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Peo
p
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with
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d
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6
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[
8
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an
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.
Alth
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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I
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Dyn
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au
x
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s
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s
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h
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.
Ho
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ies
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till
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Gao
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[
2
0
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u
s
ed
class
ical
m
ath
em
atica
l
m
eth
o
d
s
to
an
aly
ze
th
e
o
p
e
r
atio
n
o
f
a
r
o
b
o
t
with
a
co
iled
tail
r
o
d
m
ec
h
an
is
m
to
b
alan
ce
its
ce
n
ter
o
f
g
r
av
ity
.
Ho
wev
e
r
,
th
e
r
esear
ch
was
n
o
t
f
ea
s
ib
le
in
th
e
p
r
o
ce
s
s
o
f
tr
an
s
p
o
r
tin
g
p
eo
p
le.
T
h
e
d
y
n
am
ics
o
f
a
wh
ee
lch
air
m
o
v
in
g
with
a
wh
ee
l
ass
em
b
ly
an
d
a
s
u
p
p
o
r
t
m
ec
h
an
is
m
wer
e
s
tu
d
ied
[
2
1
]
.
T
h
e
r
o
b
o
t
m
o
v
in
g
u
p
s
tair
s
with
o
u
t
a
lo
ad
s
h
o
wed
th
e
ab
ilit
y
to
cl
im
b
s
tair
s
an
d
s
tab
ilit
y
at
a
f
ix
ed
s
tair
s
ize.
R
esear
ch
b
y
T
ian
-
ci
J
ian
g
an
d
Gr
ze
g
o
r
z
D
o
b
r
zy
ń
s
k
i
an
aly
ze
d
th
e
ty
p
es
o
f
r
o
b
o
ts
ca
p
a
b
le
o
f
clim
b
in
g
s
tair
s
an
d
p
r
o
p
o
s
ed
a
r
o
b
o
t
d
esig
n
with
a
u
s
er
-
co
n
tr
o
lled
ce
n
ter
o
f
g
r
av
ity
to
lim
it tip
p
in
g
; h
o
w
ev
er
,
th
e
r
esu
lts
wer
e
o
n
ly
s
im
u
latio
n
s
[
2
2
]
,
[
2
3
]
.
R
o
b
o
ts
ca
p
ab
le
o
f
s
ea
t
ad
ju
s
tm
en
t
an
d
d
am
p
in
g
a
r
e
d
es
ig
n
ed
in
3
D
s
o
f
twar
e
p
r
o
p
o
s
ed
b
y
Pro
f
.
S.M
.
R
am
n
an
i
an
d
co
lleag
u
es;
h
o
w
ev
er
,
th
e
cu
r
r
en
t
s
y
s
tem
is
li
m
ited
in
s
ize
an
d
th
e
au
to
m
ati
c
ca
p
ab
ilit
ies
o
f
th
e
b
alan
cin
g
an
d
an
ti
-
tilt
in
g
s
y
s
tem
[
2
4
]
.
D
o
b
r
z
y
ń
s
k
i
et
a
l.
[
2
5
]
u
s
es a
b
alan
cin
g
s
lid
er
to
p
er
f
o
r
m
th
e
p
r
o
ce
s
s
o
f
m
o
v
in
g
u
p
s
tair
s
;
th
e
r
o
b
o
t'
s
d
y
n
am
ic
eq
u
atio
n
s
ar
e
also
p
r
esen
ted
,
b
u
t
s
till
in
a
3
D
en
v
ir
o
n
m
en
t,
an
d
o
s
cillatio
n
s
ex
is
t.
C
h
awa
p
h
an
et
a
l.
[
2
6
]
u
s
in
g
s
en
s
o
r
s
in
th
e
p
r
o
ce
s
s
o
f
ce
n
ter
o
f
g
r
av
ity
co
n
tr
o
l
is
also
s
o
m
ewh
at
f
ea
s
ib
le,
alth
o
u
g
h
i
t
is
in
th
e
test
in
g
p
h
ase.
So
m
e
r
o
b
o
ts
ca
n
ca
r
r
y
lo
ad
s
f
r
o
m
3
k
g
to
1
2
0
k
g
[
2
7
]
an
d
ca
n
m
o
v
e
o
n
s
tair
s
;
h
o
wev
er
,
th
e
ce
n
ter
o
f
g
r
av
ity
c
o
n
tr
o
l
p
r
o
ce
s
s
is
n
o
t
y
et
ca
p
ab
le
o
f
m
o
v
in
g
o
n
d
if
f
er
en
t step
s
,
an
d
th
e
s
tr
u
ct
u
r
e
is
q
u
ite
co
m
p
lex
[
2
8
]
.
B
ased
o
n
th
e
k
i
n
em
atic
eq
u
atio
n
s
an
d
d
y
n
am
ics o
f
th
e
r
o
b
o
t,
a
clo
s
ed
-
lo
o
p
e
r
r
o
r
c
o
n
tr
o
l
s
y
s
tem
to
m
ain
tain
s
tab
ilit
y
d
u
r
in
g
th
e
r
o
b
o
t'
s
m
o
v
em
en
t
was
s
tu
d
ied
[
2
9
]
,
[
3
0
]
.
C
u
r
r
en
t
s
tu
d
ies
h
av
e
ac
h
iev
ed
s
o
m
e
s
u
cc
ess
in
th
e
p
r
o
ce
s
s
o
f
th
e
r
o
b
o
t
m
o
v
in
g
u
p
s
tair
s
;
h
o
wev
er
,
it
is
s
till
n
o
t tr
u
ly
ef
f
ec
tiv
e
in
tr
an
s
p
o
r
tin
g
p
eo
p
le
u
p
a
n
d
d
o
wn
s
tair
s
.
I
n
th
is
s
tu
d
y
,
a
m
o
d
el
o
f
a
r
o
b
o
t
tr
an
s
p
o
r
tin
g
p
e
o
p
le
u
p
s
tair
s
u
s
in
g
tr
ac
k
s
,
em
p
lo
y
i
n
g
lin
ea
r
ac
tu
ato
r
s
in
an
ti
-
r
o
ll
co
n
t
r
o
l
a
n
d
o
s
cillatio
n
r
ed
u
ctio
n
,
is
p
r
o
p
o
s
ed
.
T
h
e
c
h
an
g
e
in
th
e
r
o
b
o
t's
ce
n
ter
o
f
g
r
av
ity
ac
co
r
d
in
g
t
o
th
e
s
tair
s
lo
p
e
is
ev
alu
ated
th
r
o
u
g
h
th
e
d
y
n
am
ic
eq
u
atio
n
s
b
u
ilt
th
r
o
u
g
h
o
u
t
th
e
o
p
er
atio
n
.
T
h
e
r
esu
lts
o
f
th
e
an
aly
s
is
an
d
ev
alu
atio
n
o
f
th
e
r
o
b
o
t'
s
o
p
er
atin
g
s
tate
ar
e
v
er
if
ied
in
s
im
u
latio
n
an
d
ex
p
er
im
en
t
to
co
n
f
ir
m
th
e
co
r
r
ec
tn
ess
o
f
th
e
co
n
s
tr
u
cted
d
y
n
am
ic
eq
u
a
tio
n
s
an
d
to
s
er
v
e
as
a
b
asi
s
f
o
r
b
u
ild
in
g
an
an
ti
-
r
o
ll c
o
n
tr
o
l a
lg
o
r
ith
m
f
o
r
th
e
r
o
b
o
t tr
an
s
p
o
r
tin
g
p
eo
p
le.
2.
H
UM
AN
T
RANSP
O
R
T
RO
B
O
T
M
O
DE
L
2
.
1
.
B
uil
din
g
a
m
o
del o
f
a
hu
m
a
n t
ra
ns
po
rt
ro
bo
t
T
h
e
h
u
m
a
n
tr
an
s
p
o
r
t
r
o
b
o
t
is
d
esig
n
ed
m
o
v
e
o
n
f
lat
s
u
r
f
ac
e
s
u
s
in
g
wh
ee
ls
an
d
to
ascen
d
s
tair
s
with
cr
awle
r
s
.
T
h
e
b
alan
ci
n
g
m
ec
h
an
is
m
is
co
n
n
ec
ted
to
th
e
s
ea
t,
au
to
m
atica
lly
ad
j
u
s
tin
g
t
h
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
to
c
h
an
g
e
ac
c
o
r
d
in
g
t
o
th
e
s
lo
p
e
o
f
t
h
e
s
tair
s
.
T
h
e
an
ti
-
r
o
ll
m
ec
h
an
is
m
b
e
h
in
d
p
er
f
o
r
m
s
th
e
task
o
f
s
u
p
p
o
r
tin
g
th
e
wo
r
k
er
,
r
ed
u
cin
g
v
ib
r
atio
n
,
an
d
i
n
cr
ea
s
in
g
t
h
e
r
o
b
o
t'
s
an
ti
-
r
o
ll
ab
ilit
y
.
T
h
e
r
o
b
o
t
is
d
esig
n
ed
to
alwa
y
s
b
e
in
co
n
tact
with
at
l
ea
s
t
two
s
tep
s
,
wh
ich
h
elp
s
p
r
ev
en
t
f
allin
g
b
y
en
s
u
r
in
g
s
ta
b
le
co
n
tact
p
o
in
ts
.
T
h
e
s
ch
em
atic
d
iag
r
am
Fig
u
r
e
1
(
a
)
an
d
3
D
m
o
d
el
o
f
th
e
h
u
m
an
tr
an
s
p
o
r
t r
o
b
o
t a
r
e
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
T
h
e
r
o
b
o
t
p
er
f
o
r
m
s
o
n
e
-
way
m
o
v
em
en
t
u
p
a
n
d
d
o
wn
s
tair
s
,
m
o
v
es
u
p
s
tair
s
with
a
b
ac
k
w
ar
d
m
o
v
em
e
n
t,
an
d
m
o
v
es d
o
wn
s
tair
s
in
th
e
f
o
r
w
ar
d
d
ir
ec
tio
n
,
in
th
e
s
am
e
d
ir
e
ctio
n
as th
e
u
s
er
'
s
v
iew.
(
a)
(
b
)
Fig
u
r
e
1
.
Hu
m
an
tr
an
s
p
o
r
t r
o
b
o
t m
o
d
el
(
a
)
s
ch
em
atic
d
iag
r
a
m
an
d
(
b
)
3
D
m
o
d
el
M
o
v
e
o
n
f
l
a
t
su
r
f
a
c
e
s
C
r
a
w
l
e
r
w
h
e
e
l
A
d
a
p
t
i
v
e
mec
h
a
n
i
sm
B
a
l
a
n
c
e
stru
c
tu
re
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
3
8
-
650
640
2
.
2
.
Dy
na
m
ics o
f
a
ro
bo
t
t
ra
ns
po
rt
ing
peo
ple u
p a
nd
do
wn st
a
irs
T
h
e
d
y
n
a
m
ic
eq
u
atio
n
s
o
f
r
o
b
o
t
tr
an
s
p
o
r
tin
g
p
eo
p
le
ar
e
co
n
s
id
er
ed
with
m
o
v
em
e
n
t
o
n
a
f
lat
s
u
r
f
ac
e
u
s
in
g
cir
cu
lar
wh
ee
ls
,
as
s
h
o
wn
in
Fig
u
r
e
2
(
a)
,
a
n
d
m
o
v
e
m
en
t
o
n
s
tair
s
u
s
in
g
tr
ac
k
s
as
Fig
u
r
e
2
(
b
)
.
T
h
e
r
o
b
o
t'
s
co
o
r
d
in
ate
s
y
s
tem
is
estab
lis
h
ed
at
th
e
p
o
s
itio
n
o
f
th
e
p
ass
iv
e
tr
ac
k
at
th
e
f
r
o
n
t
o
f
th
e
r
o
b
o
t,
with
th
e
OX
ax
is
p
ar
allel
to
th
e
g
r
o
u
n
d
an
d
th
e
OY
ax
is
p
er
p
en
d
icu
lar
to
it.
T
h
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
b
eg
in
s
to
ch
an
g
e
w
h
en
th
e
r
o
b
o
t
s
witch
es
to
s
tair
m
o
v
em
en
t
m
o
d
e.
T
h
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
a
v
ity
is
d
eter
m
in
ed
b
y
th
e
r
elatio
n
s
h
ip
b
etwe
en
t
h
e
c
en
ter
o
f
g
r
av
ity
o
f
t
h
e
r
o
b
o
t
f
r
am
e
(
,
)
an
d
th
e
ce
n
ter
o
f
g
r
a
v
ity
o
f
t
h
e
s
ea
t
(
,
)
.
T
h
e
ce
n
ter
o
f
g
r
a
v
ity
o
f
th
e
s
ea
t is ad
ju
s
ted
ac
co
r
d
in
g
to
th
e
ch
a
n
g
e
in
t
h
e
r
o
b
o
t'
s
tilt
an
g
le.
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
e
r
o
b
o
t'
s
s
tair
-
cli
m
b
in
g
p
h
ase
in
(
a)
wh
ile
o
n
a
f
lat
s
u
r
f
ac
e
an
d
(
b
)
clim
b
in
g
t
h
e
f
ir
s
t step
T
h
e
ce
n
ter
o
f
g
r
a
v
ity
o
f
th
e
r
o
b
o
t
f
r
a
m
e
an
d
t
h
e
ce
n
ter
o
f
g
r
av
ity
o
f
th
e
s
ea
t
wh
en
th
e
r
o
b
o
t
m
o
v
es
o
n
a
p
la
n
e
(
Fig
u
r
e
2
(
a
)
)
ar
e
s
e
t a
s
(
1
)
:
{
=
=
;
{
=
2
−
0
=
+
0
(
1
)
W
h
er
e
(
)
,
(
)
is
th
e
co
o
r
d
in
ate
o
f
th
e
r
o
b
o
t
f
r
am
e'
s
ce
n
ter
o
f
g
r
av
i
ty
,
an
d
(
)
,
(
)
i
s
th
e
co
o
r
d
in
ate
o
f
th
e
s
ea
t
alo
n
g
th
e
OX
an
d
OY
ax
es,
L
(
m
m
)
is
th
e
d
is
tan
ce
b
etwe
en
th
e
co
o
r
d
in
ate
s
y
s
tem
an
d
th
e
ce
n
ter
o
f
g
r
av
ity
,
1
(
m
m
)
is
th
e
d
is
tan
ce
b
etwe
en
th
e
p
ass
iv
e
wh
ee
l
an
d
th
e
p
o
s
itio
n
o
f
th
e
ch
air
'
s
r
o
tatio
n
ax
is
alo
n
g
t
h
e
x
-
ax
is
,
C
(
m
m
)
is
th
e
d
is
tan
ce
f
r
o
m
t
h
e
ch
air
'
s
r
o
tatio
n
ax
is
to
th
e
g
r
o
u
n
d
,
0
(
0
)
is
th
e
ch
air
'
s
r
o
tatio
n
an
g
le,
β
(
0
)
is
th
e
an
g
le
o
f
th
e
r
o
b
o
t
f
r
am
e'
s
ce
n
ter
o
f
g
r
a
v
ity
r
elativ
e
to
th
e
tr
ac
k
s
u
r
f
ac
e,
b
(
m
m
)
is
th
e
d
is
tan
ce
f
r
o
m
th
e
ch
air
'
s
ce
n
ter
o
f
g
r
av
ity
to
th
e
r
o
tatio
n
ax
is
,
2
(
)
is
th
e
p
r
o
ject
io
n
o
f
th
e
d
is
tan
ce
f
r
o
m
th
e
co
o
r
d
in
ate
a
x
is
to
th
e
an
g
le
o
f
r
o
tatio
n
o
n
to
th
e
OX
ax
is
.
As
it
m
o
v
es,
th
e
r
o
b
o
t
b
eg
in
s
to
tilt
at
an
a
n
g
le
θ
ac
co
r
d
i
n
g
to
th
e
s
lo
p
e
o
f
th
e
s
tair
s
,
as
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
T
h
e
r
o
b
o
t'
s
co
o
r
d
in
ate
s
y
s
tem
is
s
et
ac
co
r
d
in
g
to
th
e
tilt
as
(
3
)
:
{
=
(
+
)
=
(
+
)
;
{
=
1
os
(
+
)
−
0
=
+
1
(
+
)
+
0
(
2
)
T
h
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
a
v
ity
(
,
)
is
d
eter
m
in
ed
u
s
in
g
th
e
co
o
r
d
in
ates
o
f
th
e
r
o
b
o
t
f
r
am
e'
s
ce
n
ter
o
f
g
r
av
ity
an
d
th
e
s
ea
t
'
s
ce
n
ter
o
f
g
r
av
ity
b
ased
o
n
th
e
tilt
an
g
le
(
θ)
.
T
h
e
p
o
s
itio
n
,
is
s
et
a
s
f
o
r
m
u
l
a
(
3
)
,
an
d
it
is
a
u
to
m
atica
lly
a
d
ju
s
ted
ac
co
r
d
in
g
to
th
e
tilt
a
n
g
l
e.
T
h
e
r
o
b
o
t
ce
n
ter
o
f
g
r
a
v
ity
p
o
s
itio
n
is
ad
j
u
s
ted
to
b
e
s
tab
le
at
th
e
in
itial
p
o
s
itio
n
,
wh
ich
ca
n
lim
it
th
e
p
h
e
n
o
m
en
o
n
o
f
tip
p
in
g
o
v
er
,
a
n
d
th
e
s
ea
t
ce
n
ter
o
f
g
r
av
ity
d
ete
r
m
in
es th
e
r
o
b
o
t c
en
ter
o
f
g
r
av
ity
p
o
s
itio
n
.
{
=
+
=
+
⇒
{
̇
=
̇
+
̇
̇
=
̇
+
̇
(
3
)
W
h
er
e
(
)
,
(
)
is
th
e
m
ass
o
f
th
e
p
er
s
o
n
an
d
th
e
m
ass
o
f
th
e
r
o
b
o
t;
(
)
=
+
is
th
e
to
tal
m
ass
o
f
th
e
r
o
b
o
t.
T
h
e
o
p
er
atin
g
s
tate
o
f
th
e
r
o
b
o
t w
h
en
clim
b
in
g
s
tair
s
is
s
h
o
wn
in
Fig
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dyn
a
mic
a
n
a
lysi
s
o
f a
h
u
ma
n
-
tr
a
n
s
p
o
r
tin
g
r
o
b
o
t c
limb
in
g
s
ta
ir
s
(
Du
o
n
g
Ta
n
Da
t
)
641
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
3
.
Stag
es o
f
th
e
r
o
b
o
t c
lim
b
in
g
s
tair
s
: (
a)
f
ir
s
t step
,
(
b
)
ascen
d
in
g
,
(
c)
p
r
ep
ar
i
n
g
to
m
o
u
n
t th
e
lan
d
in
g
,
(
d
)
f
in
al
s
tep
,
an
d
(
e)
d
escen
d
in
g
T
h
e
r
o
b
o
t
m
o
v
es
o
n
a
f
lat
s
u
r
f
ac
e
u
s
in
g
cir
cu
lar
wh
ee
ls
,
with
th
e
ass
i
s
tan
ce
o
f
au
x
iliar
y
s
u
p
p
o
r
t
wh
ee
ls
to
h
elp
it
ad
ap
t
to
th
e
s
tair
s
,
as
s
h
o
wn
in
Fig
u
r
e
2
(
a
)
.
Du
r
in
g
th
is
p
h
ase,
th
e
r
o
b
o
t
p
r
ep
ar
es
to
clim
b
th
e
s
tair
s
,
an
d
th
e
cir
cu
lar
wh
ee
ls
ar
e
ass
u
m
ed
to
r
ea
ch
th
e
m
ax
im
u
m
C
o
u
lo
m
b
f
r
ictio
n
li
m
it.
T
h
e
k
in
em
atic
eq
u
atio
n
s
ar
e
estab
lis
h
ed
as
(
4
)
:
∑
=
c
os
−
3
+
+
+
=
m
̈
∑
=
−
+
1
+
4
+
3
(
+
)
=
0
∑
=
1
−
4
−
+
−
=
0
=
2
−
(
4
)
W
h
er
e
1
(
)
,
4
(
)
,
3
(
)
is
th
e
r
ea
ctio
n
f
o
r
c
e,
(
m
m
)
is
th
e
d
is
tan
ce
b
et
wee
n
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
an
d
th
e
s
u
p
p
o
r
t
wh
ee
l
p
o
s
itio
n
;
(
m
m
)
is
th
e
d
is
tan
ce
b
etwe
en
th
e
r
o
b
o
t'
s
wh
ee
l
o
n
th
e
g
r
o
u
n
d
;
η
is
th
e
co
ef
f
icien
t
o
f
f
r
ictio
n
;
(
N)
is
th
e
tr
ac
tio
n
f
o
r
ce
o
f
th
e
cr
awle
r
;
(
0
)
is
th
e
cr
awle
r
an
g
le,
(
/
2
)
is
th
e
ac
ce
ler
atio
n
o
f
g
r
av
ity
,
2
(
)
is
th
e
d
is
tan
ce
f
r
o
m
th
e
co
o
r
d
in
ate
s
y
s
tem
to
t
h
e
au
x
iliar
y
s
u
p
p
o
r
t
wh
ee
l.
T
h
e
d
y
n
am
ic
eq
u
atio
n
s
d
escr
i
b
in
g
r
o
b
o
t
m
o
tio
n
d
u
r
in
g
th
e
ascen
t
o
f
th
e
f
ir
s
t
s
tair
s
tep
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
(
a
)
,
ar
e
f
o
r
m
u
lated
as (
5
)
:
∑
=
(
)
+
1
(
)
−
3
(
)
=
̈
∑
=
s
in
(
)
+
1
+
3
c
os
(
)
−
=
̈
∑
=
(
2
−
−
4
)
+
1
(
−
1
c
os
−
4
)
=
[
+
1
2
]
̈
1
=
√
(
2
−
−
4
)
2
+
(
−
)
2
(
5
)
W
h
er
e
1
(
m
m
)
is
th
e
d
is
tan
ce
f
r
o
m
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
a
v
ity
to
th
e
f
ir
s
t
s
tep
,
4
(
m
m
)
i
s
th
e
d
is
tan
ce
f
r
o
m
t
h
e
s
tep
to
th
e
ce
n
ter
o
f
th
e
ch
air
'
s
p
iv
o
t
ax
is
,
(
m
m
)
i
s
th
e
s
tep
h
eig
h
t,
an
d
(
.
2
)
is
th
e
m
o
m
en
t
o
f
in
er
tia.
T
h
e
r
o
b
o
t'
s
o
v
er
tu
r
n
in
g
m
o
m
e
n
t
is
lar
g
est
wh
en
th
e
cr
awle
r
m
o
v
es
co
m
p
letely
o
n
th
e
s
tep
an
d
o
n
ly
co
n
tacts
two
s
tep
s
,
s
ee
Fig
u
r
e
3
(
b
)
.
T
h
e
d
y
n
a
m
ic
eq
u
atio
n
o
f
th
e
r
o
b
o
t
in
co
n
tact
with
tw
o
s
tep
s
is
p
r
esen
ted
as
(
6
)
:
∑
=
c
os
(
)
+
(
2
−
3
)
c
os
(
)
-
N
2
(
)
=
̈
cx
∑
=
(
)
+
(
2
+
3
)
(
)
+
(
2
+
3
)
(
)
−
=
̈
∑
=
(
1
s
in
(
)
-
Hc
os
(
)
)
-
g
w
2
+
3
(
+
1
)
=
0
(
6
)
W
h
er
e
2
(
m
m
)
is
th
e
d
is
tan
ce
f
r
o
m
th
e
f
ir
s
t
s
tep
to
th
e
p
r
o
jec
tio
n
o
f
th
e
ce
n
ter
o
f
g
r
av
ity
in
th
e
d
ir
ec
tio
n
o
f
m
o
v
em
en
t,
1
(
m
m
)
is
th
e
wid
th
o
f
th
e
s
tep
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
3
8
-
650
642
T
h
e
r
o
b
o
t
ex
p
er
ien
ce
s
an
im
b
alan
ce
an
d
f
lip
s
b
ac
k
war
d
as
i
t
b
eg
in
s
to
lea
v
e
th
e
s
tair
ca
s
e,
as
s
h
o
wn
in
Fig
u
r
e
3
(
c
)
.
T
h
e
g
r
ea
ter
t
h
e
d
is
tan
ce
f
r
o
m
t
h
e
r
o
b
o
t'
s
ce
n
ter
to
th
e
last
s
tep
o
f
th
e
s
tair
ca
s
e
3
(
m
m
)
,
th
e
f
u
r
th
er
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
s
h
if
ts
b
ac
k
war
d
.
T
h
e
th
r
u
s
t f
o
r
ce
(
)
d
f
r
o
m
th
e
elec
tr
ic
c
y
lin
d
er
o
f
th
e
d
am
p
in
g
m
ec
h
an
is
m
p
r
ev
en
t
s
th
e
r
o
b
o
t
f
r
o
m
f
lip
p
in
g
b
a
ck
war
d
.
T
h
e
d
y
n
am
ic
eq
u
atio
n
f
o
r
d
am
p
in
g
th
e
r
o
b
o
t is as
(
7
)
:
∑
=
c
os
−
(
3
+
N
4
−
2
)
c
os
+
c
os
(
+
)
−
(
3
+
N
2
)
s
in
=
(
̈
cx
+
̈
cy
)
∑
=
+
(
2
+
3
)
+
(
2
+
3
)
+
4
+
(
+
)
−
=
[
̈
+
̈
c
os
]
∑
=
(
Hc
os
−
)
+
+
2
(
+
)
+
4
−
(
3
c
os
(
+
)
−
−
cx
)
=
(
+
3
)
̈
3
=
√
(
3
c
os
(
+
)
−
−
cx
)
2
+
(
−
(
3
(
+
)
−
1
)
)
2
(
7
)
W
h
er
e
1
(
)
l
is
th
e
cy
lin
d
er
len
g
th
,
(
)
is
th
e
d
is
p
lace
m
en
t
o
f
th
e
elec
tr
ic
cy
lin
d
er
,
3
(
)
is
th
e
d
is
tan
ce
o
f
th
e
v
ib
r
atio
n
-
d
a
m
p
in
g
m
ec
h
a
n
is
m
f
r
o
m
th
e
co
o
r
d
in
ate
s
y
s
tem
,
an
d
(
0
)
is
th
e
an
g
le
o
f
th
e
v
ib
r
atio
n
-
d
am
p
in
g
m
ec
h
a
n
is
m
r
elativ
e
to
th
e
tr
ac
k
s
u
r
f
ac
e.
T
h
e
r
o
b
o
t
r
ea
ch
es
th
e
f
in
al
s
tep
with
th
e
au
x
iliar
y
s
u
p
p
o
r
t
s
tr
u
ctu
r
e
e
n
g
ag
e
d
,
as
s
h
o
wn
in
Fig
u
r
e
3
(
d
)
.
Alth
o
u
g
h
th
e
r
o
b
o
t’
s
ce
n
ter
o
f
g
r
av
ity
is
lo
c
ated
o
n
th
e
s
tair
p
latf
o
r
m
,
a
b
ac
k
war
d
tip
p
in
g
ten
d
en
cy
s
till
ex
is
ts
.
Acc
o
r
d
in
g
ly
,
th
e
d
y
n
am
ic
e
q
u
atio
n
s
f
o
r
th
is
s
tag
e
ar
e
g
iv
en
b
y
(
8
).
∑
=
cos
+
F
cos
(
+
)
−
(
3
+
4
)
cos
−
3
s
in
=
(
̈
cos
+
̈
s
in
)
∑
=
s
in
+
F
s
in
(
+
)
+
(
3
−
4
)
+
3
cos
+
4
−
gcos
=
(
̈
cos
−
̈
s
in
)
∑
=
+
3
2
+
−
(
−
3
cos
(
+
)
−
(
3
(
+
)
−
1
)
=
(
+
4
)
̈
4
=
√
(
−
(
3
cos
(
+
)
−
(
3
(
+
)
−
1
)
)
2
+
(
−
(
3
(
+
)
−
1
)
)
2
(
8
)
W
h
er
e
4
(
m
m
)
is
th
e
d
is
tan
ce
f
r
o
m
th
e
ce
n
ter
o
f
g
r
av
ity
t
o
th
e
last
s
tep
o
f
th
e
s
tair
ca
s
e.
At
th
e
en
d
o
f
t
h
e
u
p
h
ill
p
h
ase,
th
e
r
o
b
o
t'
s
tilt
an
g
le
r
etu
r
n
s
to
its
o
r
ig
in
al
p
o
s
itio
n
.
Nex
t,
th
e
r
o
b
o
t
b
eg
in
s
th
e
d
o
wn
h
ill
p
h
ase
as
s
h
o
wn
in
Fig
u
r
e
3
(
e
)
.
T
h
e
r
o
b
o
t
ad
a
p
ts
to
th
e
s
tair
s
lo
p
e
u
s
in
g
an
a
u
x
iliar
y
s
u
p
p
o
r
t
m
ec
h
an
is
m
.
T
h
e
a
n
ti
-
r
o
ll
m
ec
h
an
is
m
ad
ju
s
ts
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
lin
ea
r
l
y
ac
co
r
d
i
n
g
to
th
e
ch
an
g
e
in
tilt
an
g
le.
T
h
e
d
y
n
a
m
ic
eq
u
atio
n
s
f
o
r
th
e
r
o
b
o
t'
s
d
o
wn
h
ill m
o
v
e
m
en
t a
r
e
p
r
esen
t
ed
as
(
9
)
:
∑
=
c
os
+
(
+
)
−
(
1
+
4
)
c
os
=
[
̈
cx
c
os
+
̈
cy
s
in
]
∑
=
+
1
+
4
+
(
+
)
−
(
1
+
4
)
−
=
[
̈
cy
−
̈
cx
]
∑
=
3
(
+
)
+
4
−
4
(
1
(
+
)
−
)
−
=
(
+
6
)
̈
6
=
√
2
+
2
(
9
)
3.
SI
M
UL
A
T
I
O
N
A
ND
E
XP
E
RIM
E
N
T
AT
I
O
N
3
.
1
.
Sim
ula
t
io
n r
esu
lt
s
T
h
e
s
im
u
latio
n
was
s
et
u
p
in
MA
T
L
AB
Simu
lin
k
s
o
f
twar
e
an
d
u
s
ed
t
h
e
e
q
u
atio
n
s
d
ev
elo
p
ed
i
n
s
ec
tio
n
2
to
ev
alu
ate
th
e
v
ar
iatio
n
o
f
th
e
ce
n
ter
o
f
g
r
av
ity
,
o
s
cillatio
n
p
h
en
o
m
en
a,
an
d
th
e
s
y
s
tem
'
s
ab
il
ity
to
ad
ap
t
to
ch
an
g
es
in
th
e
tilt
a
n
g
le.
T
h
e
in
p
u
t
s
ig
n
al
is
a
s
tep
f
u
n
ctio
n
s
ig
n
al;
th
e
p
ar
a
m
eter
s
u
s
ed
in
th
e
s
im
u
latio
n
ar
e
p
r
esen
ted
in
T
ab
le
1
.
Simu
ltan
eo
u
s
ly
,
ass
u
m
p
tio
n
s
ab
o
u
t
s
lip
p
ag
e,
n
o
n
-
lin
ea
r
r
o
b
o
t
m
o
v
em
en
t,
an
d
i
n
s
tan
tan
eo
u
s
ef
f
ec
ts
wh
en
th
e
r
o
b
o
t
g
o
es u
p
an
d
d
o
wn
s
tair
s
wer
e
ig
n
o
r
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dyn
a
mic
a
n
a
lysi
s
o
f a
h
u
ma
n
-
tr
a
n
s
p
o
r
tin
g
r
o
b
o
t c
limb
in
g
s
ta
ir
s
(
Du
o
n
g
Ta
n
Da
t
)
643
T
ab
le
1
.
T
h
e
p
ar
am
ete
r
s
u
s
ed
f
o
r
s
im
u
latio
n
S
y
mb
o
l
D
e
scri
p
t
i
o
n
V
a
l
u
e
U
n
i
t
M
a
x
i
m
u
m
mo
t
o
r
sp
e
e
d
(
a
ss
u
m
e
d
)
2
0
0
0
R
P
M
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o
b
o
t
m
a
ss
1
5
0
Kg
1
D
i
st
a
n
c
e
f
r
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m
t
h
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t
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2
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s
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0
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mm
3
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p
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9
0
0
mm
Tr
a
c
t
i
o
n
f
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e
1
7
2
0
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t
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0
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me
n
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o
f
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n
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a
1
2
0
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2
g
G
r
a
v
i
t
a
t
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c
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e
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e
r
a
t
i
o
n
9
.
8
/
2
C
o
e
f
f
i
c
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e
n
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f
f
r
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c
t
i
o
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6
A
u
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a
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(
a
ssu
m
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0
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mm
Ti
l
t
a
n
g
l
e
35
°
A
n
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l
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b
e
t
w
e
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n
t
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a
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i
l
i
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p
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h
a
n
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a
n
d
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X
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a
x
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s
30
°
S
t
a
i
r
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e
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1
5
0
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1
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t
a
i
r
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i
d
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h
3
0
0
mm
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
an
d
d
y
n
am
ic
m
o
m
en
t
o
v
e
r
tim
e
ar
e
p
r
esen
ted
in
Fig
u
r
e
4
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
v
elo
city
at
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
av
ity
alo
n
g
t
h
e
X
-
ax
is
r
ea
ch
es
a
m
ax
im
u
m
i
n
ab
o
u
t
0
.
2
5
s
ec
o
n
d
s
,
th
en
g
r
ad
u
ally
d
ec
r
ea
s
es
in
Fig
u
r
e
4
(
a)
.
I
n
itially
,
t
h
e
f
o
r
war
d
v
elo
city
alo
n
g
th
e
X
-
ax
is
in
c
r
ea
s
es
u
n
til
t
h
e
r
o
b
o
t
r
ea
ch
es
th
e
f
ir
s
t
s
tep
,
th
en
ten
d
s
to
d
ec
r
ea
s
e.
T
h
e
v
elo
city
alo
n
g
th
e
Y
-
ax
is
d
ec
r
ea
s
es
r
ap
id
ly
an
d
r
ea
ch
es
a
m
in
im
u
m
in
ab
o
u
t
0
.
2
s
ec
o
n
d
s
,
th
en
b
eg
in
s
to
in
cr
ea
s
e
s
lig
h
tly
with
th
e
an
g
le
o
f
in
clin
atio
n
θ
in
F
ig
u
r
e
4
(
b
)
.
R
eg
ar
d
in
g
th
e
p
o
s
itio
n
o
f
th
e
ce
n
ter
o
f
g
r
av
ity
alo
n
g
th
e
X
-
ax
is
,
it
in
cr
ea
s
es,
th
en
d
ec
r
ea
s
es
to
w
ar
d
s
th
e
s
lo
p
e
o
f
th
e
s
tair
s
in
Fig
u
r
e
4
(
c
)
,
wh
ile
th
e
p
o
s
itio
n
alo
n
g
th
e
Y
-
ax
is
in
itially
d
ec
r
ea
s
es
s
lig
h
tly
,
th
en
s
tab
ilizes
an
d
b
eg
in
s
to
in
cr
ea
s
e
at
0
.
5
s
ec
o
n
d
s
in
F
ig
u
r
e
4
(
d
)
.
T
h
e
r
esu
lts
o
f
th
e
m
o
m
en
t
s
u
r
v
ey
o
f
t
h
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
a
v
ity
s
h
o
w
th
at
th
e
r
o
b
o
t
is
in
a
f
air
ly
s
tab
le
s
tate,
with
o
u
t
tip
p
in
g
o
v
er
.
T
h
e
b
alan
cin
g
m
o
m
en
t
o
f
th
e
r
o
b
o
t'
s
ce
n
te
r
o
f
g
r
av
ity
in
cr
ea
s
es
r
ap
id
l
y
an
d
s
tab
ilizes
in
0
.
5
s
ec
o
n
d
s
,
as
s
h
o
wn
in
Fi
g
u
r
e
4
(
e
)
.
T
h
e
r
o
b
o
t'
s
o
v
er
tu
r
n
in
g
m
o
m
en
t
r
ea
c
h
es
a
m
ax
im
u
m
in
th
e
f
i
r
s
t
0
.
7
s
ec
o
n
d
s
an
d
th
e
n
g
r
ad
u
a
lly
d
ec
r
ea
s
es
in
Fig
u
r
e
4
(
f
)
.
T
h
e
tilt
an
g
le
θ
v
ar
ies
o
v
e
r
tim
e,
as
s
h
o
wn
i
n
Fig
u
r
e
4
(
g
)
,
d
escr
ib
i
n
g
th
e
v
ar
iatio
n
o
f
th
e
r
o
b
o
t’
s
in
clin
atio
n
wh
ile
ascen
d
in
g
t
h
e
s
tair
s
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
Fig
u
r
e
4
.
Simu
latio
n
r
esu
lts
o
f
th
e
in
itial st
air
-
clim
b
in
g
s
tag
e
: (
a)
–
(
d
)
ce
n
ter
-
of
-
g
r
av
ity
v
el
o
cities an
d
p
o
s
itio
n
s
alo
n
g
th
e
X
-
an
d
Y
-
ax
es,
(
e)
b
alan
ci
n
g
m
o
m
en
t,
(
f
)
o
v
er
t
u
r
n
in
g
m
o
m
e
n
t,
an
d
(
g
)
in
clin
atio
n
an
g
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
3
8
-
650
644
Fig
u
r
e
5
p
r
esen
ts
th
e
s
im
u
lat
io
n
r
esu
lts
o
f
th
e
p
h
ase
wh
il
e
o
n
th
e
s
tair
s
,
s
h
o
win
g
th
at
th
e
r
o
b
o
t'
s
ce
n
ter
o
f
g
r
a
v
ity
v
elo
city
r
ea
ch
es
its
m
ax
im
u
m
in
0
.
2
5
s
ec
o
n
d
s
an
d
th
e
n
g
r
ad
u
ally
d
ec
r
ea
s
es,
as
s
h
o
wn
in
Fig
u
r
e
5
(
a
)
,
a
n
d
th
e
v
elo
cit
y
alo
n
g
th
e
o
y
a
x
is
r
ea
ch
es
its
m
in
im
u
m
an
d
in
cr
ea
s
es
af
t
er
0
.
2
s
ec
o
n
d
s
in
Fig
u
r
e
5
(
b
)
.
Du
r
in
g
th
e
p
h
ase
wh
en
th
e
r
o
b
o
t
is
m
o
v
in
g
u
p
th
e
s
tair
s
,
th
e
ce
n
ter
o
f
g
r
av
i
ty
alo
n
g
th
e
x
-
ax
is
ten
d
s
to
r
ea
ch
its
m
ax
im
u
m
a
n
d
th
e
n
g
r
ad
u
ally
d
ec
r
ea
s
e
in
Fig
u
r
e
5
(
c)
,
wh
ile
th
e
ce
n
ter
o
f
g
r
av
ity
alo
n
g
th
e
Y
-
ax
is
g
r
ad
u
ally
d
ec
r
ea
s
es
o
v
er
tim
e
in
Fig
u
r
e
5
(
d
)
,
i
n
d
icatin
g
th
at
th
e
ce
n
ter
o
f
g
r
av
ity
b
alan
cin
g
m
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(
b
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(
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(
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(
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Fig
u
r
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5
.
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r
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o
r
th
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r
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atin
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ter
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en
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te
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h
e
s
im
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h
o
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t
h
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d
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h
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wn
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Fig
u
r
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s
6
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a)
a
n
d
6
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b
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v
elo
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th
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ter
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g
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l
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ctu
ates
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ir
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t
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o
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d
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ter
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e
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g
r
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d
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c
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ea
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h
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in
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icate
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p
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is
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ates
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ir
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i
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s
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e
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e
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as illu
s
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6
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n
d
6
(
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.
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h
e
s
im
u
latio
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h
o
w
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th
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u
r
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e
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i
s
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7
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icted
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im
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em
o
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ated
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ase
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ter
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a)
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b
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u
r
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7
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latio
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r
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o
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u
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ated
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2
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