I
nte
rna
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA
)
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
,
p
p
.
1
5
1
~
1
6
7
I
SS
N:
2089
-
4
8
5
6
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
r
a.
v
6
i3
.
p
p
1
5
1
-
16
7
151
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
RA
The
Influe
nce
o
f
No
n
-
pla
na
r (
Spa
t
ia
l)
Lin
k
s
in
t
he
S
tatic
Cha
ra
cter
isti
cs B
eha
v
io
r
o
f
Plana
r
P
a
ra
llel Ma
nipul
a
tor
G
a
nes
h
M
.
1
,
K
a
rt
hik
ey
a
n
R
.
2
,
Ven
k
it
a
cha
la
m
P
.
3
,
G
urug
uh
a
n
G
.
4
,
S.
S
hrini
t
h
i
5
,
K
a
nn
a
n
S
.
6
,
Anj
a
n K
u
m
a
r
Da
s
h
7
1
,
2,
3,
4
,
5,
7
S
c
h
o
o
l
o
f
M
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
.
S
A
S
T
R
A
Un
iv
e
r
sit
y
,
In
d
ia
6
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
.
S
A
S
T
R
A
Un
iv
e
rsit
y
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
y
2
,
2
0
1
7
R
ev
i
s
ed
J
u
l 3
,
2
0
1
7
A
cc
ep
ted
J
u
l 1
7
,
2
0
1
7
Co
n
v
e
n
ti
o
n
a
l
p
lan
a
r
m
a
n
ip
u
lat
o
rs
h
a
v
e
a
ll
th
e
ir
li
n
k
s
in
a
sin
g
le
p
lan
e
.
In
c
re
a
sin
g
p
a
y
lo
a
d
a
t
th
e
e
n
d
-
e
ffe
c
ter/
m
o
b
il
e
p
latf
o
rm
c
a
n
in
d
u
c
e
h
ig
h
stre
ss
in
t
h
e
li
n
k
s
d
u
e
to
c
a
n
ti
lev
e
r
n
a
t
u
re
o
f
li
n
k
s.
T
h
u
s
it
li
m
it
s
th
e
to
tal
v
e
rti
c
a
l
lo
a
d
t
h
a
t
c
a
n
b
e
a
p
p
l
ied
o
n
t
h
e
m
o
b
il
e
p
latf
o
rm
.
In
c
o
n
tras
t
to
t
h
e
li
n
k
s
in
c
o
n
v
e
n
ti
o
n
a
l
p
la
n
a
r
p
a
ra
ll
e
l
m
e
c
h
a
n
ism
s,
n
o
n
-
p
lan
a
r
li
n
k
s
a
re
p
ro
p
o
se
d
in
th
is
p
a
p
e
r,
i.
e
.
,
li
n
k
s
a
re
m
a
d
e
in
c
li
n
e
d
t
o
th
e
h
o
rizo
n
tal
p
lan
e
a
n
d
n
o
n
p
lan
a
r
leg
s
a
r
e
c
o
n
stru
c
ted
.
A
lt
h
o
u
g
h
th
e
li
n
k
s
a
re
m
a
d
e
n
o
n
-
p
lan
a
r,
th
e
ro
tary
(o
r
p
rism
a
ti
c
)
jo
in
ts
a
x
e
s
re
m
a
in
p
e
r
p
e
n
d
ic
u
lar
(o
r
p
a
ra
ll
e
l)
to
th
e
p
l
a
n
e
o
f
th
e
b
a
se
p
latf
o
rm
,
w
h
ich
re
tain
s
th
e
p
lan
a
r
m
o
ti
o
n
o
f
th
e
e
n
d
-
e
ffe
c
ter.
F
o
r
stu
d
y
in
g
th
e
a
p
p
li
c
a
ti
o
n
o
f
su
c
h
n
o
n
p
la
n
a
r
li
n
k
s
in
p
la
n
a
r
m
a
n
ip
u
lato
rs,
n
e
w
m
o
d
e
ls
o
f
in
e
rti
a
,
stiff
n
e
s
s
a
n
d
leg
d
y
n
a
m
ics
h
a
v
e
to
b
e
d
e
v
e
lo
p
e
d
.
In
t
h
is
a
rti
c
le,
th
e
se
m
o
d
e
ls
a
re
d
e
v
e
lo
p
e
d
a
n
d
w
it
h
th
e
d
e
v
e
lo
p
e
d
m
o
d
e
ls,
th
e
sta
ti
c
a
n
a
ly
sis
is
d
o
n
e
o
n
th
e
p
lan
a
r
m
a
n
ip
u
lat
o
rs
w
it
h
n
o
n
-
p
lan
a
r
li
n
k
s
a
n
d
th
e
p
e
rf
o
r
m
a
n
c
e
is
c
o
m
p
a
re
d
w
it
h
th
e
c
o
rre
sp
o
n
d
i
n
g
c
o
n
v
e
n
ti
o
n
a
l
p
lan
a
r
m
a
n
ip
u
lat
o
rs.
K
ey
w
o
r
d
:
3
-
R
R
R
p
la
n
ar
p
ar
allel
r
o
b
o
t
A
N
SYS
Mo
m
en
t o
f
in
er
tia
Op
ti
m
izatio
n
Sti
f
f
n
es
s
an
al
y
s
is
Co
p
y
rig
h
t
©
2
0
1
7
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Gan
es
h
M
.,
Sch
o
o
l o
f
M
ec
h
a
n
ical
E
n
g
in
e
er
in
g
,
S
A
ST
R
A
Un
i
v
er
s
i
t
y
,
T
h
an
j
av
u
r
–
6
1
3
4
0
2
,
I
n
d
ia.
E
m
ail:
g
an
e
s
h
m
@
m
ec
h
.
s
astra
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
P
ar
allel
r
o
b
o
ts
h
av
e
b
ee
n
u
n
d
er
in
ten
s
iv
e
s
t
u
d
y
f
o
r
o
v
er
m
o
r
e
th
an
o
n
e
d
ec
ad
e.
I
t
is
w
ell
k
n
o
w
n
th
at
p
ar
allel
k
i
n
e
m
a
tic
s
tr
u
ct
u
r
es
o
f
f
er
ad
v
an
ta
g
es
s
u
c
h
as
h
ig
h
ac
c
u
r
ac
y
,
p
a
y
lo
ad
-
to
-
w
eig
h
t
r
atio
,
h
i
g
h
n
atu
r
a
l
f
r
eq
u
en
c
ies
a
n
d
r
ig
id
it
y
co
m
p
ar
ed
to
s
er
ial
m
a
n
ip
u
lato
r
s
.
O
f
th
e
p
ar
allel
m
an
ip
u
lato
r
s
,
3
-
d
o
f
p
lan
ar
p
ar
allel
m
an
ip
u
lato
r
s
ar
e
w
id
el
y
u
s
ed
as P
ar
allel
Ki
n
e
m
a
tic
Ma
c
h
i
n
e.
So
it
h
as
attr
ac
ted
m
a
n
y
r
es
ea
r
ch
er
s
to
s
tu
d
y
o
n
its
w
o
r
k
s
p
ac
e
[
1
]
,
[
2
]
,
d
ir
ec
t k
in
e
m
a
tics
[
3
]
s
in
g
u
lar
it
y
A
n
a
l
y
s
is
[
4
]
,
[
5
]
an
d
o
p
tim
al
d
esi
g
n
[
6
]
,
[
7
]
.
P
lan
ar
m
a
n
ip
u
lato
r
s
f
i
n
d
its
ap
p
licatio
n
in
f
ast
p
o
s
itio
n
in
g
o
r
ass
e
m
b
l
y
o
p
er
atio
n
s
.
Su
c
h
a
p
p
licatio
n
s
m
ak
e
u
s
e
o
f
th
e
h
i
g
h
s
p
ee
d
ca
p
ab
ilit
y
w
i
th
m
i
n
i
m
u
m
p
o
s
itio
n
i
n
g
er
r
o
r
,
lar
g
e
s
ti
f
f
n
e
s
s
[
8
]
,
[
9
]
an
d
lo
w
in
er
tia[
1
0
]
o
f
p
ar
allel
p
lan
ar
m
an
ip
u
lato
r
s
.
P
ar
allel
P
lan
ar
m
an
ip
u
lato
r
s
b
elo
n
g
i
n
g
to
s
u
c
h
ca
te
g
o
r
y
is
s
h
o
w
n
in
Fi
g
u
r
e
1
.
I
n
ap
p
licatio
n
s
w
h
er
e
th
er
e
i
s
a
h
ea
v
y
lo
ad
o
n
th
e
p
lat
f
o
r
m
,
th
e
v
er
tica
l
lo
ad
w
il
l
cr
ea
te
a
ca
n
tile
v
er
ac
tio
n
o
n
ea
c
h
o
f
t
h
e
li
n
k
s
.
T
h
u
s
th
er
e
i
s
a
ch
a
n
ce
t
h
at
it
m
a
y
li
m
it
t
h
e
to
tal
v
er
tica
l
lo
ad
th
at
ca
n
b
e
ap
p
lied
.
I
n
th
is
p
ap
er
,
p
lan
ar
m
an
ip
u
lato
r
w
it
h
n
o
n
-
p
la
n
ar
lin
k
s
i
s
p
r
o
p
o
s
ed
.
Fo
r
a
m
a
n
ip
u
lato
r
w
it
h
n
o
n
-
pl
an
ar
lin
k
s
,
li
n
k
s
ar
e
n
o
t
i
n
s
in
g
le
p
lan
e
.
T
h
e
lin
k
s
ar
e
ele
v
ated
an
d
d
is
tan
ce
b
et
w
ee
n
b
as
e
p
latf
o
r
m
a
n
d
to
p
p
latf
o
r
m
i
s
r
aised
.
I
n
t
h
is
p
r
o
p
o
s
ed
d
esig
n
,
ea
c
h
li
n
k
is
i
n
cli
n
ed
w
ith
r
esp
ec
t
to
th
e
h
o
r
izo
n
tal
p
lan
e
a
n
d
it
i
s
ex
p
ec
ted
to
ca
r
r
y
a
h
i
g
h
er
p
a
y
lo
ad
an
d
d
ec
r
ea
s
e
th
e
ca
n
tile
v
er
n
atu
r
e
o
f
t
h
e
li
n
k
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
5
1
–
16
7
152
Fig
u
r
e
1
a.
A
p
lan
ar
3
-
R
R
R
M
an
ip
u
lato
r
Fig
u
r
e
1
b
.
A
p
lan
ar
r
o
b
o
t w
ith
3
-
P
R
R
co
n
f
i
g
u
r
atio
n
[
1
1
]
I
n
n
at
u
r
e
also
,
t
h
is
d
esi
g
n
i
s
m
o
r
e
clo
s
el
y
o
r
ien
ted
to
w
ar
d
s
th
e
b
eh
av
io
r
o
f
m
a
n
y
l
iv
i
n
g
en
titi
e
s
.
T
h
e
f
o
llo
w
in
g
ill
u
s
tr
atio
n
s
d
ep
ict
th
e
u
s
a
g
e
o
f
i
n
cli
n
ed
lin
k
s
.
Fig
u
r
e
2
s
h
o
w
s
th
e
u
s
a
g
e
o
f
in
cl
in
ed
li
n
k
s
f
o
r
ca
r
r
y
i
n
g
th
e
h
ea
v
y
lo
ad
s
.
T
h
e
in
cli
n
ed
leg
o
f
t
h
e
in
s
ec
t
co
m
es
h
an
d
y
to
m
a
n
eu
v
er
th
e
lo
ad
o
f
th
e
in
s
ec
t
b
o
d
y
.
I
n
an
o
th
er
ca
s
e,
i
n
cli
n
ed
lin
k
s
o
f
th
e
h
an
d
is
u
s
ed
to
tr
an
s
m
it
h
ig
h
f
o
r
ce
s
an
d
ac
cu
r
ate
p
o
s
itio
n
in
g
w
it
h
o
u
t
ca
u
s
i
n
g
s
tr
ai
n
to
th
e
li
n
k
s
.
Fig
u
r
e
2
.
T
h
e
u
s
ag
e
o
f
i
n
cli
n
e
d
lin
k
s
I
n
p
r
ac
tice
,
th
e
lo
ad
b
ea
r
in
g
ca
p
ab
ilit
y
ca
n
b
e
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
ed
w
i
th
i
n
cli
n
ed
lin
k
s
w
h
ic
h
ca
n
b
e
ap
p
r
ec
iated
f
r
o
m
th
e
ab
o
v
e
f
i
g
u
r
e
s
.
I
t
is
also
o
b
v
io
u
s
t
h
at
n
o
n
-
p
lan
ar
l
in
k
s
ar
e
g
o
i
n
g
to
i
n
f
lu
e
n
ce
m
a
n
y
o
th
er
ch
ar
ac
ter
is
tic
s
.
Ou
t
o
f
t
h
e
m
,
t
h
e
f
o
llo
w
i
n
g
f
ea
t
u
r
es
o
f
th
e
m
a
n
ip
u
lato
r
–
mo
men
t
o
f
in
erti
a
,
s
tiff
n
ess
,
w
o
r
ksp
a
ce
,
in
erti
a
fo
r
ce
s
an
d
ma
s
s
in
mo
tio
n
a
r
e
ad
d
r
ess
ed
in
t
h
is
ar
ticle.
T
h
e
ex
i
s
ti
n
g
m
ath
e
m
atica
l
m
o
d
el
s
f
o
r
th
e
ab
o
v
e
p
ar
am
eter
s
ar
e
r
en
d
er
ed
to
r
ef
lect
th
e
ch
an
g
es
in
th
e
m
o
d
el.
I
n
th
i
s
ar
ticle,
th
e
au
t
h
o
r
s
w
ill
b
e
r
ef
er
r
in
g
to
t
h
e
m
an
ip
u
lato
r
w
it
h
No
n
-
P
lan
ar
L
i
n
k
A
r
r
a
n
g
e
m
e
n
t
as
„
NP
L
A
m
an
ip
u
lat
o
r
‟
th
r
o
u
g
h
o
u
t
th
e
p
ap
er
,
f
o
r
s
im
p
le
u
s
a
g
e
o
f
lan
g
u
a
g
e.
Ass
u
m
in
g
c
y
li
n
d
r
ical
lin
k
s
(
with
cir
cu
lar
cr
o
s
s
s
ec
tio
n
)
f
o
r
th
e
m
an
ip
u
lato
r
leg
s
,
mo
men
t
o
f
in
erti
a
an
d
Ma
s
s
mo
men
t
o
f
in
erti
a
o
f
th
e
li
n
k
s
ar
e
d
eter
m
i
n
ed
.
C
o
n
v
en
t
io
n
al
S
tiff
n
es
s
a
n
a
lysi
s
is
u
s
u
all
y
d
o
n
e
b
y
J
ac
o
b
ian
m
et
h
o
d
[
1
2
]
w
h
ic
h
p
r
esu
m
es
t
h
e
lin
k
s
as
r
ig
id
elem
en
ts
an
d
o
n
l
y
ac
t
iv
e
j
o
in
t
s
ti
f
f
n
e
s
s
is
co
n
s
id
er
ed
[
1
3
]
.
I
n
Ma
tr
ix
s
tr
u
ct
u
r
al
an
al
y
s
i
s
[
1
4
]
,
th
e
lin
k
s
ar
e
f
le
x
ib
le
an
d
th
e
p
as
s
iv
e
j
o
in
t
s
ti
f
f
n
e
s
s
is
also
i
n
clu
d
ed
.
I
n
th
is
ar
ticle,
t
h
e
m
a
tr
ix
s
tr
u
ct
u
r
al
ap
p
r
o
ac
h
is
f
o
llo
w
ed
to
s
t
u
d
y
t
h
e
p
r
o
p
o
s
ed
m
an
ip
u
lato
r
d
esig
n
w
it
h
n
o
n
-
p
lan
ar
lin
k
s
.
W
h
ile
d
esig
n
i
n
g
a
p
ar
allel
m
an
ip
u
lato
r
f
o
r
a
p
ar
ticu
lar
ap
p
licatio
n
,
th
e
s
in
g
u
la
r
ity
-
fr
ee
w
o
r
ksp
a
ce
a
r
ea
is
o
f
m
aj
o
r
c
o
n
ce
r
n
.
Vo
id
s
in
s
id
e
th
e
w
o
r
k
s
p
ac
e
f
all
u
n
d
er
th
e
ca
teg
o
r
y
o
f
Typ
e
-
I
s
i
n
g
u
la
r
ities
.
I
t
ca
n
b
e
s
h
o
w
n
t
h
at
th
e
Typ
e
I
I
s
in
g
u
la
r
ities
o
cc
u
r
w
h
e
n
t
h
e
w
r
e
n
ch
es
ar
e
p
ar
allel
o
r
i
n
ter
s
ec
ti
n
g
at
o
n
e
co
m
m
o
n
p
o
in
t
[
1
5
]
.
Sin
ce
t
h
e
w
r
en
c
h
es
o
r
t
h
e
li
n
es
ass
o
ciate
d
w
it
h
th
e
d
i
s
tal
li
n
k
s
,
b
e
h
av
e
id
en
tical
to
t
h
e
co
n
v
e
n
tio
n
al
m
an
ip
u
lato
r
,
th
is
p
ap
er
w
ill
b
e
ad
d
r
ess
in
g
o
n
l
y
T
y
p
e
-
I
s
i
n
g
u
lar
itie
s
w
h
ile
o
p
t
i
m
izi
n
g
t
h
e
d
esi
g
n
p
ar
am
eter
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
I
n
flu
en
ce
o
f No
n
-
p
la
n
a
r
(
S
p
a
tia
l)
Lin
ks in
th
e
S
ta
tic
C
h
a
r
a
cteris
tic
s
B
eh
a
vio
r
o
f…
(
Ga
n
esh
M
.
)
153
T
h
e
d
esig
n
p
ar
a
m
eter
s
f
o
r
a
s
p
ec
if
ic
m
an
ip
u
lato
r
ar
e
o
p
ti
m
ized
.
T
h
e
m
ai
n
d
esi
g
n
p
ar
a
m
eter
o
f
in
ter
est
h
er
e
i
s
t
h
e
i
n
clin
a
tio
n
an
g
le.
Alth
o
u
g
h
i
t
ca
n
b
e
ea
s
il
y
u
n
d
er
s
to
o
d
th
at
i
n
cr
ea
s
in
g
t
h
e
i
n
cli
n
atio
n
an
g
le
i
m
p
r
o
v
es
t
h
e
lo
ad
b
ea
r
in
g
ca
p
ab
ilit
y
a
n
d
s
ti
f
f
n
e
s
s
,
b
u
t
it
m
a
y
a
f
f
ec
t
th
e
w
o
r
k
s
p
a
ce
o
r
m
a
s
s
o
f
ma
n
ip
u
la
to
r
in
m
o
tio
n
.
I
t
w
ill
b
e
o
f
th
e
r
ea
d
er
s
‟
i
n
ter
est to
k
n
o
w
th
e
ap
p
r
o
p
r
i
ate
in
clin
atio
n
an
g
le
w
h
ic
h
d
o
es
n
o
t
co
m
p
r
o
m
i
s
e
a
n
y
s
i
g
n
if
ica
n
t
f
ea
t
u
r
e
o
f
t
h
e
m
a
n
ip
u
la
to
r
.
I
n
t
h
is
ar
t
icle,
t
h
e
m
an
ip
u
lat
o
r
is
o
p
ti
m
ized
to
h
av
e
lo
w
m
a
s
s
in
m
o
tio
n
,
h
ig
h
s
ti
f
f
n
e
s
s
a
n
d
m
ax
i
m
u
m
f
o
r
ce
tr
an
s
m
i
s
s
io
n
i
n
a
p
r
escr
ib
ed
v
o
id
-
f
r
ee
w
o
r
k
s
p
ac
e
ar
ea
.
T
h
e
n
e
w
m
o
d
els
f
o
r
t
h
e
a
b
o
v
e
m
e
n
tio
n
ed
s
p
ec
i
f
ic
k
i
n
e
m
a
tic
p
ar
a
m
e
ter
s
ar
e
o
b
t
ain
ed
w
it
h
g
en
er
alize
d
R
R
co
n
f
i
g
u
r
atio
n
an
d
it
is
to
b
e
n
o
ted
th
at
t
h
is
co
n
f
i
g
u
r
atio
n
f
ea
tu
r
e
s
is
in
ea
ch
le
g
o
f
t
h
e
m
an
ip
u
lato
r
.
A
3
-
R
R
R
NP
L
A
m
an
ip
u
lato
r
is
tak
e
n
as
ca
s
e
s
tu
d
y
to
d
is
cu
s
s
th
e
r
es
u
lt
s
o
f
th
e
an
al
y
s
i
s
.
I
t
is
s
h
o
w
n
t
h
at
t
h
e
m
o
d
els
ca
n
al
s
o
b
e
d
ev
elo
p
ed
f
o
r
o
th
er
m
a
n
ip
u
lato
r
s
(
w
it
h
n
o
n
-
p
la
n
ar
lin
k
s
)
s
u
c
h
as
3
-
P
R
R
an
d
3
–
R
P
R
,
f
o
llo
w
i
n
g
th
e
m
e
th
o
d
o
lo
g
y
d
escr
ib
ed
.
T
h
e
p
r
o
p
o
s
ed
d
esig
n
is
in
tr
o
d
u
ce
d
in
s
ec
tio
n
2
w
i
th
ill
u
s
tr
a
tio
n
s
.
I
n
s
ec
tio
n
3
,
t
h
e
r
o
tatio
n
al
i
n
er
tia
(
m
ass
m
o
m
e
n
t
o
f
i
n
er
tia)
f
o
r
th
e
in
cli
n
ed
lin
k
s
i
s
o
b
tain
ed
.
Ass
u
m
in
g
th
e
li
n
k
s
to
b
e
f
lex
i
b
le,
co
m
p
u
tat
io
n
o
f
th
e
s
ti
f
f
n
es
s
m
atr
i
x
f
o
r
R
R
co
n
f
i
g
u
r
atio
n
i
s
d
o
n
e.
T
h
ese
c
o
m
p
u
tatio
n
s
ar
e
s
h
o
w
n
i
n
co
m
p
ar
i
s
o
n
w
it
h
t
h
e
co
n
v
e
n
tio
n
al
m
a
n
ip
u
la
to
r
.
Fo
r
NP
L
A
3
-
R
R
R
,
J
ac
o
b
ian
b
ase
d
s
tatic
f
o
r
ce
an
al
y
s
i
s
an
d
t
h
e
r
esu
lt
s
o
f
s
ti
f
f
n
es
s
an
al
y
s
is
i
s
d
is
cu
s
s
ed
in
s
ec
ti
o
n
4
.
Fin
all
y
an
o
p
ti
m
ized
in
cli
n
atio
n
a
n
g
le
i
s
o
b
tain
ed
f
o
r
th
e
No
n
-
p
la
n
ar
(
s
p
atial)
lin
k
s
o
f
3
-
R
R
R
.
2.
P
RO
P
O
SE
D
DE
SI
G
N
O
F
N
O
N
-
P
L
ANAR
L
I
NK
S
I
n
th
e
p
r
o
p
o
s
ed
d
esig
n
,
th
e
li
n
k
s
ar
e
n
o
t
in
a
s
in
g
le
h
o
r
izo
n
t
al
p
lan
e.
T
h
e
lin
k
s
ar
e
m
ad
e
n
o
n
-
p
la
n
ar
b
y
m
a
k
i
n
g
it
in
c
lin
ed
ab
o
u
t
X
-
Y
p
la
n
e.
T
h
is
r
esu
lts
in
an
in
cr
ea
s
ed
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
b
ase
p
latf
o
r
m
a
n
d
m
o
b
ile
p
lat
f
o
r
m
.
T
h
e
p
r
in
cip
le
id
ea
o
f
elev
atin
g
o
n
e
o
f
t
h
e
lin
k
s
is
s
h
o
w
n
in
F
ig
u
r
e
3
.
T
h
e
f
ir
s
t
lin
k
L
1
o
f
th
is
m
ec
h
a
n
i
s
m
is
r
o
tated
b
y
θ1
d
eg
r
ee
s
ab
o
u
t
Z
-
ax
is
.
B
y
t
h
is
L
1
is
s
h
i
f
ted
to
L
i
′
i
n
XY
p
lan
e
a
s
s
h
o
w
n
in
Fig
u
r
e
3
.
I
t
is
ag
ain
r
o
tated
δ1
d
eg
r
ee
s
,
b
u
t
th
is
ti
m
e
it
i
s
a
b
o
u
t
Y
ax
is
o
f
L
1
′.
T
h
u
s
L
1
′
is
s
h
i
f
ted
to
L
1
′′
.
T
h
e
s
a
m
e
p
r
o
ce
d
u
r
e
is
r
ep
ea
ted
f
o
r
th
e
o
th
er
li
n
k
s
o
f
t
h
e
le
g
.
Fo
r
s
y
m
m
etr
y
p
u
r
p
o
s
e
δ
is
k
ep
t
co
n
s
ta
n
t
f
o
r
all
th
e
lin
k
s
.
Dep
e
n
d
in
g
o
n
th
e
r
o
tatio
n
o
f
li
n
k
s
ab
o
u
t it
s
Y
-
ax
is
(
δ
1
)
,
th
e
h
ei
g
h
t o
f
th
e
to
p
p
latf
o
r
m
an
d
t
h
e
r
ad
i
u
s
o
f
th
e
to
p
p
latf
o
r
m
ca
n
b
e
v
ar
ied
.
T
h
is
is
d
ec
id
ed
b
ased
o
n
r
eq
u
ir
em
e
n
t
o
f
k
i
n
e
m
at
ics
p
ar
a
m
eter
s
s
u
ch
a
s
w
o
r
k
s
p
ac
e,
s
ti
f
f
n
es
s
an
d
f
o
r
ce
tr
an
s
m
is
s
io
n
.
Fig
u
r
e
3
.
P
r
in
cip
le
o
f
I
n
clin
ati
o
n
I
f
L
1
′
′
is
p
r
o
j
ec
ted
u
n
to
th
e
b
ase
p
lan
e
,
its
len
g
t
h
/
m
ag
n
it
u
d
e
w
il
l
b
e
L
1
′′
co
s
δ
1
as
s
h
o
w
n
i
n
F
ig
u
r
e.
3
.
I
f
th
e
li
n
k
L
1
′′
is
r
o
tated
an
y
f
u
r
th
er
ab
o
u
t
Z
a
x
i
s
,
i.e
.
w
it
h
a
n
y
c
h
an
g
e
i
n
t
h
e
v
al
u
e
o
f
θ
1
,
t
h
e
d
is
ta
n
ce
(
L
1
′′
co
s
δ
1
)
r
em
a
in
s
u
n
ch
a
n
g
ed
.
Hen
c
e,
t
h
e
k
i
n
e
m
at
ics
f
o
r
th
is
m
o
d
el
w
ill
b
e
r
ea
lize
d
o
n
a
p
r
o
j
ec
ted
h
o
r
izo
n
tal
p
lan
e
w
it
h
t
h
e
li
n
k
le
n
g
th
s
b
ein
g
t
h
e
h
o
r
izo
n
tal
d
is
ta
n
ce
b
et
w
ee
n
a
n
y
t
w
o
j
o
in
ts
.
T
h
e
ab
o
v
e
m
e
n
tio
n
ed
p
r
o
ce
d
u
r
e
is
ap
p
lied
f
o
r
all
t
h
e
leg
s
.
Fo
r
t
h
e
p
r
o
p
o
s
ed
NP
L
ar
r
an
g
e
m
e
n
t,
alth
o
u
g
h
t
h
e
li
n
k
s
ar
e
m
ad
e
in
cli
n
ed
to
t
h
e
h
o
r
izo
n
t
al
p
la
n
e
,
t
h
e
r
o
tar
y
(
o
r
p
r
is
m
atic)
j
o
in
ts
ax
e
s
r
e
m
ai
n
p
er
p
en
d
icu
lar
(
o
r
p
ar
allel
as
th
e
ca
s
e
m
a
y
b
e)
to
th
e
p
lan
e
o
f
t
h
e
b
ase
p
latf
o
r
m
,
w
h
ic
h
r
etai
n
s
th
e
p
lan
ar
m
o
tio
n
o
f
t
h
e
en
d
-
e
f
f
ec
ter
.
T
h
e
co
n
ce
iv
ed
p
r
o
p
o
s
al
f
o
r
th
e
f
o
llo
w
i
n
g
co
n
f
ig
u
r
atio
n
s
3
R
R
R
,
3
-
P
R
R
a
n
d
3
-
R
R
P
is
ill
u
s
tr
ated
in
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
5
1
–
16
7
154
T
ab
le
1
.
Sh
o
w
s
t
h
e
Sc
h
e
m
a
tic
o
f
NP
L
A
in
I
n
d
iv
id
u
al
L
eg
o
f
P
lan
ar
Ma
n
ip
u
lato
r
s
P
l
a
n
a
r
M
a
n
i
p
u
l
a
t
o
r
s
S
i
n
g
l
e
L
e
g
-
C
o
n
v
e
n
t
i
o
n
a
l
S
i
n
g
l
e
l
e
g
-
N
P
L
A
A
r
r
a
n
g
e
me
n
t
3.
R
E
S
E
ARCH
M
E
T
H
O
D
Ne
w
m
a
th
e
m
atica
l
m
o
d
el
s
ar
e
r
eq
u
ir
ed
f
o
r
s
t
u
d
y
i
n
g
t
h
e
i
n
f
l
u
en
ce
o
f
t
h
e
in
cl
in
atio
n
a
n
g
le
in
r
elatio
n
to
th
e
f
o
llo
w
i
n
g
p
ar
a
m
e
ter
s
-
m
o
m
e
n
t o
f
i
n
er
tia,
s
t
if
f
n
es
s
,
s
t
atic
f
o
r
ce
s
,
m
a
s
s
i
n
m
o
tio
n
an
d
w
o
r
k
s
p
ac
e
.
3
.
1
.
F
o
r
m
ula
t
io
n o
f
I
nert
ia
T
ens
o
r
Ass
u
m
in
g
c
y
lin
d
r
ical
li
n
k
s
(
w
it
h
cir
cu
lar
cr
o
s
s
s
ec
tio
n
)
f
o
r
th
e
m
a
n
ip
u
la
to
r
leg
s
,
M
o
m
e
n
t
o
f
I
n
er
tia(
MO
I
)
an
d
Ma
s
s
m
o
m
e
n
t
o
f
in
er
t
ia
f
o
r
th
e
li
n
k
s
ar
e
d
eter
m
in
ed
.
L
et
t
h
e
in
c
lin
ed
l
in
k
b
e
o
f
r
ad
iu
s
R
an
d
len
g
t
h
L
i
n
X
Z
-
p
lan
e.
I
n
o
r
d
er
to
d
eter
m
in
e
t
h
e
m
o
m
en
t
o
f
i
n
er
tia
(
s
ec
o
n
d
m
o
m
en
t
o
f
ar
ea
)
ab
o
u
t
th
e
Z
-
ax
is
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
4
,
th
e
cr
o
s
s
s
ec
tio
n
ar
ea
o
f
t
h
e
i
n
cli
n
ed
lin
k
i
n
t
h
e
X
-
Y
p
la
n
e
is
co
n
s
id
er
ed
.
T
h
e
cr
o
s
s
s
ec
tio
n
ar
ea
is
a
n
e
llip
s
e
w
i
th
m
i
n
o
r
d
ia
m
eter
eq
u
als
R
a
n
d
m
aj
o
r
d
iam
e
ter
is
R
/
co
s
δ,
as
th
e
lin
k
is
in
cl
in
ed
ab
o
u
t a
n
an
g
le
δ
.
Fig
u
r
e
4.
A
li
n
k
i
s
s
h
o
w
n
i
n
X
Z
p
lan
e
w
i
th
a
n
in
c
lin
at
io
n
o
f
δ
° ab
o
u
t X
ax
i
s
.
T
h
e
lin
k
h
as
an
ellip
tical
cr
o
s
s
s
ec
tio
n
in
XY
p
lan
e
.
T
h
is
ell
ip
tical
cr
o
s
s
s
ec
tio
n
ar
ea
is
u
s
ed
f
o
r
co
m
p
u
ti
n
g
t
h
e
m
o
m
e
n
t o
f
in
er
tia
R
R
R
R
R
P
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
I
n
flu
en
ce
o
f No
n
-
p
la
n
a
r
(
S
p
a
tia
l)
Lin
ks in
th
e
S
ta
tic
C
h
a
r
a
cteris
tic
s
B
eh
a
vio
r
o
f…
(
Ga
n
esh
M
.
)
155
Ass
u
m
in
g
t
h
e
li
n
k
as a
3
D
s
p
r
in
g
m
o
d
el,
th
e
co
m
p
lia
n
ce
m
a
tr
ix
f
o
r
th
e
l
in
k
ele
m
en
t
is
(
1
)
z
z
y
y
y
y
z
z
M
I
L
I
I
L
I
J
G
L
E
I
L
I
I
L
I
A
L
E
C
/
0
0
0
2
/
1
0
0
/
0
2
/
1
0
0
0
0
.
.
0
0
0
0
2
/
1
0
.
3
/
1
0
0
2
/
1
0
0
0
3
/
1
0
0
0
0
0
0
/
1
(
1
)
I
n
t
h
e
m
atr
ix
ele
m
en
ts
,
cr
o
s
s
s
ec
tio
n
ar
ea
A
a
n
d
i
n
er
tia
I
will
b
e
co
r
r
esp
o
n
d
in
g
to
t
h
e
el
li
p
tical
cr
o
s
s
s
ec
tio
n
an
d
th
e
y
ar
e
g
i
v
en
b
y
e
q
u
atio
n
(
2
)
an
d
(
3
)
r
esp
ec
tiv
el
y
A
r
ea
o
f
cr
o
s
s
s
ec
tio
n
c
o
s
r
r
A
(
2
)
P
o
lar
m
o
m
e
n
t o
f
i
n
er
tia
x
y
z
I
I
I
3
4
c
o
s
1
c
o
s
1
4
r
(
3
)
Du
e
to
th
e
p
r
esen
ce
o
f
co
s
δ
ter
m
in
e
q
u
a
tio
n
2
an
d
3
,
m
o
m
e
n
t o
f
i
n
er
tia
in
cr
ea
s
es
n
o
n
li
n
ea
r
l
y
w
it
h
δ
.
W
ith
th
e
r
is
e
i
n
m
o
m
en
t o
f
i
n
er
tia,
th
e
co
m
p
lia
n
ce
o
f
t
h
e
lin
k
s
i
s
v
er
y
m
u
ch
r
ed
u
ce
d
i
n
co
m
p
ar
is
o
n
to
th
e
lin
k
s
o
f
p
lan
ar
leg
s
.
Ma
s
s
Mo
men
t o
f in
erti
a
T
h
e
m
ass
m
o
m
e
n
t
o
f
in
er
tia
o
f
th
e
li
n
k
s
is
v
er
y
m
u
c
h
r
ed
u
ce
d
as
t
h
e
cr
o
s
s
s
ec
tio
n
ar
ea
ab
o
u
t
t
h
e
v
er
tical
a
x
is
h
a
s
c
h
a
n
g
ed
.
T
h
i
s
w
ill
i
n
f
lu
e
n
ce
t
h
e
a
cc
u
r
ate
m
o
d
eli
n
g
o
f
le
g
d
y
n
a
m
ic
s
.
T
h
e
m
o
m
en
t
o
f
in
er
t
ia
o
f
th
e
t
h
i
n
ellip
tical
d
is
c
s
h
o
wn
in
F
ig
u
r
e
5
ab
o
u
t th
e
ax
is
AB
is
g
iv
e
n
as
(
4
)
2
4
1
Ma
I
AB
w
h
er
e
δ
R
a
c
o
s
(
4
)
Fig
u
r
e
5
.
T
h
in
ellip
tical
d
is
c
r
eg
io
n
o
f
i
n
cli
n
ed
li
n
k
T
o
ca
lcu
late
th
e
Mo
m
en
t o
f
I
n
er
t
ia
ab
o
u
t X
-
ax
is
p
ass
in
g
t
h
r
o
u
g
h
o
n
e
e
n
d
o
f
th
e
li
n
k
,
p
ar
allel
ax
is
t
h
eo
r
e
m
i
s
ap
p
lied
(5
-
6
)
2
.
x
dm
I
I
AB
xx
W
h
e
r
e
dx
L
M
dm
c
o
s
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
5
1
–
16
7
156
2
2
2
2
c
o
s
3
1
c
o
s
4
1
ML
MR
I
xx
(
6
)
Si
m
i
lar
to
th
e
b
e
n
d
in
g
m
o
m
en
t
i
n
er
tia
as
d
is
cu
s
s
ed
ab
o
v
e,
th
e
p
r
esen
ce
o
f
δ
ter
m
s
i
g
n
i
f
ica
n
tl
y
in
f
lu
e
n
ce
s
th
e
m
a
s
s
m
o
m
e
n
t
o
f
in
er
tia.
B
y
an
al
y
zi
n
g
E
q
n
6
,
it
ca
n
b
e
u
n
d
er
s
to
o
d
th
at
t
h
e
v
a
lu
e
o
f
t
h
e
f
ir
s
t
ter
m
r
aise
s
th
e
in
er
tia
v
al
u
e
w
h
er
ea
s
t
h
e
s
ec
o
n
d
ter
m
lo
wer
s
th
e
i
n
er
tia
v
alu
e,
d
u
e
to
th
e
o
cc
u
r
r
en
ce
o
f
s
in
δ
ter
m
.
Sin
ce
t
h
e
len
g
t
h
to
d
ia
m
eter
r
atio
is
s
ig
n
i
f
ican
tl
y
h
i
g
h
,
t
h
e
in
f
l
u
en
ce
o
f
t
h
e
f
ir
s
t
t
er
m
is
v
er
y
le
s
s
an
d
o
v
er
all
in
er
tia
f
ac
to
r
is
r
ed
u
c
ed
.
I
t
ca
n
b
e
n
o
ted
th
at
t
h
e
m
as
s
m
o
m
e
n
t
o
f
i
n
er
tia
i
s
th
e
r
o
tatio
n
al
in
er
tia
,
w
h
ic
h
w
h
e
n
r
ed
u
ce
d
is
m
u
c
h
f
av
o
r
ab
le
f
o
r
th
e
r
o
tar
y
m
o
to
r
ac
tu
atio
n
.
3
.
2
.
Stif
f
nes
s
m
o
deli
ng
o
f
RR
co
nfig
ura
t
io
n
A
s
m
e
n
tio
n
ed
i
n
th
e
i
n
tr
o
d
u
ctio
n
s
ec
tio
n
,
th
e
m
atr
ix
s
tr
u
ctu
r
al
ap
p
r
o
ac
h
is
ad
o
p
ted
to
s
tu
d
y
t
h
e
s
tiff
n
es
s
o
f
n
o
n
-
p
lan
ar
lin
k
s
.
W
ith
th
i
s
m
o
d
elin
g
ap
p
r
o
ac
h
,
t
h
e
i
n
er
tia
p
ar
a
m
eter
s
m
o
d
if
ied
i
n
t
h
e
ab
o
v
e
s
ec
tio
n
ar
e
s
u
b
s
tit
u
ted
i
n
t
h
e
c
o
m
p
lia
n
ce
m
atr
i
x
o
f
li
n
k
ele
m
en
ts
.
T
h
e
i
n
f
l
u
en
ce
is
s
t
u
d
ied
i
n
co
m
p
ar
is
o
n
w
i
th
th
e
p
lan
ar
p
ar
allel
m
a
n
ip
u
lato
r
.
T
h
e
f
o
llo
w
in
g
m
et
h
o
d
o
lo
g
y
a
s
p
r
o
p
o
s
ed
b
y
Na
g
ai
a
n
d
L
i
u
[
1
7
]
d
eter
m
in
e
s
t
h
e
s
ti
f
f
n
es
s
m
o
d
el
f
o
r
a
p
ar
allel
m
ec
h
a
n
is
m
.
I
n
t
h
is
m
e
th
o
d
th
e
p
ar
allel
m
ec
h
a
n
i
s
m
i
s
s
u
b
-
d
iv
id
ed
in
to
k
in
e
m
atic
ch
ain
s
r
ep
r
esen
ti
n
g
ea
ch
le
g
.
E
a
c
h
ch
a
in
is
f
u
r
t
h
e
r
d
iv
id
ed
in
to
m
ec
h
a
n
ical
m
o
d
u
les
i
n
w
h
ic
h
th
e
m
o
d
u
le
r
e
p
r
esen
ts
a
j
o
in
t
a
n
d
its
ass
o
ciate
d
li
n
k
[
a]
.
T
h
e
s
tiff
n
e
s
s
o
f
th
e
k
i
n
e
m
at
ic
ch
ai
n
i
s
o
b
tain
ed
b
y
i
ter
ativ
el
y
ad
d
in
g
ea
c
h
m
ec
h
a
n
ical
m
o
d
u
le.
Step
b
y
s
tep
p
r
o
ce
d
u
r
e
is
g
i
v
en
b
elo
w
an
d
ill
u
s
tr
ate
d
in
F
ig
u
r
e
6
.
a.
Ste
p
1
L
i
n
k
s
ar
e
ass
u
m
ed
f
le
x
ib
le.
A
2
D
o
r
3
D
s
p
r
in
g
m
o
d
e
l
is
u
s
ed
to
d
eter
m
in
e
th
e
co
m
p
lian
ce
f
o
r
t
h
e
lin
k
.
b.
Ste
p
2
J
o
i
n
t c
o
m
p
lia
n
ce
is
d
et
er
m
in
ed
b
y
t
h
e
co
n
v
en
tio
n
al
m
et
h
o
d
.
c.
T
h
e
lin
k
co
m
p
lian
ce
a
n
d
t
h
e
j
o
in
t
co
m
p
lia
n
ce
to
g
e
th
er
r
e
p
r
esen
t
th
e
co
m
p
lian
ce
o
f
a
m
ec
h
an
ical
m
o
d
u
le.
d.
Ste
p
3
T
h
e
co
m
p
lia
n
ce
f
o
r
th
e
m
ec
h
a
n
ical
m
o
d
u
le
i
s
tr
an
s
f
o
r
m
ed
to
g
lo
b
al
r
ef
er
e
n
ce
b
y
s
u
i
tab
le
tr
an
s
f
o
r
m
atio
n
s
.
e.
Ste
p
4
S
tep
s
1
to
3
ar
e
r
ep
ea
te
d
f
o
r
ea
ch
m
o
d
u
le.
(
E
ac
h
j
o
in
t
an
d
its
ass
o
ciate
l
in
k
)
f.
Ste
p
5
T
h
e
c
o
m
p
lia
n
ce
m
atr
i
x
h
en
ce
o
b
tain
ed
f
o
r
ea
ch
m
o
d
u
le
is
cu
m
u
lati
v
el
y
ad
d
ed
t
o
g
i
v
e
t
h
e
to
tal
co
m
p
lia
n
ce
o
f
t
h
e
k
in
e
m
atic
c
h
ain
.
T
h
e
in
v
er
s
e
o
f
t
h
e
to
tal
c
o
m
p
lia
n
ce
g
iv
e
s
t
h
e
s
ti
f
f
n
e
s
s
o
f
ea
ch
ch
a
in
.
[a]
Fo
r
a
n
th
j
o
in
t,
n
-
1
th
li
n
k
d
en
o
tes t
h
e
ass
o
ciate
d
k
in
e
m
at
ic
ch
ain
.
Fig
u
r
e
6
.
s
h
o
w
s
t
h
e
f
lo
w
c
h
ar
t
o
f
m
et
h
o
d
o
lo
g
y
i
n
d
eter
m
i
n
in
g
th
e
s
ti
f
f
n
es
s
o
f
a
k
in
e
m
atic
c
h
ain
T
h
e
s
tiff
n
es
s
a
n
al
y
s
i
s
is
ca
r
r
ie
d
f
o
r
R
R
co
n
f
i
g
u
r
atio
n
o
f
th
e
m
an
ip
u
lato
r
a
n
d
e
x
ten
d
ed
f
o
r
th
e
o
t
h
er
leg
s
.
T
h
e
s
t
u
d
y
is
d
o
n
e
i
n
co
m
p
ar
i
s
o
n
w
i
th
th
e
p
la
n
ar
li
n
k
s
.
Fo
r
p
lan
ar
lin
k
s
,
th
e
m
o
d
e
lin
g
is
b
ased
o
n
2
d
i
m
en
s
io
n
al
ap
p
r
o
ac
h
,
w
h
er
e
as
f
o
r
n
o
n
-
p
la
n
ar
lin
k
s
t
h
e
m
o
d
elin
g
is
b
y
a
3
-
d
i
m
e
n
s
io
n
a
l
ap
p
r
o
ac
h
.
S
tiff
n
e
ss
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
I
n
flu
en
ce
o
f No
n
-
p
la
n
a
r
(
S
p
a
tia
l)
Lin
ks in
th
e
S
ta
tic
C
h
a
r
a
cteris
tic
s
B
eh
a
vio
r
o
f…
(
Ga
n
esh
M
.
)
157
11
10
11
J
L
T
C
C
C
C
11
10
11
J
L
T
C
C
C
C
mo
d
el
fo
r
R
R
c
o
n
fig
u
r
a
tio
n
-
F
ir
s
t
Mech
a
n
ica
l
mo
d
u
le
(
1
s
t
jo
in
t
a
n
d
its
p
r
ev
io
u
s
lin
k)
Sin
ce
th
e
f
ir
s
t
j
o
in
t
is
an
ac
ti
v
e
j
o
in
t,
th
e
co
m
p
lian
c
e
f
o
r
th
e
j
o
in
t
11
J
C
is
tak
e
n
a
s
)
,
0
,
0
(
1
11
S
diag
.
T
h
e
ac
ti
v
e
j
o
in
t
w
it
h
f
ir
s
t
li
n
k
(
L
eg
-
1)
co
n
v
e
n
tio
n
al
d
esi
g
n
a
n
d
m
o
d
if
ied
d
esig
n
as
s
h
o
w
n
i
n
F
i
g
u
r
e
s
7
a
an
d
7
b
.
C
o
n
s
id
er
in
g
th
e
f
ir
s
t
lin
k
o
f
L
e
g
-
1
(
7
a)
w
h
er
e
11
C
C
d
en
o
tes
th
e
c
u
m
u
lat
iv
e
co
m
p
lia
n
ce
(
1
st
jo
in
t
an
d
0
th
tr
an
s
f
o
r
m
ed
lin
k
)
.
R
ef
er
ap
p
en
d
ix
A
f
o
r
th
e
n
o
tatio
n
Fig
u
r
e
7
a.
T
h
e
ac
tiv
e
j
o
in
t
w
it
h
f
ir
s
t li
n
k
(
L
eg
-
1)
-
C
o
n
v
e
n
tio
n
al
d
esi
g
n
C
o
n
s
id
er
in
g
t
h
e
f
ir
s
t li
n
k
o
f
L
eg
-
1
(
7
b
)
Fig
u
r
e
7
b
.
T
h
e
ac
tiv
e
j
o
in
t
w
it
h
f
ir
s
t li
n
k
(
L
eg
-
1
)
-
Mo
d
if
ied
d
esig
n
T
h
e
tr
an
s
f
o
r
m
ed
co
m
p
lia
n
ce
11
C
T
C
f
o
r
th
is
m
ec
h
a
n
ical
m
o
d
u
le
(
1
s
t
jo
in
t
an
d
p
r
ev
io
u
s
li
n
k
to
g
eth
er
)
is
co
m
p
u
ted
b
y
e
q
u
atio
n
(
8
)
as sh
o
w
n
b
elo
w
(
8
a)
(
8
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
5
1
–
16
7
158
S
ec
o
n
d
Mech
a
n
ica
l m
o
d
u
le
(
2
n
d
jo
in
t
a
n
d
its
p
r
ev
io
u
s
1
s
t li
n
k)
L
i
n
k
s
ar
e
a
s
s
u
m
ed
n
o
t
to
b
e
r
ig
id
.
So
co
m
p
lian
ce
f
o
r
th
e
li
n
k
s
i
s
o
b
tain
ed
b
y
m
ater
ial
s
s
cien
ce
–
Stru
ct
u
r
al
an
al
y
s
is
ap
p
r
o
ac
h
.
A
2
D
s
p
r
i
n
g
m
o
d
el
i
s
as
s
u
m
ed
f
o
r
th
i
s
ap
p
r
o
ac
h
e
q
u
atio
n
(
9
a)
r
ep
r
esen
ts
th
e
co
m
p
lia
n
ce
co
m
p
o
n
e
n
t
s
I
L
I
L
I
L
I
L
A
L
E
C
L
2
0
2
3
0
0
0
1
2
2
3
(
9
a)
A
3
D
s
p
r
in
g
m
o
d
el
i
s
as
s
u
m
e
d
f
o
r
th
e
m
o
d
i
f
ied
d
esi
g
n
to
i
n
co
r
p
o
r
ate
all
d
ef
lectio
n
s
alo
n
g
a
n
d
ar
o
u
n
d
X,
Y
an
d
Z
ax
e
s
o
f
th
e
C
ar
tesi
a
n
s
p
ac
e
in
eq
u
atio
n
9
b
.
T
h
e
co
m
p
lian
ce
m
atr
i
x
is
g
i
v
en
b
y
e
q
u
a
t
io
n
(
1
)
(
S
ec
tio
n
3
)
.
T
h
e
ex
p
r
ess
io
n
s
o
f
th
e
co
m
p
li
an
ce
m
a
tr
ix
ele
m
e
n
ts
ar
e
m
o
d
if
ied
an
d
t
h
e
y
ar
e
ill
u
s
tr
ated
in
s
ec
tio
n
3
.
1
.
T
h
is
m
ak
e
s
an
i
m
p
ac
t i
n
th
e
s
ti
f
f
n
e
s
s
m
atr
ix
ca
lc
u
latio
n
s
M
L
C
C
(
9
b
)
T
h
e
co
m
p
lian
ce
m
atr
ix
i
n
eq
u
atio
n
.
(
9
)
r
e
p
r
esen
ts
th
e
lo
ca
l
s
tiff
n
es
s
m
atr
i
x
.
I
t
h
as
to
b
e
tr
an
s
f
o
r
m
ed
g
lo
b
all
y
b
y
r
o
tatio
n
a
l tr
an
s
f
o
r
m
a
tio
n
a
s
s
h
o
w
n
b
elo
w
i
n
e
q
u
at
io
n
.
(
1
0
)
.
1
0
0
0
0
1
1
1
1
1
C
S
S
C
R
R
o
tatio
n
ab
o
u
t
Z
ax
i
s
(
1
0
a)
1
0
0
0
0
1
1
1
1
1
C
S
S
C
R
1
1
1
1
0
0
1
0
0
C
S
S
C
R
o
tatio
n
ab
o
u
t
Z
ax
i
s
R
o
tatio
n
ab
o
u
t Y
ax
i
s
(
1
0
b
)
Fo
r
th
e
co
n
v
e
n
tio
n
al
p
la
n
ar
m
an
ip
u
lato
r
,
t
h
e
f
o
llo
w
i
n
g
e
q
u
atio
n
(
1
1
a)
d
eter
m
in
e
s
t
h
e
tr
an
s
f
o
r
m
ed
li
n
k
co
m
p
lia
n
ce
.
T
R
C
R
C
L
L
T
1
1
11
(
1
1
a)
Fo
r
th
e
m
o
d
i
f
ied
NP
L
A
d
e
s
ig
n
,
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
(
1
1
b
)
d
eter
m
i
n
es
t
h
e
tr
a
n
s
f
o
r
m
ed
lin
k
co
m
p
l
ian
ce
.
eq
u
atio
n
(
9
b
)
an
d
(
1
0
b
)
ar
e
s
u
b
s
titu
ted
i
n
eq
u
atio
n
(
1
1
b
)
1
1
11
0
0
R
R
C
L
T
C
L
T
T
R
R
1
1
0
0
(
1
1
b
)
T
h
e
to
tal
s
ti
f
f
n
es
s
12
C
C
is
co
m
b
i
n
at
io
n
o
f
2
n
d
j
o
in
t
s
ti
f
f
n
e
s
s
an
d
1
s
t
lin
k
s
ti
f
f
n
e
s
s
.
S
in
ce
th
e
s
e
co
n
d
j
o
in
t
is
a
p
ass
iv
e
j
o
in
t,
its
co
m
p
lian
ce
12
J
C
is
n
eg
lecte
d
.
T
h
u
s
(
1
2
)
,
12
11
12
J
L
T
C
C
C
C
(
1
2
)
A
p
p
l
y
in
g
t
h
e
s
a
m
e
m
et
h
o
d
o
f
tr
an
s
f
o
r
m
atio
n
as d
o
n
e
in
e
q
u
atio
n
(
8
)
,
th
e
f
o
llo
w
in
g
e
q
u
at
i
o
n
(
1
3
)
is
o
b
tain
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
I
n
flu
en
ce
o
f No
n
-
p
la
n
a
r
(
S
p
a
tia
l)
Lin
ks in
th
e
S
ta
tic
C
h
a
r
a
cteris
tic
s
B
eh
a
vio
r
o
f…
(
Ga
n
esh
M
.
)
159
1
0
]
[
12
T
ij
ij
B
ij
B
C
T
P
R
R
C
12
C
C
1
]
[
0
T
ij
ij
B
ij
B
P
R
R
(
1
3
)
Th
ir
d
Mech
a
n
ica
l m
o
d
u
le
(
3
r
d
jo
in
t a
n
d
its
p
r
ev
io
u
s
2
n
d
lin
k)
T
h
e
tr
an
s
f
o
r
m
ed
lin
k
co
m
p
li
an
ce
is
r
ep
ea
ted
f
o
r
s
ec
o
n
d
lin
k
o
f
leg
1
.
T
h
e
s
am
e
s
tep
s
ar
e
r
e
p
ea
ted
.
T
h
e
g
en
er
alize
d
l
in
k
le
n
g
th
L
w
ill
b
e
eq
u
iv
ale
n
t
to
l
d
i
n
t
h
e
co
m
p
lian
ce
m
a
tr
ix
.
T
h
e
r
o
tatio
n
m
atr
i
x
R
2
w
i
ll
h
av
e
θ
2
.
Fo
r
s
y
m
m
etr
y
p
u
r
p
o
s
e
δ
2
is
tak
en
δ
1
F
ig
u
r
e
8
.
Fig
u
r
e
8
.
T
h
ir
d
Me
ch
an
ical
m
o
d
u
le
o
f
m
o
d
if
ied
d
esi
g
n
No
w
,
co
n
s
id
er
in
g
th
e
t
h
ir
d
j
o
i
n
t a
s
p
ass
iv
e,
t
h
e
f
o
llo
w
i
n
g
e
q
u
atio
n
(
1
4
)
is
o
b
tain
ed
.
13
12
13
J
L
T
C
C
C
C
(
1
4
)
R
ep
ea
tin
g
t
h
e
s
a
m
e
tr
an
s
f
o
r
m
atio
n
u
s
ed
in
e
q
u
atio
n
(
8
)
as f
o
llo
w
(
1
5
)
1
0
]
[
13
T
ij
ij
B
ij
B
C
T
P
R
R
C
13
C
C
1
]
[
0
T
ij
ij
B
ij
B
P
R
R
(
1
5
)
A
d
d
in
g
e
q
u
atio
ns
(
8
)
,
(
1
3
)
an
d
(
1
5
)
,
th
e
to
tal
s
tiff
n
ess
o
f
a
ch
ain
o
f
R
R
R
i
s
d
eter
m
i
n
ed
as
g
iv
e
n
b
elo
w
(
1
6
)
.
13
12
11
1
C
T
C
T
C
T
C
C
C
C
(
1
6
)
T
ak
in
g
i
n
v
er
s
e
o
f
e
q
u
atio
n
(
1
6
)
,
th
e
s
tiff
n
es
s
o
f
o
n
e
le
g
is
o
b
tain
ed
.
3
.
3
.
A
c
a
s
e
s
t
ud
y
-
3
-
RRR
m
a
nip
ula
t
o
r
An
i
n
itial
p
r
o
to
t
y
p
e
o
f
3
-
R
R
R
p
lan
ar
m
a
n
ip
u
lato
r
is
f
ab
r
i
c
ated
f
o
r
w
it
h
n
o
n
-
p
la
n
ar
li
n
k
s
as
s
h
o
wn
F
ig
u
r
e
9
.
I
n
o
r
d
er
t
o
h
av
e
a
s
i
m
p
li
f
ied
k
i
n
e
m
atics,
d
i
f
f
er
en
t
g
eo
m
etr
ic
p
ar
a
m
e
te
r
s
c
h
o
s
en
ar
e
as
f
o
llo
w
s
.
T
h
e
k
in
e
m
at
ics
is
d
ec
id
ed
f
o
r
a
li
n
k
le
n
g
t
h
o
f
1
0
0
m
m
a
n
d
m
o
b
ile
p
latf
o
r
m
s
ize
o
f
18
0
m
m
.
I
n
s
u
c
h
ca
s
e,
t
h
e
ac
tu
al
li
n
k
le
n
g
t
h
w
ill b
e
L
=
100/
co
s
δ
1
T
h
e
h
eig
h
t
o
f
t
h
e
m
o
b
ile
p
la
tf
o
r
m
f
r
o
m
t
h
e
b
ase
i
s
c
h
o
s
e
n
as
2
5
0
m
m
.
So
ea
c
h
li
n
k
h
as
to
b
e
elev
ated
1
2
5
m
m
,
i
f
t
h
e
e
x
p
e
cted
p
r
o
j
ec
tio
n
to
b
e
s
a
m
e
f
o
r
ea
ch
o
f
t
h
e
li
n
k
s
.
He
n
ce
t
h
e
an
g
le
o
f
ele
v
atio
n
b
ec
o
m
e
s
ta
n
δ
1
= 1
2
5
/1
0
0
δ
1
=
5
1
.
3
2
°
Fo
r
ea
s
e
in
m
a
n
u
f
ac
tu
r
i
n
g
,
δ i
s
tak
e
n
as 5
0
°
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
5
1
–
16
7
160
Fig
u
r
e
9
.
C
o
n
v
e
n
tio
n
al
3
-
R
R
R
p
lan
ar
r
o
b
o
t[
1
5
]
an
d
th
e
p
r
o
p
o
s
ed
m
a
n
ip
u
la
to
r
p
r
o
to
ty
p
e[
1
9
]
3
.
3
.
1
J
a
co
bia
n Ana
ly
s
is
o
f
3
-
RRR
NP
L
A
M
a
nip
ula
t
o
r
Usi
n
g
th
e
p
r
in
cip
le
o
f
Scr
e
w
th
eo
r
y
,
f
o
r
ce
j
ac
o
b
ian
is
o
b
tai
n
ed
f
o
r
3
-
R
R
R
p
lan
ar
m
a
n
ip
u
l
ato
r
w
i
t
h
th
e
n
o
n
-
p
lan
ar
li
n
k
s
.
T
h
is
j
ac
o
b
ian
i
s
r
eq
u
ir
ed
f
o
r
a
n
al
y
zin
g
t
h
e
s
tatic
f
o
r
ce
s
i
n
c
o
m
p
ar
is
o
n
w
it
h
t
h
e
co
n
v
e
n
tio
n
al
p
lan
ar
m
an
ip
u
l
ato
r
.
T
w
is
t
a
n
n
i
h
ilato
r
s
ar
e
u
s
ed
f
o
r
eli
m
in
a
tio
n
o
f
t
h
e
i
d
le
v
ar
iab
les
i
n
t
h
e
k
in
e
m
at
ic
r
elatio
n
s
[
1
8
]
.
T
h
e
E
n
d
-
e
f
f
ec
to
r
s
t
w
is
t i
s
li
n
ea
r
l
y
r
e
lated
to
th
e
j
o
in
t
-
r
at
e
v
ec
to
r
,
b
y
(
1
7
)
t
J
w
h
er
e
J
is
th
e
s
cr
e
w
b
ased
Ja
co
b
ia
n
ma
tr
ix,
o
f
th
e
m
an
ip
u
lat
o
r
u
n
d
er
s
tu
d
y
.
P
w
t
r
e
r
e
r
e
e
e
e
J
i
i
i
,
,
3
2
1
3
3
2
2
1
1
3
2
1
(
1
7
)
w
h
er
e
r
i
is
th
e
v
ec
to
r
d
ir
ec
ted
f
r
o
m
i
th
j
o
in
t
to
e
n
d
–
ef
f
ec
t
o
r
s
h
o
w
n
as
in
F
i
g
u
r
e
1
0
,
a
n
d
P
is
t
h
e
p
o
s
itio
n
v
ec
to
r
o
f
th
e
e
n
d
–
ef
f
ec
ter
.
Fig
u
r
e
1
0
.
Sin
g
le
le
g
o
f
a
n
o
n
-
p
lan
ar
3
-
R
R
R
So
lv
i
n
g
b
y
Gau
s
s
ia
n
eli
m
i
n
ati
o
n
,
w
e
g
et
th
e
e
x
p
r
ess
io
n
o
f
a
ctiv
e
j
o
in
t f
o
r
a
s
i
n
g
le
le
g
I
(
1
8
)
1
1
2
3
2
1
2
3
2
1
)
)(
(
)
)(
(
x
x
y
y
y
y
x
x
p
p
y
x
y
y
x
y
x
x
y
y
x
x
)
(
)
(
)
(
)
(
2
3
2
2
2
3
2
3
2
3
(
1
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.