r
s
to
t
h
eir
co
n
n
ec
tio
n
p
o
in
ts
to
t
h
e
s
et
o
f
b
ev
el
g
ea
r
s
.
Fro
m
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u
r
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6
[
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o
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,
5
,
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d
6
.
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h
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atic
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m
ic
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
0
8
9
-
4856
IJ
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Vo
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5
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ased
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it.
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r
t
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ata
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p
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etc.
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.
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p
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ater
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(
1
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s
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3
0
4
,
(
2
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m
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u
m
(
A
l
2
2
1
9
-
T
8
7
)
a
n
d
(
3
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titan
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m
(
T
it
/
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i
-
8
Al
-
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-
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V)
an
d
th
eir
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n
ical
p
r
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ties
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e
p
r
esen
ted
r
esp
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t
iv
el
y
in
r
e
f
er
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ce
No
.
[
2
1
]
.
Fig
u
r
e
7.
Ov
er
all
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ie
w
o
f
th
e
o
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ter
s
tr
u
ct
u
r
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o
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t
h
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C
A
D
m
o
d
el
o
f
th
e
6
DOF
R
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o
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ar
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:
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)
R
o
b
o
t’
s
b
ase
(
lo
ca
tio
n
o
f
m
o
to
r
s
o
f
j
o
in
ts
)
;
2
)
lin
k
No
.
1
; 3
)
lin
k
No
.
2
; 4
)
lin
k
No
.
3
; 5
)
lin
k
No
.
4
; 6
)
li
n
k
No
.
5
; 7
)
lin
k
No
.
6
(
en
d
ef
f
ec
to
r
)
; 8
)
j
o
in
t 2
; 9
)
j
o
in
t 3
;
1
0
)
m
o
to
r
o
f
j
o
in
t 2
.
Fig
u
r
e
8
.
v
ie
w
o
f
t
h
e
in
n
er
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tr
u
ct
u
r
e
o
f
th
e
r
o
b
o
t’
s
b
ase
o
n
w
h
ich
t
h
e
m
o
to
r
s
f
o
r
th
e
j
o
in
ts
ar
e
p
lace
d
:
1
)
co
n
tain
er
o
f
m
o
to
r
s
an
d
th
e
l
in
k
s
co
n
n
ec
ted
to
th
e
m
in
r
o
b
o
t
b
ase;
2
)
lin
k
No
.
1
(
ar
m
o
f
j
o
in
t
1
)
;
3
)
j
o
in
t
2
;
4
)
lin
k
No
.
2
;
5
)
m
o
to
r
o
f
j
o
in
t
1
;
6
)
m
o
to
r
o
f
j
o
in
t
2
;
7
)
m
o
to
r
o
f
j
o
in
t
3
;
8
)
m
o
to
r
o
f
jo
in
t
4
;
9
)
m
o
to
r
o
f
j
o
in
t 5
; 1
0
)
m
o
to
r
o
f
j
o
in
t 6
.
Fig
u
r
e
9
.
a
v
ie
w
o
f
th
e
in
n
e
r
s
tr
u
ct
u
r
e
o
f
l
in
k
No
.
2
,
u
n
til
t
h
e
en
d
ef
f
ec
to
r
o
f
r
o
b
o
t
w
h
er
e
t
h
e
ar
r
an
g
e
m
en
t
o
f
m
o
ti
v
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co
m
p
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en
t
s
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f
m
ec
h
an
i
s
m
i
s
o
b
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ed
:
1
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ar
m
o
f
j
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in
t
No
.
2
an
d
th
e
li
n
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it
;
2
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j
o
in
t
3
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lin
k
No
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3
an
d
s
et
o
f
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r
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o
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m
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lin
k
No
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4
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li
n
k
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5
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lin
k
No
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6
(
en
d
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to
r
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2
.
2
.
K
inem
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Rela
t
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ns
hip
s
bet
w
ee
n J
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ints Spa
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a
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Act
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rs Spa
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
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N:
2089
-
4856
A
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ew 6
DOF
R
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b
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tic
A
r
m
w
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th
Lin
ka
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e
Mo
tio
n
Mech
a
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m
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d
A
ct
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to
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...
(
Mo
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en
S
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a
h
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o
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41
As
m
en
t
io
n
ed
i
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t
h
e
I
n
tr
o
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c
tio
n
,
th
e
r
o
tatio
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o
f
t
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t
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is
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t
ar
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ter
r
elate
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d
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e
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m
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s
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j
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ts
3
th
r
o
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h
6
ar
e
d
ep
en
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en
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o
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th
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tatio
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s
o
f
th
e
o
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o
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ts
.
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t
is
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m
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tan
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latio
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f
ac
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w
it
h
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t
k
n
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w
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t
h
is
r
elatio
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ip
,
it
i
s
n
o
t
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o
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s
ib
le
to
co
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m
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m
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d
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w
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m
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to
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ase
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cc
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Fig
u
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6
,
w
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s
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ts
5
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6
.
T
h
e
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r
s
No
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1
to
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6
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w
h
ich
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e
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e
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e
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f
ec
ti
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e
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ar
ts
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n
d
r
atio
s
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et
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ee
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th
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m
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air
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e
eq
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al
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1
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e
eq
u
al
to
:
f
o
r
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ea
r
s
No
.
1
:
6
,
No
.
2
:
6
,
No
.
3
:
6
5
4
,
No
.
4
:
0
,
No
.
5
:
5
an
d
No
.
6
:
45
.
T
h
ese
am
o
u
n
ts
ar
e
g
iv
en
b
ased
o
n
th
e
p
r
ac
tical
r
o
tatio
n
an
g
le
o
f
th
e
r
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o
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s
m
a
in
j
o
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ts
.
An
d
also
f
o
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th
e
r
o
tatio
n
o
f
j
o
in
ts
5
an
d
6
in
th
e
p
o
s
it
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v
e
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ir
ec
tio
n
.
I
n
th
e
f
o
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g
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d
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co
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to
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h
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v
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f
r
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m
Fi
g
u
r
e
6
,
w
e
r
ev
ie
w
Fi
g
u
r
e
5
an
d
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
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ec
ti
f
ier
m
ec
h
a
n
i
s
m
.
I
t
is
i
m
p
o
r
tan
t
to
n
o
te
in
th
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s
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t
io
n
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h
at
t
h
e
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n
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m
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tio
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o
f
g
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r
s
No
.
2
an
d
4
in
Fi
g
u
r
e
5
is
eq
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al
to
th
e
a
m
o
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n
t
o
f
r
o
tatio
n
o
f
g
ea
r
s
No
.
3
an
d
6
in
Fi
g
u
r
e
6
,
b
ec
au
s
e
t
h
e
g
ea
r
s
ar
e
j
o
in
ed
m
u
tu
al
l
y
to
e
ac
h
o
th
er
b
y
m
ea
n
s
o
f
n
ested
s
h
a
f
ts
7
an
d
8
,
as
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
C
o
n
s
id
er
in
g
th
is
f
ac
t,
w
e
e
x
a
m
in
ed
t
h
e
r
o
tatio
n
al
an
g
le
s
o
f
g
ea
r
s
No
.
1
th
r
o
u
g
h
6
in
Fi
g
u
r
e
5
,
w
h
ic
h
ar
e
th
e
o
n
l
y
ef
f
ec
t
iv
e
m
o
v
i
n
g
p
ar
ts
in
t
h
e
r
ec
ti
f
ier
m
ec
h
a
n
i
s
m
.
T
h
e
r
atio
s
b
et
w
e
en
t
h
e
m
ar
e
p
air
w
i
s
e
eq
u
al
to
1
.
T
h
ese
v
alu
e
s
ar
e
eq
u
al
to
:
f
o
r
g
ea
r
s
No
.
1
:
6
5
4
,
No
.
2
:
6
5
4
,
No
.
3
:
54
,
No
.
4
:
54
,
No
.
5
:
4
an
d
No
.
6
:
4
.
T
h
ese
r
o
tatio
n
v
alu
es
o
f
t
h
e
g
ea
r
s
ar
e
g
i
v
en
b
as
ed
o
n
th
e
p
r
ac
tical
r
o
tatio
n
an
g
le
o
f
th
e
r
o
b
o
t’
s
m
ai
n
j
o
in
ts
,
w
h
ic
h
ca
n
r
o
tate
jo
in
ts
No
.
4
,
5
,
an
d
6
in
th
e
p
o
s
itiv
e
d
ir
ec
tio
n
.
I
n
th
e
n
e
x
t
s
tep
,
co
n
s
id
er
in
g
t
h
e
ca
lcu
latio
n
s
i
n
th
i
s
s
ec
tio
n
w
h
ich
h
a
v
e
d
eter
m
i
n
ed
th
e
r
o
tatio
n
s
o
f
g
ea
r
s
No
.
1
,
3
an
d
5
o
f
Fig
5
,
an
d
th
e
r
elatio
n
s
h
ip
s
o
f
m
o
ti
o
n
b
et
w
ee
n
th
e
ac
tu
a
to
r
s
an
d
th
e
in
ter
n
al
m
o
b
ile
co
m
p
o
n
e
n
t
s
in
l
in
k
s
No
.
2
,
No
.
3
an
d
th
e
b
ase
o
f
r
o
b
o
t,
th
ese
w
er
e
alr
ea
d
y
ca
lc
u
lated
i
n
s
ec
tio
n
2
an
d
b
ased
o
n
Fig
s
.
2
,
3
an
d
4
(
eq
u
atio
n
s
No
.
1
to
4
)
.
B
ec
au
s
e
th
e
r
o
tatio
n
al
ax
e
s
o
f
th
o
s
e
g
ea
r
s
(
g
e
ar
s
No
.
1
,
3
an
d
5
)
an
d
th
e
r
o
tatio
n
al
ax
e
s
o
f
j
o
in
ts
No
.
2
an
d
3
ar
e
th
e
s
am
e
an
d
in
o
n
e
d
ir
ec
tio
n
w
e
ca
n
s
u
m
t
h
e
a
m
o
u
n
ts
o
f
th
o
s
e
r
o
tatio
n
al
a
n
g
les
s
o
w
e
ca
n
ca
lcu
late
t
h
e
k
i
n
e
m
atic
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
m
o
b
i
le
co
m
p
o
n
e
n
ts
a
n
d
th
e
ac
t
u
a
to
r
s
f
o
r
all
s
i
x
j
o
in
ts
o
f
th
e
6
-
DOF
r
o
b
o
tic
ar
m
d
is
cu
s
s
ed
in
t
h
is
p
ap
er
,
co
n
s
i
d
er
in
g
t
h
e
p
o
s
itiv
e
d
ir
ec
tio
n
o
f
r
o
tatio
n
f
o
r
th
e
ac
tu
ato
r
s
s
h
o
w
n
i
n
Fi
g
u
r
e
8
.
T
h
is
r
elatio
n
s
h
ip
ca
n
b
e
ex
p
r
ess
e
d
as sh
o
w
n
b
elo
w
:
(
2
)
(
3
)
(
2
)
(
3
)
(
2
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(
3
)
(
2
)
(
3
)
(
3
)
(
2
)
(
2
)
(
1
)
(
1
)
aa
aa
aa
a
a
m
am
am
+
(
4
)
(
5
)
(
6
)
(
4
)
(
5
)
(
4
)
a
a
a
aa
a
(
2
)
(
3
)
(
4
)
(
5
)
(
6
)
(
6
)
(
2
)
(
3
)
(
4
)
(
5
)
(
5
)
(
2
)
(
3
)
(
4
)
(
4
)
(
2
)
(
3
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(
3
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(
2
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(
2
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(
1
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(
1
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a
a
a
a
a
m
a
a
a
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m
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a
a
m
a
a
m
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am
C
o
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s
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s
f
r
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m
eq
u
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n
4
C
o
n
clu
s
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n
s
f
r
o
m
F
ig
s
5
Kin
e
m
atic
r
elatio
n
s
b
et
w
e
en
ac
tu
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r
s
ap
ac
e
(
f
r
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ase
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to
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o
in
t 3
)
.
an
d
6
(
f
r
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m
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t 3
u
p
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s
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o
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(5
-
1)
en
d
ef
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ec
to
r
)
.
(5
-
2)
(5
-
3)
*
m
: r
o
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r
elate
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th
e
m
o
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jo
in
t;
a
:
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elate
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e
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t.
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n
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e
k
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e
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i
m
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ta
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e
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elate
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a
n
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E
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5
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w
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atic
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ed
in
t
h
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p
ap
er
.
3
.
SI
M
UL
AT
I
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N
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AN
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
5
,
No
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1
,
Ma
r
ch
2
0
1
6
:
3
5
–
4
8
42
Ou
r
g
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MA
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m
Me
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Ot
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a
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T
o
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k
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b
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,
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s
h
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ld
d
o
th
e
f
o
llo
w
in
g
s
tep
s
in
o
r
d
er
:
[
1
]
C
a
lcu
la
te
th
e
p
a
th
g
en
era
tio
n
o
f
d
esir
ed
kin
ema
tic
elem
en
ts
:
a
p
r
o
ce
s
s
th
at
h
as
f
o
u
r
in
ter
n
al
s
tag
e
s
,
i.e
.
,
1
.
1
.
C
alcu
latio
n
o
f
t
h
e
i
n
v
er
s
e
k
i
n
e
m
atic;
1
.
2
.
C
alcu
latio
n
o
f
th
e
v
elo
cit
y
o
f
j
o
in
t
s
b
a
s
ed
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n
t
h
e
s
p
ee
d
o
f
th
e
e
n
d
ef
f
ec
to
r
a
n
d
t
h
e
J
ac
o
b
ian
m
atr
ix
;
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.
3
.
C
alcu
latio
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o
f
t
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p
at
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-
g
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er
atio
n
f
o
r
m
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las
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ased
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th
ir
d
o
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f
i
f
th
d
e
g
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m
i
als.
1
.
4
.
C
alcu
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o
f
t
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e
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es
ir
ed
k
in
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m
atic
ele
m
e
n
ts
to
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m
u
late
r
o
b
o
t in
j
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ts
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p
ac
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ased
o
n
th
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p
at
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g
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f
o
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m
u
la
s
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d
th
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s
i
m
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n
t
i
m
e.
T
h
e
m
e
th
o
d
s
o
f
ca
lcu
lat
io
n
in
t
h
is
s
ec
tio
n
ar
e
t
h
e
s
a
m
e
a
s
th
o
s
e
f
o
r
o
th
er
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o
b
o
tic
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m
s
.
T
h
er
ef
o
r
e,
to
av
o
id
ex
ce
s
s
i
v
e
an
d
r
ep
etitiv
e
in
f
o
r
m
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n
,
w
e
d
id
n
o
t
p
r
o
v
id
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th
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eq
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s
a
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tio
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s
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er
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Fo
r
m
o
r
e
in
f
o
r
m
atio
n
,
s
ee
r
ef
er
en
ce
No
.
[
1
9
]
(
C
h
.
4
,
5
a
n
d
7
)
.
[
2
]
C
a
lcu
la
tin
g
th
e
va
lu
es
o
f
th
e
kin
ema
tic
elem
en
ts
o
f
th
e
a
ctu
a
to
r
s
:
w
h
ich
ar
e
en
ter
ed
to
th
e
r
o
b
o
t
as
co
m
m
a
n
d
v
alu
e
s
.
T
h
ese
a
m
o
u
n
ts
w
ill b
e
ca
lcu
la
ted
o
n
t
h
e
b
asis
o
f
t
h
e
v
al
u
es t
h
at
ar
e
d
ef
i
n
ed
as
d
es
ir
ed
v
alu
e
s
f
o
r
th
e
m
o
tio
n
o
f
j
o
in
t
s
f
r
o
m
th
e
p
ath
g
e
n
er
atio
n
b
l
o
ck
an
d
also
t
h
e
r
elatio
n
s
h
ip
s
b
et
w
ee
n
t
h
e
ac
tu
ato
r
s
s
p
ac
e
an
d
j
o
in
ts
(
in
ter
n
a
l
m
o
ti
v
e
p
ar
ts
)
s
p
ac
e
th
at
ar
e
cr
ea
ted
b
ec
au
s
e
o
f
th
i
s
m
o
tio
n
tr
an
s
m
is
s
io
n
m
ec
h
an
i
s
m
(
as e
x
p
lain
ed
i
n
s
ec
tio
n
2
.
2
)
.
[
3
]
R
o
ta
tio
n
a
l
p
o
s
itio
n
err
o
r
:
W
e
i
m
p
le
m
en
ted
k
i
n
e
m
a
tic
s
i
m
u
l
atio
n
o
f
t
h
e
r
o
b
o
t
in
th
e
r
o
tati
o
n
al
s
p
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e
o
f
th
e
j
o
in
ts
,
s
o
er
r
o
r
s
in
th
e
r
o
tat
io
n
al
p
o
s
itio
n
o
f
t
h
e
j
o
in
ts
ca
n
b
e
d
ef
in
ed
as f
o
llo
w
s
.
6
[
1
9
]
)
d
o
E
*
o
: o
u
tp
u
t o
f
s
i
m
u
la
tio
n
v
alu
es,
d
: d
esire
d
v
alu
e
s
Fig
u
r
e
1
0
.
S
h
o
w
s
a
B
lo
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Dia
g
r
a
m
o
f
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Op
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L
o
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p
C
o
n
tr
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l S
y
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o
f
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Ki
n
e
m
atic
Si
m
u
latio
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o
f
T
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R
o
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A
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m
B
ased
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Dis
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Fig
u
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e
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Diag
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Kin
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d
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esire
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c
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o
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r
r
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T
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e
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o
f
t
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Si
m
Me
c
h
an
ic
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m
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d
el
f
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k
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m
ati
c
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A
p
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3
.
1
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K
inem
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ic
pro
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s
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Fig
u
r
e
1
1
an
d
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ab
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s
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o
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r
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m
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elate
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w
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icate
th
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k
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m
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w
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De
n
av
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[
2
2
]
p
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ex
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(
Her
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L
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=
4
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5
m
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,
L
2
=
4
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0
m
m
,
an
d
L
3
=
4
4
2
m
m
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
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4856
A
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DOF
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43
Fig
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A
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Fra
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et
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Den
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in
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tab
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s
h
o
w
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an
g
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o
f
r
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T
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Used in t
he
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1
2
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ap
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n
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(
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4
Fig
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Evaluation Warning : The document was created with Spire.PDF for Python.