I
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t
er
na
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l J
o
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l o
f
Ro
bo
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nd
Aut
o
m
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t
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(
I
J
RA)
Vo
l.
13
,
No
.
4
,
Dec
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b
er
20
24
,
p
p
.
3
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0
~
3
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0
I
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N:
2722
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2
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DOI
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1
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v
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.
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390
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K
ey
w
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s
:
Dam
p
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Def
lectio
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R
o
b
o
t m
an
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lato
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Stab
ilit
y
Sti
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ess
Yo
u
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’
s
m
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T
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is i
s
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p
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c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
J
ia
Ud
d
in
AI
an
d
B
ig
Data
Dep
ar
tm
en
t,
E
n
d
ico
tt C
o
lleg
e,
W
o
o
s
o
n
g
Un
iv
er
s
ity
Dae
jeo
n
,
So
u
th
Ko
r
ea
E
m
ail: jia.
u
d
d
in
@
wsu
.
ac
.
k
r
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
f
ield
o
f
r
o
b
o
tics
an
d
a
u
to
m
atio
n
,
ac
h
iev
in
g
s
tab
ilit
y
in
m
an
ip
u
lato
r
s
y
s
tem
s
h
as
lo
n
g
b
ee
n
a
p
r
im
ar
y
g
o
al
[
1
]
.
T
o
en
s
u
r
e
s
af
e
an
d
e
f
f
ec
tiv
e
f
u
n
ctio
n
i
n
g
,
th
ese
s
y
s
tem
s
m
u
s
t
r
em
ain
s
tab
le
as
th
ey
b
ec
o
m
e
m
o
r
e
co
m
p
lex
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d
wid
esp
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ea
d
in
a
v
ar
iet
y
o
f
i
n
d
u
s
tr
ial
an
d
co
m
m
er
cial
ap
p
licatio
n
s
[
2
]
.
Ho
wev
er
,
attain
in
g
s
tab
ilit
y
in
m
an
ip
u
lato
r
s
y
s
t
em
s
n
ec
ess
itates
a
co
m
p
lex
in
ter
ac
tio
n
b
etwe
en
a
wid
e
r
an
g
e
o
f
elem
e
n
ts
,
in
clu
d
in
g
e
n
v
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o
n
m
en
tal
v
ar
i
ab
les,
co
n
tr
o
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alg
o
r
ith
m
s
,
m
a
ter
ial
p
r
o
p
er
ties
,
an
d
s
tr
u
ct
u
r
al
d
esig
n
[
3
]
.
T
h
is
r
esear
ch
ef
f
o
r
t
em
p
h
asizes
th
e
m
ater
ial
p
r
o
p
er
ties
,
d
elv
in
g
in
to
th
e
in
tr
icate
r
elatio
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s
h
ip
b
etwe
en
m
ater
ial
p
ar
am
eter
s
an
d
m
an
ip
u
lat
o
r
s
y
s
tem
s
tab
ilit
y
[
4
]
.
T
h
i
s
r
e
s
ea
r
ch
t
ak
e
s
a
m
o
r
e
h
o
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ti
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ap
p
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k
n
o
w
led
g
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th
e
im
p
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r
tan
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f
m
a
ter
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l
p
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p
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ti
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in
s
h
ap
in
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m
an
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u
l
ato
r
s
’
o
v
er
a
ll
s
tab
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it
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ch
ar
a
ct
er
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s
ti
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s
,
as
o
p
p
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ed
to
tr
ad
it
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wo
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k
p
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r
s
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s
to
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ter
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tio
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ig
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t
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tab
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f
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an
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m
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to
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s
b
y
m
eth
o
d
ic
al
ly
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v
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ti
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at
in
g
an
d
a
s
s
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s
in
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in
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lu
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ce
o
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m
at
er
i
al
f
a
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r
s
s
u
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a
s
s
ti
f
f
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s
,
d
am
p
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,
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d
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l
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tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
A
h
o
lis
tic
a
p
p
r
o
a
c
h
o
f
s
ta
b
ilit
y
u
s
in
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ma
teri
a
l p
a
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mete
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f m
a
n
ip
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la
to
r
s
(
S
h
a
b
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Mu
s
ta
r
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)
381
W
e
r
eg
ar
d
th
e
m
ec
h
an
ical
s
tiff
n
ess
o
f
a
m
an
ip
u
lato
r
as
a
s
ig
n
if
ican
t
ch
ar
ac
ter
is
tic
f
o
r
ev
alu
atin
g
r
o
b
o
t
p
er
f
o
r
m
a
n
ce
[
5
]
–
[
7
]
.
I
n
d
u
s
tr
ial
r
o
b
o
ts
h
av
e
h
is
to
r
ical
ly
ex
p
e
r
ien
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d
s
tatic
an
d
d
y
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am
ic
d
ef
o
r
m
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s
,
as
well
as
ch
atter
v
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atio
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s
,
d
u
e
t
o
th
eir
co
m
p
ar
ativ
ely
l
o
w
s
tiff
n
ess
.
E
x
ter
n
al
f
o
r
ce
s
ac
tin
g
o
n
th
e
e
n
d
-
ef
f
ec
to
r
s
d
u
r
i
n
g
th
e
m
illi
n
g
p
r
o
ce
s
s
in
d
u
ce
th
ese
d
ef
o
r
m
atio
n
s
an
d
v
ib
r
atio
n
s
.
Fo
r
o
p
ti
m
al
p
er
f
o
r
m
an
ce
,
a
r
o
b
o
t
with
h
ig
h
r
i
g
id
ity
is
ess
en
tial,
wh
er
ea
s
lo
w
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tiff
n
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i
s
n
ec
ess
ar
y
f
o
r
s
af
ety
p
u
r
p
o
s
e
s
[
8
]
,
[
9
]
.
Dam
p
in
g
ca
p
ac
ity
r
ef
er
s
to
a
m
ater
ial
’
s
ca
p
ab
ilit
y
to
d
is
p
er
s
e
elastic
s
tr
ain
en
er
g
y
wh
en
s
u
b
jecte
d
to
m
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h
a
n
ical
v
ib
r
atio
n
o
r
wav
e
p
r
o
p
ag
atio
n
[
1
0
]
.
Hig
h
-
d
am
p
in
g
m
ater
ial
s
ar
e
o
n
ly
n
ec
ess
ar
y
in
ce
r
tain
s
itu
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s
b
ec
au
s
e
th
ey
d
im
in
is
h
p
h
y
s
ical
an
d
m
ec
h
an
ical
p
r
o
p
er
ties
[
1
1
]
.
W
h
en
a
f
o
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ce
is
ap
p
lied
,
t
h
e
r
o
b
o
t
m
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s
en
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-
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t
will
d
e
f
lect,
a
n
d
t
h
e
ex
ten
t
o
f
d
ef
lectio
n
d
e
p
en
d
s
o
n
t
h
e
ar
m
’
s
s
tiff
n
ess
an
d
t
h
e
m
ag
n
itu
d
e
o
f
th
e
f
o
r
ce
ap
p
lied
[
1
2
]
.
T
h
e
r
esear
ch
ex
p
lo
r
es
th
e
r
e
latio
n
s
h
ip
b
etwe
en
m
ater
ial
p
r
o
p
er
ties
an
d
s
tab
ilit
y
m
etr
i
cs,
u
s
in
g
th
eo
r
etica
l
an
aly
s
es,
s
im
u
latio
n
s
,
an
d
ex
p
er
im
en
tal
v
alid
at
io
n
s
.
I
t
aim
s
to
im
p
r
o
v
e
m
an
ip
u
lato
r
tech
n
o
lo
g
y
d
esig
n
,
o
p
tim
izatio
n
,
an
d
co
n
t
r
o
l,
r
esu
ltin
g
in
s
af
er
,
m
o
r
e
r
el
iab
le,
an
d
m
o
r
e
ef
f
icien
t r
o
b
o
t
ic
s
y
s
tem
s
.
T
h
is
s
tu
d
y
m
ak
es
s
ev
e
r
al
s
ig
n
if
ican
t
co
n
tr
ib
u
tio
n
s
to
war
d
s
s
tab
ilit
y
co
n
s
id
er
in
g
th
e
m
ater
ial
p
ar
am
eter
s
o
f
r
o
b
o
t m
an
ip
u
lato
r
s
as f
o
llo
ws
.
−
W
e
ex
am
in
e
th
e
s
tab
ilit
y
o
f
r
o
b
o
t
m
an
i
p
u
lato
r
s
u
s
in
g
m
ate
r
ial
p
r
o
p
er
ties
lik
e
Yo
u
n
g
’
s
m
o
d
u
lu
s
,
wh
ic
h
af
f
ec
t sti
f
f
n
ess
,
d
am
p
in
g
,
an
d
d
ef
lectio
n
.
−
I
n
th
is
r
esear
ch
,
we
f
o
cu
s
ed
o
n
ad
v
an
ce
d
m
an
i
p
u
lato
r
s
lik
e
AB
B
an
d
FANUC
,
em
p
h
asizin
g
th
e
im
p
o
r
tan
ce
o
f
m
ater
ial
s
elec
tio
n
f
o
r
s
tab
ilit
y
an
d
im
p
r
o
v
in
g
r
o
b
o
tic
tech
n
o
lo
g
y
d
esig
n
.
−
A
s
tab
ilit
y
m
o
d
el
is
d
ev
elo
p
e
d
,
class
if
y
in
g
s
tab
ilit
y
lev
els as lo
w,
m
ed
iu
m
,
o
r
h
ig
h
.
−
T
h
e
s
tu
d
y
r
ev
ea
ls
th
at
s
tab
ilit
y
is
d
ir
ec
tly
r
elate
d
t
o
s
tiff
n
ess
an
d
in
v
er
s
ely
r
elate
d
to
d
am
p
in
g
an
d
d
ef
lectio
n
.
−
T
h
e
im
p
o
r
tan
ce
o
f
s
tab
ilit
y
is
h
ig
h
lig
h
ted
in
b
o
th
ex
is
tin
g
an
d
n
ew
r
o
b
o
ts
.
T
h
e
p
ap
e
r
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws.
T
h
e
s
ec
o
n
d
s
ec
tio
n
o
f
th
e
ar
ticle
d
escr
ib
es
th
e
liter
atu
r
e
r
ev
iew
o
n
th
is
to
p
ic.
Sectio
n
3
p
r
esen
ts
th
e
r
esear
ch
m
eth
o
d
o
lo
g
y
.
Sectio
n
4
r
ep
r
esen
ts
th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
.
Sectio
n
5
p
r
esen
ts
th
e
f
i
n
al
co
n
clu
s
io
n
s
o
f
th
is
wo
r
k
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
T
h
e
s
tiff
n
ess
p
r
o
p
er
ties
o
f
in
d
u
s
tr
ial
r
o
b
o
ts
ar
e
v
er
y
s
ig
n
if
ic
an
t
f
o
r
m
an
y
in
d
u
s
tr
ial
ap
p
lic
atio
n
s
an
d
lo
w
s
tiff
n
ess
ca
u
s
es im
p
r
ec
is
e
p
r
o
d
u
cts,
d
u
e
to
th
e
r
o
b
o
t
d
ef
lectio
n
s
d
u
r
in
g
th
e
r
o
b
o
tic
task
.
T
h
e
s
tiff
n
ess
o
f
a
s
y
s
tem
in
f
lu
en
ce
s
th
e
ac
ce
ler
atio
n
th
at
m
ay
b
e
ac
h
iev
e
d
w
h
ile
m
o
v
in
g
to
war
d
a
tar
g
et
p
o
in
t.
T
h
is
h
el
p
s
to
p
r
ev
en
t
u
n
wan
ted
d
is
p
lace
m
e
n
ts
in
d
u
ce
d
b
y
th
e
in
er
tia
f
o
r
c
es
th
at
o
cc
u
r
d
u
r
i
n
g
r
a
p
id
m
a
n
ip
u
latio
n
s
.
Hen
ce
,
im
p
r
o
v
in
g
th
e
s
tiff
n
ess
s
u
s
tain
s
th
e
s
tab
ilit
y
[
1
3
]
–
[
1
6
]
.
T
o
m
ain
tain
s
tab
ilit
y
wh
en
th
e
s
tiff
n
ess
is
in
cr
ea
s
ed
,
th
e
m
o
d
u
latio
n
is
co
n
tr
o
lled
b
y
an
en
e
r
g
y
-
tan
k
-
b
ased
law
[
1
7
]
.
T
h
e
im
p
ac
t
o
f
v
ar
io
u
s
cr
o
s
s
-
s
ec
tio
n
s
an
d
lay
u
p
s
o
n
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
a
r
o
b
o
t
ar
m
f
o
r
ag
r
icu
ltu
r
al
m
o
n
ito
r
in
g
is
ev
al
u
ated
b
y
m
an
ip
u
latin
g
v
ac
u
u
m
p
r
ess
u
r
e
with
in
th
e
p
ar
ticle
ch
am
b
er
[
1
8
]
,
[
1
9
]
.
Self
-
ex
cited
v
ib
r
atio
n
in
s
y
s
tem
s
is
d
u
e
to
d
am
p
in
g
,
an
d
ex
t
er
n
al
lo
ad
s
co
m
p
en
s
ate
f
o
r
d
e
f
lectio
n
T
h
er
ef
o
r
e,
m
o
d
el
-
b
ased
ap
p
r
o
ac
h
es
a
n
al
y
ze
r
o
b
o
t
m
an
ip
u
lato
r
p
ar
am
e
ter
s
u
s
in
g
m
at
h
em
atica
l
m
eth
o
d
s
[
2
0
]
,
[
2
1
]
.
T
h
e
d
ef
lectio
n
o
f
a
ca
n
tilev
e
r
b
ea
m
d
u
e
to
f
o
r
c
e,
tr
an
s
f
o
r
m
in
g
it
in
to
a
two
-
p
o
in
t
b
o
u
n
d
a
r
y
v
alu
e
p
r
o
b
lem
an
d
a
one
-
p
a
r
am
eter
eig
e
n
v
alu
e
o
p
t
im
izatio
n
p
r
o
b
lem
u
s
in
g
a
h
e
u
r
is
tic
cu
ck
o
o
s
ea
r
c
h
alg
o
r
ith
m
,
is
ev
alu
ated
f
o
r
its
v
alid
ity
[
2
2
]
,
[
2
3
]
.
Var
io
u
s
is
s
u
es
in
th
e
f
ield
o
f
r
o
b
o
tics
h
av
e
b
ee
n
in
v
esti
g
ate
d
th
r
o
u
g
h
th
e
ex
am
in
atio
n
o
f
alter
n
ativ
e
co
n
tr
o
l
s
tr
ateg
ies,
m
ater
ials
,
m
an
u
f
ac
tu
r
in
g
m
eth
o
d
s
,
a
n
d
m
ec
h
an
ical
m
o
d
elin
g
[
2
4
]
.
X
u
et
a
l.
[
2
5
]
p
r
esen
ted
a
m
eth
o
d
o
lo
g
y
f
o
r
th
e
m
o
d
eli
n
g
o
f
s
tiff
n
ess
f
o
r
h
ea
v
y
p
a
y
lo
ad
in
d
u
s
tr
ial
r
o
b
o
ts
b
y
co
n
s
id
er
atio
n
o
f
v
a
r
io
u
s
asp
ec
ts
o
f
th
e
r
o
b
o
t
’
s
lin
k
s
.
Yan
g
et
a
l
.
[
2
6
]
cr
e
ated
th
r
ee
te
ch
n
iq
u
es
f
o
r
a
r
o
b
o
tic
m
ac
h
in
in
g
p
r
o
ce
d
u
r
e,
b
u
t
d
id
n
o
t
c
o
n
s
id
er
d
ef
lectio
n
f
a
cto
r
f
o
r
im
p
r
o
v
ed
s
tiff
n
ess
m
o
d
el
p
r
ec
is
io
n
.
Va
n
Qu
y
en
et
a
l
.
[
2
7
]
o
u
tlin
e
d
a
m
eth
o
d
o
l
o
g
y
f
o
r
ca
lcu
latin
g
th
e
d
y
n
am
ic
s
tab
ilit
y
co
n
tr
o
l
an
d
in
v
er
s
e
d
y
n
am
ics
o
f
a
s
in
g
le
-
lin
k
f
lex
ib
le
m
an
ip
u
lato
r
u
s
in
g
n
u
m
e
r
ical
s
im
u
latio
n
.
T
h
e
a
p
p
licatio
n
o
f
f
lex
ib
le
m
u
lti
-
lin
k
m
an
ip
u
lato
r
s
ca
n
en
h
an
ce
r
o
b
o
t
d
y
n
am
ic
s
tab
ilit
y
with
an
ad
d
itio
n
al
f
ee
d
b
ac
k
c
o
n
tr
o
ll
er
,
b
u
t
r
ed
u
cin
g
th
e
c
o
n
tr
o
ller
d
u
r
atio
n
ca
n
ca
u
s
e
in
s
tab
ilit
y
[
2
8
]
.
A
co
n
tr
o
ller
h
as
b
ee
n
d
ev
elo
p
ed
[
2
9
]
b
y
in
c
o
r
p
o
r
ati
n
g
d
y
n
a
m
ic
b
e
h
av
io
r
t
h
r
o
u
g
h
a
f
ee
d
b
ac
k
lin
ea
r
izatio
n
m
eth
o
d
th
at
was
th
en
ev
alu
ated
o
n
a
u
n
iv
er
s
a
l
r
o
b
o
t
(
UR
5
)
.
T
h
e
ev
al
u
atio
n
o
f
r
o
b
o
t
s
tab
ilit
y
co
n
s
id
er
s
b
o
th
s
tr
aig
h
t
an
d
n
o
n
-
s
tr
aig
h
t
d
esig
n
s
[
3
0
]
,
[
3
1
]
.
Af
ter
r
ev
iewin
g
th
e
b
ac
k
g
r
o
u
n
d
an
d
p
r
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t
s
tate
o
f
th
e
p
r
o
b
lem
o
f
t
h
is
d
o
m
ai
n
,
it
h
as
b
ee
n
f
o
u
n
d
th
at
m
o
s
t
o
f
th
e
r
esear
c
h
er
s
h
av
e
i
n
v
e
s
tig
ated
s
in
g
le
lin
k
,
o
n
e
d
eg
r
ee
o
f
f
r
ee
d
o
m
,
h
ea
v
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-
d
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ty
r
o
b
o
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,
co
n
tr
o
ller
s
,
an
d
m
o
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g
o
n
ly
s
tiff
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o
r
d
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o
r
ce
,
is
th
e
len
g
th
o
f
th
e
r
o
b
o
t lin
k
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is
th
e
Y
o
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n
g
m
o
d
u
l
u
s
,
an
d
is
th
e
m
o
m
en
t
o
f
in
er
t
ia.
An
iter
ativ
e
ca
lcu
latio
n
h
as
b
ee
n
co
m
p
leted
to
d
eter
m
i
n
e
t
h
e
m
ax
im
u
m
a
n
d
m
in
im
u
m
n
u
m
er
ical
v
alu
es
o
f
p
ar
am
eter
s
,
co
n
s
id
er
in
g
th
e
m
ax
im
u
m
a
n
d
m
in
im
u
m
Y
o
u
n
g
m
o
d
u
l
u
s
o
f
p
r
ed
ef
i
n
ed
r
o
b
o
t
m
an
ip
u
lato
r
m
ater
ial
s
h
o
wn
in
T
ab
le
s
2
to
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
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R
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b
&
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u
to
m
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Vo
l
.
13
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4
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Dec
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er
20
24
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3
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(
m
)
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ab
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4
.
T
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n
u
m
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ical
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o
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d
am
p
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mp
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3
.
3
.
P
r
o
po
s
ed
m
o
del o
f
s
t
a
bil
it
y
An
in
d
u
s
tr
ial
r
o
b
o
t
m
a
n
ip
u
la
to
r
th
at
is
s
tead
y
ca
n
m
o
v
e
an
d
p
o
s
itio
n
its
elf
with
s
tab
ilit
y
wh
ile
p
er
f
o
r
m
in
g
d
u
ties
.
Stab
le
r
o
b
o
t
m
an
ip
u
lato
r
s
ex
ec
u
te
task
s
with
g
r
ea
ter
ac
c
u
r
ac
y
an
d
co
n
s
is
ten
cy
,
h
en
ce
en
h
an
cin
g
th
e
q
u
ality
o
f
o
u
t
p
u
t.
An
en
d
u
r
in
g
r
o
b
o
tic
m
a
n
ip
u
lato
r
g
u
ar
an
tees
th
e
q
u
al
ity
o
f
a
p
r
o
d
u
ct
b
y
co
n
s
is
ten
tly
attain
in
g
its
o
b
jectiv
es.
Ma
n
u
f
ac
tu
r
e
r
s
an
d
o
p
er
ato
r
s
o
f
in
d
u
s
tr
ial
r
o
b
o
ts
s
tr
iv
e
f
o
r
s
tab
ilit
y
to
im
p
r
o
v
e
th
e
q
u
ality
,
d
ep
en
d
a
b
ilit
y
,
an
d
ef
f
icien
c
y
o
f
p
r
o
d
u
ctio
n
.
T
h
e
s
tab
ilit
y
o
f
a
r
o
b
o
t
m
an
i
p
u
lato
r
is
cr
u
cial
f
o
r
p
e
r
f
o
r
m
in
g
s
u
b
s
eq
u
en
t
ac
tio
n
s
an
d
an
al
y
zin
g
th
e
n
u
m
er
ical
v
alu
es
o
f
m
ater
ia
l
p
r
o
p
er
ties
.
I
t
h
as
b
ee
n
o
b
s
er
v
ed
th
at
th
er
e
is
a
r
elatio
n
s
h
ip
b
etwe
en
s
tab
ilit
y
an
d
f
ac
to
r
s
s
u
ch
as
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
ef
lectio
n
.
Du
e
to
th
ese
in
ce
n
tiv
es,
a
n
o
v
el
s
tr
ateg
y
h
as
b
ee
n
d
ev
elo
p
ed
to
en
s
u
r
e
th
e
s
tab
ilit
y
o
f
r
o
b
o
t
m
an
ip
u
lato
r
s
.
T
h
e
n
o
v
el
ap
p
r
o
ac
h
ca
n
b
e
e
x
p
r
ess
ed
as
∝
[
×
]
∈
[
]
∪
[
]
w
h
er
e
S
is
s
tiff
n
ess
,
D
is
d
am
p
in
g
,
δ
is
d
ef
lectio
n
,
M
is
th
e
Yo
u
n
g
m
o
d
u
l
u
s
o
f
m
ater
ial
,
a
n
d
R
is
th
e
t
y
p
e
o
f
r
o
b
o
t.
T
h
e
ap
p
r
o
ac
h
in
d
icate
s
th
at
s
tab
ilit
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d
ep
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d
s
o
n
s
tiff
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ess
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am
p
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,
a
n
d
d
e
f
lectio
n
,
wh
er
e
s
tab
ilit
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is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
s
ti
f
f
n
ess
an
d
in
v
e
r
s
ely
p
r
o
p
o
r
ti
o
n
al
to
d
am
p
in
g
a
n
d
d
e
f
lectio
n
.
T
h
e
r
elatio
n
o
f
s
tab
ilit
y
with
s
tiff
n
ess
,
d
ef
le
ctio
n
,
an
d
d
am
p
in
g
b
elo
n
g
s
to
d
if
f
er
en
t
v
alu
es
o
f
th
e
Yo
u
n
g
m
o
d
u
lu
s
o
f
m
ater
ials
an
d
m
o
d
els o
f
r
o
b
o
t
m
an
ip
u
lato
r
s
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
E
x
plo
ring
re
s
ults by
nu
m
er
ica
l v
a
lues
Mu
ltip
le
o
u
tco
m
es
r
elatin
g
to
s
tab
ilit
y
ca
n
b
e
cr
ea
ted
b
y
iter
ativ
ely
ca
lcu
latin
g
o
v
er
s
ev
er
al
eq
u
atio
n
s
(
1
)
,
(
2
)
,
a
n
d
(
3
)
u
s
i
n
g
v
ar
ied
v
alu
es
o
f
m
ater
ial
-
r
elate
d
p
ar
am
ete
r
s
.
R
ea
l
d
ata
is
u
s
ed
to
d
eter
m
i
n
e
th
e
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
ef
lectio
n
p
ar
a
m
eter
s
f
o
r
ea
ch
o
f
th
e
ch
o
s
en
r
o
b
o
t
m
an
ip
u
lato
r
m
o
d
els.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
A
h
o
lis
tic
a
p
p
r
o
a
c
h
o
f
s
ta
b
ilit
y
u
s
in
g
ma
teri
a
l p
a
r
a
mete
r
s
o
f m
a
n
ip
u
la
to
r
s
(
S
h
a
b
n
o
m
Mu
s
ta
r
y
)
385
R
eg
ar
d
in
g
th
e
m
ater
ial
attr
ib
u
te
o
f
th
e
m
an
ip
u
lato
r
ab
o
u
t
th
e
Yo
u
n
g
m
o
d
u
lu
s
,
th
e
m
ea
s
u
r
em
en
t
co
n
s
id
er
s
b
o
th
th
e
m
ax
im
u
m
an
d
m
in
im
u
m
v
alu
es.
T
ab
le
5
d
is
p
lay
s
th
e
v
al
u
es
o
f
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
e
f
lectio
n
f
o
r
AB
B
an
d
FANUC
b
ased
o
n
th
e
m
ax
im
u
m
a
n
d
m
in
im
u
m
v
alu
es
o
f
th
e
r
elev
a
n
t
m
an
ip
u
lato
r
m
ater
ial
’
s
Yo
u
n
g
m
o
d
u
lu
s
.
I
t h
as
b
ee
n
n
o
ted
th
at
s
tiff
n
ess
is
f
o
u
n
d
t
o
b
e
h
ig
h
w
h
en
th
e
Yo
u
n
g
m
o
d
u
lu
s
is
at
i
ts
h
ig
h
est
an
d
l
o
w
wh
en
it
is
a
t
its
m
in
im
u
m
.
On
th
e
o
th
er
h
an
d
,
d
am
p
i
n
g
an
d
d
ef
lectio
n
d
e
m
o
n
s
tr
ate
th
at
th
ese
two
p
ar
am
eter
s
ar
e
h
i
g
h
wh
en
th
e
Y
o
u
n
g
m
o
d
u
lu
s
is
at
its
m
in
im
u
m
an
d
lo
w
w
h
en
it
is
at
its
h
ig
h
est.
I
t
is
p
o
s
s
ib
le
to
d
e
d
u
ce
th
at
s
tab
ilit
y
is
in
v
er
s
ely
r
elate
d
to
d
am
p
in
g
a
n
d
d
e
f
lectio
n
an
d
p
r
o
p
o
r
tio
n
al
to
s
tiff
n
e
s
s
b
ased
o
n
th
ese
f
ac
ts
an
d
th
e
n
ew
m
eth
o
d
.
T
ab
le
5
.
Dif
f
e
r
en
t n
u
m
er
ical
v
alu
es o
f
AB
B
an
d
FANUC
f
o
r
s
tiff
n
ess
,
d
am
p
in
g
,
a
n
d
d
ef
lec
tio
n
co
n
s
id
er
in
g
m
in
im
u
m
an
d
m
ax
im
u
m
v
al
u
es o
f
Yo
u
n
g
m
o
d
u
lu
s
f
o
r
th
e
m
ater
ial
ty
p
e
o
f
alu
m
in
u
m
S
t
i
f
f
n
e
ss (N
/
m)
D
a
mp
i
n
g
D
e
f
l
e
c
t
i
o
n
(
m)
M
i
n
M
a
x
M
i
n
M
a
x
M
i
n
M
a
x
A
B
B
8
.
5
3
9
.
6
7
0
.
0
0
1
0
.
0
7
0
.
0
0
0
0
0
0
0
7
6
0
.
0
0
0
0
0
8
3
F
A
N
U
C
4
9
.
9
9
1
0
1
.
6
5
0
.
0
0
1
0
.
0
0
9
0
.
0
0
0
0
0
0
1
2
3
0
.
0
0
0
0
0
6
4
2
An
ex
am
p
le
is
s
h
o
wn
to
ex
p
lo
r
e
o
n
e
o
f
th
e
ca
lc
u
lativ
e
p
r
o
ce
d
u
r
es
f
o
r
b
ac
k
en
d
ca
lcu
la
tio
n
.
I
t
is
p
o
s
s
ib
le
to
e
x
p
r
ess
th
at
th
e
t
o
tal
n
u
m
b
er
o
f
n
u
m
er
ical
v
alu
es
f
o
r
ea
ch
p
a
r
am
eter
is
e
q
u
al
to
1
2
,
an
d
t
h
e
m
ec
h
an
is
m
is
as f
o
llo
ws
.
−
Fo
r
s
tiff
n
ess
:
A
to
tal
o
f
twelv
e
(
1
2
)
n
u
m
er
ical
v
alu
es
we
r
e
f
o
u
n
d
:
s
ix
(
0
6
)
v
al
u
es
ar
e
co
n
s
id
er
ed
f
o
r
m
ax
im
u
m
Yo
u
n
g
m
o
d
u
lu
s
an
d
s
ix
(
0
6
)
v
alu
es
ar
e
c
o
n
s
id
er
e
d
f
o
r
m
in
im
u
m
Yo
u
n
g
m
o
d
u
l
u
s
.
−
Fo
r
d
am
p
i
n
g
:
A
to
tal
o
f
twel
v
e
(
1
2
)
n
u
m
er
ical
v
al
u
es
wer
e
f
o
u
n
d
:
s
ix
(
0
6
)
v
alu
es
ar
e
co
n
s
id
er
ed
f
o
r
m
ax
im
u
m
Yo
u
n
g
m
o
d
u
lu
s
an
d
s
ix
(
0
6
)
v
alu
es
ar
e
c
o
n
s
id
er
e
d
f
o
r
m
in
im
u
m
Yo
u
n
g
m
o
d
u
l
u
s
.
−
Fo
r
d
ef
lectio
n
:
A
to
tal
o
f
twelv
e
(
1
2
)
n
u
m
er
ical
v
alu
es
wer
e
f
o
u
n
d
:
s
ix
(
0
6
)
v
al
u
es
ar
e
co
n
s
id
er
ed
f
o
r
m
ax
im
u
m
Yo
u
n
g
m
o
d
u
lu
s
an
d
s
ix
(
0
6
)
v
alu
es
ar
e
c
o
n
s
id
er
e
d
f
o
r
m
in
im
u
m
Yo
u
n
g
m
o
d
u
l
u
s
.
Af
ter
g
ettin
g
all
twelv
e
(
1
2
)
n
u
m
er
ical
v
alu
es
f
o
r
ea
ch
p
a
r
am
eter
,
it
is
s
o
r
te
d
to
f
in
d
t
h
e
lo
west
v
alu
es
as
a
m
in
im
u
m
a
n
d
t
h
e
h
ig
h
est
v
alu
es
as
a
m
ax
im
u
m
.
Sin
ce
th
e
n
u
m
b
er
o
f
v
alu
es
i
n
ea
ch
p
ar
am
eter
is
twelv
e
(
1
2
)
,
th
e
m
e
d
ian
v
alu
e
is
d
eter
m
in
ed
in
th
e
co
n
tex
t
o
f
an
ev
en
n
u
m
b
er
.
I
t
is
n
o
t
ed
th
at
th
is
m
ed
ian
v
alu
e
is
co
n
s
id
er
ed
as th
e
in
p
u
t m
ed
iu
m
v
al
u
e
o
f
t
h
e
r
elate
d
p
ar
am
eter
s
.
T
ab
le
6
s
h
o
ws
th
e
f
in
al
r
esu
lt
o
f
all
n
u
m
er
ical
v
alu
es
f
o
r
s
tiff
n
ess
,
d
am
p
in
g
,
a
n
d
d
ef
lectio
n
co
n
s
id
er
in
g
m
in
im
u
m
,
m
ed
ian
,
an
d
m
a
x
im
u
m
,
f
o
llo
wed
b
y
l
o
w,
m
ed
iu
m
,
an
d
h
ig
h
.
T
ab
le
6
.
Nu
m
e
r
ical
v
alu
es o
f
AB
B
an
d
FANU
C
f
o
r
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
ef
lectio
n
f
o
ll
o
wed
b
y
l
o
w,
m
ed
iu
m
,
a
n
d
h
i
g
h
Le
v
e
l
A
B
B
F
A
N
U
C
S
t
i
f
f
n
e
ss
D
a
mp
i
n
g
D
e
f
l
e
c
t
i
o
n
S
t
i
f
f
n
e
ss
D
a
mp
i
n
g
D
e
f
l
e
c
t
i
o
n
Lo
w
8
.
5
0
.
0
0
1
9
5
0
.
0
0
0
0
0
0
0
7
6
4
9
.
9
9
0
.
0
0
1
3
0
.
0
0
0
0
0
0
1
2
3
M
e
d
i
u
m
2
5
.
1
5
0
.
0
1
4
5
0
.
0
0
0
0
0
0
6
6
4
7
8
.
0
9
8
0
.
0
0
1
6
5
1
.
2
7
E
-
06
H
i
g
h
3
9
.
6
7
0
.
0
7
8
0
.
0
0
0
0
0
8
3
1
0
1
.
6
5
0
.
0
0
9
7
0
.
0
0
0
0
0
6
4
2
T
o
v
er
if
y
th
e
h
o
lis
tic
ap
p
r
o
a
ch
o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
o
f
s
tab
ilit
y
,
th
e
T
ag
u
c
h
i
m
eth
o
d
(
L
^3
)
is
em
p
lo
y
ed
to
g
en
er
ate
d
esig
n
s
en
co
m
p
ass
in
g
all
p
o
ten
tial
co
m
b
in
atio
n
s
o
f
in
p
u
t
v
a
r
iab
les
(
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
ef
lectio
n
)
class
if
ied
as
lo
w,
m
ed
iu
m
,
an
d
h
ig
h
.
B
y
u
tili
zin
g
th
e
T
ag
u
ch
i
tech
n
i
q
u
e,
it
is
f
ea
s
ib
le
t
o
ascer
tain
2
7
d
is
tin
ct
co
m
b
in
at
io
n
s
o
f
s
tiff
n
ess
,
d
am
p
i
n
g
,
a
n
d
d
ef
lectio
n
at
v
ar
y
i
n
g
d
e
g
r
ee
s
o
f
lo
w,
m
ed
i
u
m
,
an
d
h
ig
h
.
T
h
r
o
u
g
h
t
h
e
p
r
o
p
o
s
ed
h
o
lis
tic
m
o
d
el
o
f
s
tab
i
lity
,
it
is
p
o
s
s
ib
le
to
ca
lcu
late
ev
er
y
p
o
s
s
ib
le
co
m
b
in
atio
n
o
f
T
ag
u
c
h
i
m
eth
o
d
s
tak
en
as
in
p
u
t
to
g
et
th
e
o
u
tp
u
t
o
f
s
tab
ilit
y
.
B
y
ap
p
ly
in
g
th
e
T
ag
u
ch
i
m
eth
o
d
in
c
o
n
ju
n
ctio
n
with
th
e
s
tab
ilit
y
m
o
d
el,
it
is
p
o
s
s
ib
le
to
o
b
tain
2
7
d
is
tin
ct
n
u
m
er
i
ca
l
v
alu
es
f
o
r
ea
c
h
r
o
b
o
t
m
a
n
ip
u
lato
r
.
T
h
ese
v
al
u
es
m
ay
th
en
b
e
ar
r
a
n
g
ed
to
f
in
d
th
e
l
o
west
v
alu
es
as
a
m
in
im
u
m
a
n
d
th
e
h
ig
h
est
v
alu
es
as
a
m
a
x
im
u
m
.
Sin
ce
th
er
e
ar
e
v
alu
es
f
o
r
s
ta
b
ilit
y
(
2
7
)
,
th
e
m
ed
ian
v
alu
e
i
s
d
eter
m
in
ed
in
th
e
co
n
tex
t
o
f
an
e
v
en
n
u
m
b
e
r
.
G
iv
en
th
at
th
er
e
ar
e
2
7
v
alu
es
f
o
r
s
tab
ilit
y
,
th
e
m
e
d
ian
v
al
u
e
is
ca
lcu
lated
b
ased
o
n
an
o
d
d
n
u
m
b
e
r
o
f
v
alu
es.
T
h
is
m
ed
ian
n
u
m
b
er
is
r
eg
a
r
d
ed
as
a
m
ed
iu
m
m
ea
s
u
r
e
o
f
s
tab
ilit
y
.
T
ab
le
7
d
is
p
lay
s
v
ar
io
u
s
lev
els
o
f
s
tab
ilit
y
as
th
e
o
u
tp
u
t
f
o
r
ea
ch
in
d
u
s
tr
ial
r
o
b
o
t
m
an
ip
u
lato
r
,
to
g
eth
er
with
th
e
m
atch
in
g
co
n
d
itio
n
o
f
th
e
i
n
p
u
t p
ar
am
eter
s
.
I
n
all
ca
s
es,
t
h
e
m
a
x
im
u
m
s
tab
ilit
y
is
o
b
tain
ed
wh
en
s
tiff
n
ess
is
h
ig
h
,
wh
er
ea
s
d
a
m
p
in
g
an
d
d
ef
lectio
n
a
r
e
lo
w.
I
n
c
o
n
tr
as
t,
th
e
m
in
im
u
m
s
tab
ilit
y
is
in
s
p
ec
ted
wh
en
s
tiff
n
ess
is
lo
w
,
an
d
d
a
m
p
in
g
an
d
d
ef
ec
tio
n
a
r
e
h
ig
h
.
T
h
at
m
e
an
s
th
e
r
esu
lts
co
m
p
l
y
with
th
e
n
o
v
el
m
o
d
el
o
f
s
tab
ilit
y
f
o
r
all
th
e
r
o
b
o
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in
v
esti
g
ated
,
an
d
t
h
is
co
n
ce
p
t
ca
n
b
e
ap
p
lied
to
d
esig
n
a
n
ew
r
o
b
o
t
m
an
ip
u
lato
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
3
8
0
-
3
9
0
386
T
a
b
le
7
.
O
u
t
p
u
t
v
al
u
es
o
f
AB
B
a
n
d
FAN
UC
f
o
r
s
ta
b
i
lit
y
i
n
d
i
f
f
er
e
n
t
le
v
e
ls
an
d
c
o
n
d
iti
o
n
s
o
f
i
n
p
u
t
p
ar
am
ete
r
s
Le
v
e
l
A
B
B
F
A
N
U
C
S
t
a
b
i
l
i
t
y
(
o
u
t
p
u
t
)
C
o
n
d
i
t
i
o
n
s
f
o
r
i
n
p
u
t
p
a
r
a
me
t
e
r
s
S
t
a
b
i
l
i
t
y
(
o
u
t
p
u
t
)
C
o
n
d
i
t
i
o
n
s
f
o
r
i
n
p
u
t
p
a
r
a
me
t
e
r
s
Lo
w
1
3
1
2
9
4
4
0
.
8
4
W
h
e
n
s
t
i
f
f
n
e
ss
i
s
l
o
w
,
d
a
m
p
i
n
g
i
s
h
i
g
h
,
a
n
d
d
e
f
l
e
c
t
i
o
n
i
s
h
i
g
h
8
0
2
7
4
7
5
3
5
.
1
W
h
e
n
s
t
i
f
f
n
e
ss
i
s
l
o
w
,
d
a
m
p
i
n
g
i
s
h
i
g
h
,
a
n
d
d
e
f
l
e
c
t
i
o
n
i
s
h
i
g
h
M
e
d
i
u
m
2
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4
.
2
.
Va
lid
a
t
i
o
n o
f
re
s
ult
us
ing
ANO
VA
pla
t
f
o
rm
un
der
M
ini
t
a
b
W
e
h
av
e
s
tatis
tically
as
s
ess
ed
th
e
co
r
r
elatio
n
s
o
f
s
tab
ilit
y
,
d
e
f
lectio
n
,
s
tiff
n
ess
,
d
am
p
i
n
g
,
a
n
d
Yo
u
n
g
m
o
d
u
lu
s
a
n
d
th
en
v
alid
ated
th
e
co
n
clu
s
io
n
s
m
ad
e
f
r
o
m
t
h
e
o
b
s
er
v
ed
d
ata
u
s
in
g
t
h
e
ANO
VA
p
latf
o
r
m
u
n
d
er
Min
itab
.
W
e
u
tili
ze
d
th
e
Min
itab
Statis
tical
So
f
twar
e
Pack
ag
e
to
r
ev
ea
l c
o
n
ce
aled
co
r
r
elatio
n
s
am
o
n
g
v
ar
io
u
s
m
ater
ial
p
r
o
p
er
ties
em
p
lo
y
e
d
in
r
o
b
o
t
m
a
n
ip
u
lato
r
s
.
T
h
e
r
esu
lts
will
en
h
an
ce
th
e
d
ev
elo
p
m
en
t
o
f
r
o
b
o
t
m
an
ip
u
lato
r
s
b
y
in
f
o
r
m
in
g
m
o
r
e
ef
f
ec
tiv
e
d
esig
n
an
d
m
ater
i
al
s
elec
tio
n
,
u
ltima
tely
im
p
r
o
v
in
g
th
eir
s
tab
ilit
y
.
4
.
2
.
1
.
E
f
f
ec
t
s
a
nd
I
nte
ra
ct
io
n o
f
m
a
t
er
ia
l pa
ra
m
et
er
s
o
f
m
a
nip
ula
t
o
rs
T
h
e
ANOV
A
p
latf
o
r
m
was
co
n
f
ig
u
r
ed
to
o
b
s
er
v
e
m
ater
i
al
p
ar
am
eter
s
’
ef
f
ec
ts
a
n
d
in
ter
ac
tio
n
s
.
E
x
p
er
im
en
ts
s
h
o
wed
th
at
in
c
r
ea
s
ed
s
tiff
n
ess
in
cr
ea
s
es
s
ta
b
ilit
y
,
wh
ile
d
ec
r
ea
s
ed
d
ef
le
ctio
n
an
d
d
am
p
i
n
g
d
ec
r
ea
s
e
s
tab
ilit
y
.
T
h
is
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
m
ater
i
al
p
ar
am
eter
in
s
tab
ilit
y
.
Fig
u
r
e
3
s
h
o
w
s
th
e
m
ain
ef
f
ec
ts
p
lo
t f
o
r
th
e
s
tab
ilit
y
o
f
th
e
AB
B
an
d
FANU
C
r
o
b
o
t m
an
ip
u
lato
r
s
.
Fu
r
th
er
m
o
r
e
,
th
e
in
ter
ac
tio
n
o
f
m
ater
ial
p
ar
am
eter
s
in
m
an
i
p
u
lato
r
s
is
cr
u
cial
f
o
r
ac
h
iev
i
n
g
o
p
tim
al
p
er
f
o
r
m
an
ce
,
ef
f
icien
cy
,
s
af
et
y
,
an
d
s
u
s
tain
ab
ilit
y
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
r
o
b
o
tic
a
p
p
lica
tio
n
s
.
T
h
r
o
u
g
h
th
e
ex
p
er
im
en
t
to
v
alid
ate
th
e
in
ter
ac
tio
n
,
it
h
as
b
ee
n
f
o
u
n
d
th
at
th
ese
p
ar
am
eter
s
ar
e
in
d
iv
id
u
ally
af
f
ec
ted
s
tr
o
n
g
ly
a
n
d
also
in
ter
ac
t.
F
ig
u
r
e
4
s
h
o
w
s
th
e
in
ter
ac
tio
n
p
lo
t
o
f
s
tab
ilit
y
f
o
r
th
e
AB
B
an
d
FANUC
m
an
ip
u
lato
r
s
.
AB
B
FANUC
Fig
u
r
e
3
.
Ma
in
e
f
f
ec
ts
p
lo
t o
f
s
tab
ilit
y
f
o
r
th
e
m
an
i
p
u
lato
r
s
AB
B
FANUC
Fig
u
r
e
4
.
I
n
ter
ac
tio
n
p
lo
t o
f
s
tab
ilit
y
f
o
r
th
e
m
an
ip
u
lato
r
s
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I
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-
2
5
8
6
A
h
o
lis
tic
a
p
p
r
o
a
c
h
o
f
s
ta
b
ilit
y
u
s
in
g
ma
teri
a
l p
a
r
a
mete
r
s
o
f m
a
n
ip
u
la
to
r
s
(
S
h
a
b
n
o
m
Mu
s
ta
r
y
)
387
4
.
2
.
2
.
Ana
ly
s
is
o
f
v
a
ria
nce
f
o
r
s
t
a
bil
it
y
o
f
AB
B
a
nd
F
AN
UC
m
a
nip
ula
t
o
r
An
aly
s
is
o
f
v
ar
ian
ce
is
cr
u
cial
f
o
r
ass
ess
in
g
an
d
en
h
an
ci
n
g
th
e
s
tab
ilit
y
o
f
r
o
b
o
tic
m
an
ip
u
lato
r
s
b
ased
o
n
m
ater
ial
p
r
o
p
er
ties
s
u
ch
as
s
t
if
f
n
ess
,
d
ef
lectio
n
,
an
d
d
am
p
in
g
.
A
th
o
r
o
u
g
h
an
aly
s
is
h
as
b
ee
n
co
n
d
u
cte
d
u
s
in
g
th
e
ANOV
A
p
latf
o
r
m
to
g
ain
in
s
ig
h
ts
in
to
t
h
e
r
elativ
e
s
ig
n
if
ican
ce
o
f
th
e
s
e
f
ac
to
r
s
an
d
h
o
w
th
ey
in
ter
ac
t.
T
h
e
m
ain
f
o
c
u
s
was
to
u
n
d
er
s
tan
d
t
h
e
r
atio
o
f
v
ar
iab
ilit
y
b
etwe
en
d
if
f
er
en
t
g
r
o
u
p
s
c
o
m
p
ar
e
d
to
th
e
v
ar
iab
ilit
y
with
in
ea
ch
g
r
o
u
p
.
T
h
e
F
v
alu
e
is
a
cr
u
cial
r
e
s
u
lt
o
f
ANOV
A,
an
d
it
is
em
p
lo
y
ed
to
co
n
clu
d
e
th
e
d
is
p
ar
ities
am
o
n
g
g
r
o
u
p
a
v
er
ag
es.
Ad
d
itio
n
ally
,
it
is
u
til
ized
to
c
o
m
p
u
te
th
e
p
-
v
alu
e,
wh
ich
r
ep
r
esen
ts
th
e
lik
elih
o
o
d
o
f
d
etec
tin
g
t
h
e
d
at
a
u
n
d
er
t
h
e
ass
u
m
p
tio
n
th
at
t
h
e
n
u
ll
h
y
p
o
th
esis
is
ac
cu
r
ate.
A
s
m
aller
p
-
v
alu
e
in
d
icate
s
s
tr
o
n
g
er
ev
id
en
ce
a
g
ain
s
t
th
e
n
u
ll
h
y
p
o
th
esis
an
d
in
s
u
p
p
o
r
t
o
f
th
e
alter
n
ativ
e
h
y
p
o
th
esis
.
B
y
an
aly
zin
g
t
h
e
co
n
s
eq
u
en
ce
s
,
it
h
as
b
ee
n
d
ete
r
m
in
ed
th
at
d
ef
lectio
n
is
th
e
m
o
s
t
in
f
lu
e
n
tial
ch
ar
ac
ter
is
tic
am
o
n
g
t
h
e
m
ater
ial
p
r
o
p
er
ties
o
f
s
tiff
n
ess
,
d
ef
lectio
n
,
a
n
d
d
a
m
p
in
g
.
T
h
e
r
esu
lts
ar
e
s
h
o
wn
in
T
ab
le
8
.
T
ab
le
8
.
An
aly
s
is
o
f
v
ar
ian
ce
f
o
r
s
tab
ilit
y
o
f
AB
B
an
d
FANUC
S
o
u
r
c
e
DF
A
B
B
F
A
N
U
C
SS
MS
F
P
SS
MS
F
P
S
t
i
f
f
n
e
ss
2
4
.
1
4
8
5
6
E+
2
1
2
.
0
7
4
2
8
E+
2
1
0
.
9
0
0
.
4
2
1
2
.
6
7
4
9
5
E+
2
2
1
.
3
3
7
4
7
E+
2
2
1
.
1
8
0
.
3
2
8
D
e
f
l
e
c
t
i
o
n
2
2
.
1
4
7
8
2
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2
2
1
.
0
7
3
9
1
E+
2
2
4
.
6
8
0
.
0
2
2
5
.
0
3
7
0
3
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2
3
2
.
5
1
8
5
1
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2
3
2
2
.
2
4
0
.
0
0
0
D
a
mp
i
n
g
2
1
.
9
4
5
4
0
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2
2
9
.
7
2
7
0
2
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2
1
4
.
2
4
0
.
0
2
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1
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1
6
4
2
1
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2
3
5
.
8
2
1
0
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2
5
.
1
4
0
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0
1
6
Er
r
o
r
20
4
.
5
8
8
5
5
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2
2
2
.
2
9
4
2
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2
1
2
.
2
6
5
3
5
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2
3
1
.
1
3
2
6
7
E+
2
2
To
t
a
l
26
9
.
0
9
6
6
3
E+
2
2
8
.
7
3
4
0
8
E+
2
3
4
.
2
.
3
.
Su
rf
a
ce
plo
t
t
ing
o
f
s
t
a
bil
it
y
f
o
r
AB
B
a
nd
F
ANU
C
m
a
nip
ula
t
o
r
T
o
s
h
o
w
th
e
ef
f
ec
t
o
f
ch
an
g
es
in
s
tiff
n
ess
,
d
ef
lectio
n
,
an
d
d
am
p
in
g
o
n
th
e
m
an
i
p
u
lato
r
’
s
s
tab
ilit
y
,
a
s
tab
ilit
y
s
u
r
f
ac
e
p
lo
t h
as b
ee
n
m
ad
e.
T
h
ese
p
lo
ts
ca
n
b
e
an
al
y
ze
d
to
id
en
tify
th
e
r
eg
io
n
s
o
f
th
e
s
y
s
tem
th
at
ar
e
u
n
s
tab
le
o
r
s
tab
le.
T
h
e
o
p
tim
a
l
s
tiff
n
ess
lev
el
s
f
o
r
s
tab
ilit
y
a
n
d
p
er
f
o
r
m
an
ce
m
etr
ics
ca
n
al
s
o
b
e
f
o
u
n
d
u
s
in
g
th
e
s
u
r
f
ac
e
p
lo
t
o
f
s
tab
ilit
y
ag
ain
s
t
s
tiff
n
ess
.
Ad
d
itio
n
ally
,
th
e
ef
f
ec
t
o
f
s
tr
u
ctu
r
al
f
lex
ib
ili
ty
o
n
th
e
s
y
s
tem
’
s
o
v
e
r
al
l
s
ta
b
i
lit
y
c
a
n
b
e
ass
ess
e
d
b
y
e
x
a
m
i
n
i
n
g
t
h
e
r
el
ati
o
n
s
h
i
p
b
et
wee
n
d
e
f
l
ec
t
io
n
an
d
s
ta
b
i
lit
y
.
U
n
d
e
r
s
t
an
d
i
n
g
th
e
ef
f
ec
t
o
f
d
am
p
in
g
o
n
th
e
s
y
s
tem
’
s
ab
ili
ty
to
m
ain
tain
s
tab
ilit
y
in
th
e
f
ac
e
o
f
ex
ter
n
al
d
is
tu
r
b
an
ce
s
o
r
d
y
n
am
ic
lo
ad
s
r
eq
u
ir
es
an
an
aly
s
is
o
f
th
e
s
tab
ilit
y
s
u
r
f
ac
e
o
f
d
am
p
in
g
.
Fig
u
r
e
5
s
h
o
ws
th
e
s
u
r
f
ac
e
p
lo
t
o
f
s
tab
ilit
y
f
o
r
th
e
AB
B
an
d
FA
NUC
r
o
b
o
t
m
an
ip
u
lato
r
.
T
h
r
o
u
g
h
th
e
f
i
g
u
r
es,
it
ca
n
b
e
d
eter
m
in
ed
th
e
ar
ea
s
wh
er
e
th
e
s
y
s
tem
is
eith
er
s
tab
le
(
g
r
ee
n
)
o
r
u
n
s
tab
le
(
wh
ite)
.
AB
B
FANUC
Fig
u
r
e
5
.
Su
r
f
ac
e
p
lo
t
o
f
s
tab
il
ity
f
o
r
th
e
m
an
ip
u
lato
r
s
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I
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13
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4
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Dec
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er
20
24
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B
y
in
co
r
p
o
r
atin
g
s
tiff
n
ess
,
d
ef
lectio
n
,
an
d
d
a
m
p
in
g
as
in
p
u
t
p
ar
am
eter
s
,
th
e
s
u
r
f
ac
e
p
lo
t
o
f
s
tab
ilit
y
o
f
f
er
s
a
co
m
p
r
eh
e
n
s
iv
e
d
ep
ic
tio
n
o
f
h
o
w
th
ese
v
ar
iab
les
im
p
ac
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
a
r
o
b
o
t
m
a
n
ip
u
lato
r
.
T
h
ese
ca
n
s
er
v
e
as
a
r
ef
e
r
en
c
e
wh
en
d
ev
el
o
p
in
g
m
an
ip
u
lato
r
s
y
s
tem
s
th
at
m
ee
t
th
e
s
p
ec
if
ic
r
eq
u
ir
em
e
n
ts
f
o
r
s
tab
ilit
y
,
p
er
f
o
r
m
a
n
ce
,
an
d
d
e
p
en
d
ab
ilit
y
.
I
n
co
n
clu
s
io
n
,
o
u
r
ap
p
r
o
ac
h
e
x
p
lo
r
es
th
e
im
p
ac
t
o
f
m
ater
ial
p
ar
am
eter
s
lik
e
s
tiff
n
ess
,
d
a
m
p
in
g
,
an
d
d
ef
lectio
n
o
n
t
h
e
s
tab
ilit
y
o
f
r
o
b
o
t
m
a
n
ip
u
lato
r
s
.
S
ec
tio
n
3
e
v
alu
ates
s
tab
ilit
y
u
s
in
g
b
o
th
m
o
d
if
ied
an
d
co
n
v
en
tio
n
al
f
o
r
m
u
las
f
o
r
m
at
er
ial
p
r
o
p
e
r
ties
,
o
f
f
er
in
g
a
d
etailed
an
aly
s
is
o
f
h
o
w
v
ar
io
u
s
p
ar
am
eter
s
im
p
ac
t
o
v
er
all
s
tab
ilit
y
.
I
t
em
p
h
asizes
th
e
im
p
o
r
tan
ce
o
f
p
ar
am
ete
r
s
lik
e
Yo
u
n
g
M
o
d
u
l
u
s
,
m
ass
,
len
g
th
,
d
iam
ete
r
,
an
d
p
ay
l
o
ad
in
s
elec
tin
g
s
u
ita
b
le
m
ater
ials
.
Sectio
n
4
r
ev
ea
l
s
th
at
s
tiff
n
ess
d
ir
ec
tly
in
f
lu
en
ce
s
s
tab
ilit
y
,
u
n
lik
e
d
am
p
in
g
a
n
d
d
e
f
lectio
n
,
wh
ic
h
h
av
e
an
i
n
v
er
s
e
r
elatio
n
s
h
ip
.
T
h
e
r
esear
ch
u
s
es
a
h
o
lis
tic
ap
p
r
o
ac
h
,
u
s
in
g
th
e
T
ag
u
ch
i
m
eth
o
d
to
d
esig
n
s
tab
ilit
y
co
m
b
in
atio
n
s
an
d
v
ali
d
ates
th
e
ap
p
r
o
ac
h
u
s
in
g
n
u
m
er
ical
v
alu
es
an
d
s
im
u
latio
n
to
o
ls
s
u
ch
as M
in
itab
.
5.
CO
NCLU
SI
O
N
I
n
th
is
r
esear
ch
wo
r
k
,
a
h
o
lis
tic
ap
p
r
o
ac
h
is
f
o
r
m
u
lated
to
ev
alu
ate
th
e
s
tab
ilit
y
lev
el
o
f
an
in
d
u
s
tr
ial
r
o
b
o
t
m
an
i
p
u
lato
r
u
s
in
g
m
ater
ial
-
r
elate
d
p
ar
am
eter
s
o
f
s
t
if
f
n
ess
,
d
am
p
in
g
,
a
n
d
d
ef
lec
tio
n
.
T
h
e
T
ag
u
ch
i
m
eth
o
d
is
u
s
ed
to
d
esig
n
p
r
o
b
ab
le
co
m
b
in
atio
n
s
o
f
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
e
f
lectio
n
as
in
p
u
t
an
d
s
tab
ilit
y
as
o
u
tp
u
t
co
n
ce
r
n
in
g
th
e
lo
w,
m
ed
iu
m
,
an
d
h
ig
h
.
T
h
e
co
m
b
in
atio
n
o
f
th
e
o
u
tp
u
t
co
lu
m
n
o
f
th
e
T
ag
u
ch
i
m
eth
o
d
is
attr
ib
u
ted
to
s
tab
ilit
y
an
d
is
ca
lcu
lated
u
s
in
g
th
e
p
r
o
p
o
s
ed
m
o
d
el
o
f
s
tab
ilit
y
.
Mo
r
eo
v
er
,
th
e
ap
p
r
o
ac
h
is
also
ch
ec
k
ed
b
y
ex
p
lo
r
in
g
d
if
f
er
en
t
n
u
m
e
r
ical
v
alu
es
an
d
th
e
s
im
u
latio
n
to
o
l.
I
n
b
o
th
ca
s
es,
it
h
as
b
ee
n
f
o
u
n
d
th
at
s
tab
ilit
y
d
ep
en
d
s
o
n
s
ti
f
f
n
ess
,
d
am
p
in
g
,
a
n
d
d
ef
lect
io
n
,
wh
er
e
s
tab
ilit
y
is
d
ir
ec
t
ly
p
r
o
p
o
r
tio
n
al
to
s
tiff
n
ess
an
d
in
v
er
s
ely
p
r
o
p
o
r
tio
n
al
to
d
am
p
in
g
an
d
d
ef
lectio
n
.
T
h
e
r
elatio
n
o
f
s
tab
ilit
y
with
s
tiff
n
ess
,
d
ef
lectio
n
,
an
d
d
am
p
in
g
b
elo
n
g
s
to
d
if
f
e
r
en
t
v
alu
es
o
f
t
h
e
Yo
u
n
g
m
o
d
u
lu
s
o
f
m
ater
ials
an
d
m
o
d
els
o
f
r
o
b
o
t
m
an
ip
u
lato
r
s
.
Stab
ilit
y
a
b
o
u
t
s
tiff
n
ess
,
d
am
p
in
g
,
an
d
d
e
f
lectio
n
is
ess
en
tial
to
ju
s
tify
in
g
t
h
e
ex
is
tin
g
r
o
b
o
t
’
s
wo
r
k
in
g
ca
p
ac
ity
an
d
to
d
esig
n
in
g
an
d
d
ev
elo
p
i
n
g
a
n
ew
g
en
er
atio
n
o
f
r
o
b
o
ts
.
B
esid
es
,
Yo
u
n
g
m
o
d
u
lu
s
,
m
ass
,
len
g
th
,
d
iam
eter
,
an
d
p
ay
lo
ad
h
a
v
e
a
s
ig
n
if
ican
t
r
o
le
in
s
elec
tin
g
th
e
ap
p
r
o
p
r
i
ate
r
o
b
o
t
m
ater
ials
ac
co
r
d
in
g
to
th
eir
ap
p
licatio
n
s
in
in
d
u
s
tr
y
.
T
h
e
f
u
tu
r
e
p
r
es
en
ted
s
tab
ilit
y
m
eth
o
d
r
e
q
u
ir
ed
f
u
r
th
e
r
an
aly
s
is
u
s
in
g
th
e
L
y
a
p
u
n
o
v
s
tab
ilit
y
a
n
aly
s
is
ap
p
r
o
ac
h
a
n
d
its
r
elatio
n
to
th
e
ac
cu
r
ac
y
o
f
t
h
e
r
o
b
o
t
m
an
ip
u
lato
r
.
ACK
NO
WL
E
DG
E
M
E
NT
T
h
e
au
th
o
r
s
ar
e
t
h
an
k
f
u
l
to
th
e
Min
is
tr
y
o
f
Po
s
ts
,
T
elec
o
m
m
u
n
icatio
n
a
n
d
I
n
f
o
r
m
atio
n
T
ec
h
n
o
lo
g
y
,
T
h
e
Peo
p
le
’
s
R
ep
u
b
lic
o
f
B
an
g
lad
esh
,
u
n
d
er
th
e
I
n
f
o
r
m
atio
n
an
d
C
o
m
m
u
n
icatio
n
T
ec
h
n
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(
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RE
F
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R
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NC
E
S
[
1
]
O
.
K
r
o
e
mer,
S
.
N
i
e
k
u
m,
a
n
d
G
.
K
o
n
i
d
a
r
i
s
,
“
A
r
e
v
i
e
w
o
f
r
o
b
o
t
l
e
a
r
n
i
n
g
f
o
r
ma
n
i
p
u
l
a
t
i
o
n
:
c
h
a
l
l
e
n
g
e
s
,
r
e
p
r
e
se
n
t
a
t
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o
n
s
,
a
n
d
a
l
g
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r
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ms,
”
J
o
u
rn
a
l
o
f
Ma
c
h
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e
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Re
se
a
rc
h
,
v
o
l
.
2
2
,
2
0
2
1
.
[
2
]
M
.
J
a
v
a
i
d
,
A
.
H
a
l
e
e
m,
R
.
P
.
S
i
n
g
h
,
a
n
d
R
.
S
u
m
a
n
,
“
S
u
b
st
a
n
t
i
a
l
c
a
p
a
b
i
l
i
t
i
e
s
o
f
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s
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n
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h
a
n
c
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g
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n
d
u
st
r
y
4
.
0
i
mp
l
e
m
e
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t
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t
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o
n
,
”
C
o
g
n
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t
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v
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R
o
b
o
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c
s
,
v
o
l
.
1
,
p
p
.
5
8
–
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,
2
0
2
1
,
d
o
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:
1
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.
c
o
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.
[
3
]
V
.
S
a
t
y
a
D
u
r
g
a
M
a
n
o
h
a
r
S
a
h
u
,
P
.
S
a
mal
,
a
n
d
C
.
K
u
mar
P
a
n
i
g
r
a
h
i
,
“
M
o
d
e
l
l
i
n
g
,
a
n
d
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
s
o
f
r
o
b
o
t
i
c
m
a
n
i
p
u
l
a
t
o
r
s
:
a
r
e
v
i
e
w
,
”
M
a
t
e
ri
a
l
s
T
o
d
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y
:
P
ro
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d
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s
,
v
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ma
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.
[
4
]
C
.
S
.
T
i
w
a
r
y
e
t
a
l
.
,
“
F
i
v
e
d
e
c
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d
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s
o
f
r
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sea
r
c
h
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n
t
h
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d
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p
m
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r
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m
a
t
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r
i
a
l
s,
”
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g
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ss
i
n
M
a
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ri
a
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s
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c
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c
e
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v
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1
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p
ma
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[
5
]
R
.
H
.
T
a
y
l
o
r
,
“
M
e
d
i
c
a
l
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o
b
o
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i
c
s
a
n
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c
o
mp
u
t
e
r
-
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n
t
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g
r
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d
i
n
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r
v
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n
t
i
o
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a
l
med
i
c
i
n
e
,
”
i
n
Me
d
i
c
a
l
I
m
a
g
i
n
g
2
0
1
2
:
I
m
a
g
e
-
G
u
i
d
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d
Pro
c
e
d
u
r
e
s,
Ro
b
o
t
i
c
I
n
t
e
rve
n
t
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o
n
s
,
a
n
d
M
o
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n
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.
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2
,
v
o
l
.
8
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o
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:
1
0
.
1
1
1
7
/
1
2
.
9
1
6
5
0
0
.
[
6
]
A
.
Za
c
h
a
r
a
k
i
,
I
.
K
o
st
a
v
e
l
i
s,
A
.
G
a
s
t
e
r
a
t
o
s
,
a
n
d
I
.
D
o
k
a
s
,
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