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J
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2
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1
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DOI
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142
135
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Vo
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9
,
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2
,
J
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2
0
2
0
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35
–
1
42
136
as
w
e
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as
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p
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3
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lato
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r
ep
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ted
b
y
Y.
D
P
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[
4
]
.
Y.
D
P
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al.
ar
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ca
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[
5
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is
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–
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A
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Sel
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2
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m
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3
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[
7
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Saio
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Her
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2
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R
U
-
1
P
R
S
p
ar
allel
m
an
ip
u
lato
r
in
p
lace
o
f
3
P
R
S
p
ar
allel
m
a
n
ip
u
la
to
r
f
o
r
k
in
e
m
atic
in
v
e
s
ti
g
atio
n
[
8
]
.
I
n
p
ar
allel
m
an
ip
u
lato
r
,
to
r
q
u
e
at
j
o
in
ts
a
n
d
an
g
u
lar
tilt
o
f
m
o
b
ile
p
latf
o
r
m
ar
e
k
e
y
p
a
r
a
m
eter
s
f
o
r
ac
cu
r
ate
p
o
s
itio
n
as
w
el
l
as
o
r
ie
n
tatio
n
.
C
o
m
p
ar
ativ
e
s
t
u
d
y
o
f
3
-
UP
S,
3
-
R
P
R
a
n
d
3
-
R
P
S
3
DO
F
p
ar
allel
m
a
n
ip
u
lato
r
s
ar
e
ca
r
r
ied
o
u
t
b
ased
o
n
th
e
to
r
q
u
e
at
j
o
in
ts
,
an
g
u
lar
tilt
o
f
m
o
v
in
g
p
latf
o
r
m
an
d
p
o
s
iti
o
n
al
ac
cu
r
ac
y
b
y
A
.
A
r
o
ck
ia
et
al.
[
9
]
.
A
3
-
P
R
S
p
ar
allel
m
a
n
ip
u
lat
o
r
w
it
h
ad
j
u
s
tab
le
la
y
o
u
t
an
g
le
o
f
ac
t
u
ato
r
s
is
u
s
ed
f
o
r
k
i
n
e
m
ati
c
in
v
e
s
ti
g
atio
n
.
Yan
g
m
i
n
L
i
et
al.
r
ep
o
r
ted
m
ax
i
m
u
m
r
ea
ch
ab
l
e
w
o
r
k
s
p
ac
e
o
cc
u
r
r
ed
at
[
1
0
]
.
P
ar
d
esh
i
et
al.
p
r
esen
ted
p
ar
allel
m
ec
h
a
n
is
m
w
it
h
les
s
d
eg
r
ee
o
f
f
r
ee
d
o
m
i
s
m
o
r
e
s
u
itab
le
f
o
r
d
r
illi
n
g
,
m
i
llin
g
,
w
e
ld
in
g
an
d
tap
p
in
g
ap
p
licatio
n
.
3
DOF
p
ar
allel
m
a
n
ip
u
lato
r
s
h
av
e
g
r
ater
ad
v
an
tag
es
o
v
er
h
i
g
h
d
eg
r
ee
o
f
f
r
ee
d
o
m
p
ar
allel
m
a
n
ip
u
lato
r
s
in
ter
m
s
o
f
m
a
n
u
f
ac
t
u
r
i
n
g
an
d
o
p
er
atin
g
co
s
t.
3
D
OF
p
ar
allel
m
an
ip
u
lato
r
s
ca
n
b
e
class
i
f
ied
in
t
h
r
ee
ca
teg
o
r
ies
‖
-
P
lan
n
er
p
ar
allel
m
a
n
ip
u
lato
r
(
3
tr
an
s
latio
n
al
m
o
tio
n
)
-
Sp
h
er
ical
p
ar
allel
m
a
n
ip
u
la
to
r
(
3
r
o
tatio
n
al
m
o
tio
n
)
-
Sp
atial
p
ar
allel
m
an
ip
u
lato
r
(
Mix
ed
m
o
tio
n
)
[
1
1
]
.
T
s
ai
et
al.
[
1
2
]
r
ep
r
esen
t
th
e
g
eo
m
e
tr
ic
r
elatio
n
b
et
w
ee
n
s
lid
er
s
,
lin
k
s
an
d
m
o
v
in
g
p
lat
f
o
r
m
ar
e
b
u
ilt
to
f
o
r
m
u
late
th
r
e
e
n
o
n
lin
ea
r
t
r
ig
o
n
o
m
e
tr
ic
eq
u
atio
n
s
an
d
t
h
is
n
o
n
li
n
ea
r
eq
u
atio
n
ar
e
s
o
lv
ed
u
s
i
n
g
B
ez
o
u
t
s
m
et
h
o
d
s
.
C
h
er
f
ia
et
al.
[
1
3
]
ar
e
ca
r
r
ied
o
u
t
in
v
er
s
e
a
n
d
d
ir
ec
t
k
in
e
m
atic
a
n
al
y
s
i
s
o
f
co
n
s
tr
a
in
ed
p
ar
allel
r
o
b
o
t
w
it
h
3
d
o
f
a
n
d
f
o
u
r
p
ass
i
v
e
s
e
g
m
e
n
t
s
.
Val
id
a
te
t
h
e
r
es
u
lt
s
o
f
d
ir
ec
t
a
n
d
i
n
v
er
s
e
k
i
n
e
m
atic
w
it
h
e
x
p
er
i
m
e
n
tal
p
r
o
to
ty
p
e.
Z
h
an
g
et
al.
[
1
4
]
c
ar
r
ied
o
u
t
in
v
er
s
e
p
o
s
itio
n
an
al
y
s
i
s
o
f
3
DOF
A
3
h
ea
d
.
Z
h
an
g
et
al.
[
1
4
]
s
tate
th
at
s
tr
u
c
tu
r
al
p
ar
a
m
eter
s
o
f
3
-
R
P
S
m
ec
h
an
i
s
m
h
av
e
a
s
li
g
h
t
e
f
f
ec
t
o
n
t
h
e
j
o
in
ts
m
o
t
io
n
.
Z
h
an
g
et
al.
[
1
5
]
d
ep
icts
th
e
e
f
f
ec
t
o
f
th
e
r
ad
ii
o
f
t
h
e
p
latf
o
r
m
an
d
t
h
e
b
ase
alo
n
g
w
it
h
t
h
e
cr
o
s
s
-
s
ec
tio
n
o
f
th
e
li
m
b
o
n
t
h
e
lo
w
er
o
r
d
er
f
r
eq
u
en
c
y
.
T
h
is
d
ata
is
u
s
e
f
u
l i
n
th
e
d
esi
g
n
s
ta
g
e.
I
n
th
i
s
p
ap
er
,
s
p
atial
p
ar
allel
m
an
ip
u
lato
r
w
it
h
lin
ea
r
ac
t
u
a
tio
n
s
o
f
lead
s
cr
e
w
ar
e
d
eter
m
i
n
ed
f
o
r
d
r
illi
n
g
h
o
les
o
n
i
n
cli
n
ed
s
u
r
f
ac
es
w
i
th
co
n
f
in
ed
w
o
r
k
s
p
ac
e.
3
DOF
p
ar
allel
m
an
ip
u
lato
r
w
it
h
m
o
v
in
g
p
latf
o
r
m
is
co
n
n
ec
ted
w
i
th
b
ase
p
latf
o
r
m
b
y
m
ea
n
s
o
f
lin
k
s
w
it
h
p
r
is
m
atic
-
r
ev
o
l
u
te
–
s
p
h
er
ical
j
o
in
ts
.
R
ev
o
l
u
te
an
d
s
p
h
er
ical
j
o
in
ts
ar
e
p
ass
iv
e
w
h
er
ea
s
p
r
is
m
a
tic
j
o
in
ts
ar
e
ac
tiv
e
j
o
in
ts
.
T
h
is
p
ap
er
d
ea
ls
w
i
th
in
v
er
s
e
k
i
n
e
m
a
tic
a
n
al
y
s
is
o
f
s
aid
p
ar
allel
m
a
n
ip
u
lato
r
o
n
i
n
cli
n
ed
p
r
is
m
ati
c
s
u
r
f
ac
es.
T
h
is
w
o
r
k
is
o
r
g
an
ized
in
f
i
v
e
s
ec
tio
n
s
i
n
th
i
s
p
ap
er
.
A
r
ch
itect
u
r
e
o
f
p
r
o
p
o
s
ed
m
a
n
ip
u
lato
r
i
s
d
is
cu
s
s
ed
i
n
s
ec
o
n
d
s
ec
tio
n
.
T
h
ir
d
s
ec
tio
n
d
ea
ls
w
it
h
m
o
b
il
it
y
eq
u
atio
n
as
w
ell
a
s
d
eg
r
ee
o
f
f
r
ee
d
o
m
ca
lcu
latio
n
f
o
r
3
-
P
R
S
p
ar
all
el
m
ec
h
an
is
m
.
I
n
v
er
s
e
k
i
n
e
m
atic
a
n
al
y
s
i
s
o
f
3
-
P
R
S
p
ar
allel
m
a
n
ip
u
lato
r
is
ca
r
r
ied
o
u
t
in
f
o
u
r
th
s
ec
tio
n
.
I
n
th
e
f
if
t
h
s
ec
tio
n
,
p
o
s
itio
n
an
al
y
s
i
s
f
o
r
d
r
illi
n
g
an
d
p
r
o
f
ile
g
en
er
atio
n
is
ca
r
r
ied
o
u
t f
o
r
p
r
o
p
o
s
ed
m
an
ip
u
lato
r
.
2.
ARCH
I
T
E
C
T
URA
L
D
E
SC
RIPT
I
O
N
T
h
e
s
ch
e
m
atic
r
ep
r
esen
ta
tio
n
o
f
p
r
o
p
o
s
ed
3
-
DOF
p
ar
allel
m
an
ip
u
lato
r
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
Mo
v
in
g
p
latf
o
r
m
is
co
n
n
ec
ted
to
th
e
b
ase
p
latf
o
r
m
b
y
t
h
r
ee
li
m
b
s
.
E
ac
h
li
m
b
co
n
s
is
t
s
o
f
p
r
is
m
a
tic
-
r
ev
o
l
u
te
-
s
p
h
er
ical
j
o
in
ts
.
T
h
ese
th
r
ee
li
m
b
s
w
ill
m
ak
e
m
a
n
ip
u
lato
r
s
y
m
m
etr
ic.
E
ac
h
li
m
b
h
as
o
n
e
ac
ti
v
e
p
r
is
m
atic
j
o
in
t
an
d
t
w
o
p
ass
iv
e
r
e
v
o
lu
te
an
d
s
p
h
er
ical
j
o
in
ts
.
All
ac
ti
v
e
j
o
in
ts
ar
e
lo
ca
ted
o
n
/n
ea
r
to
t
h
e
b
ase
p
lat
f
o
r
m
.
T
h
r
ee
ac
tiv
e
p
r
is
m
atic
j
o
in
ts
h
av
e
r
ec
ir
cu
latin
g
b
all
s
cr
e
w
m
ec
h
an
is
m
w
h
ic
h
e
n
ab
les
u
s
to
s
to
p
p
r
is
m
atic
m
o
t
io
n
a
t
an
y
i
n
s
ta
n
t
w
i
th
o
u
t
a
n
y
s
lip
p
ag
e.
Si
m
u
ltan
eo
u
s
v
ar
iab
le
m
o
tio
n
s
o
f
p
r
is
m
atic
j
o
in
ts
ar
e
r
es
p
o
n
s
ib
le
f
o
r
th
e
an
g
u
lar
tilt
o
f
t
h
e
m
o
v
i
n
g
p
latf
o
r
m
,
w
h
ic
h
i
s
d
esire
d
f
o
r
d
r
illi
n
g
ap
p
licatio
n
.
Her
e,
,
,
an
d
ar
e
len
g
th
s
o
f
co
n
n
ec
ti
n
g
li
n
k
s
1
,
2
an
d
3
r
esp
ec
tiv
el
y
.
A
ll
p
r
is
m
atic
j
o
in
ts
m
a
k
es
w
ith
ea
ch
o
th
er
,
i
f
v
ec
to
r
s
ar
e
d
r
aw
n
f
r
o
m
o
r
ig
i
n
‗
O
‘
in
XY
p
lan
e.
Fi
x
ed
an
d
m
o
v
in
g
p
latf
o
r
m
s
ar
e
eq
u
ilater
a
l
tr
ian
g
le
s
in
s
h
ap
e
as sh
o
w
n
i
n
Fi
g
u
r
e
2
.
3.
M
O
B
I
L
I
T
Y
A
ND
DE
G
R
E
E
O
F
F
RE
E
DO
M
Mo
b
ilit
y
an
al
y
s
i
s
is
ca
r
r
ied
o
u
t
f
o
r
m
a
n
y
p
ar
allel
m
a
n
ip
u
l
ato
r
s
u
s
i
n
g
Gr
ü
b
ler
–
K
u
tzb
ac
h
cr
iter
io
n
.
Usi
n
g
Gr
ü
b
ler
–
Ku
tzb
ac
h
eq
u
a
tio
n
f
o
r
3
P
R
S p
ar
allel
m
ec
h
a
n
is
m
,
Evaluation Warning : The document was created with Spire.PDF for Python.
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kin
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137
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∑
(
1
)
(
)
(
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=3
h
er
e,
d
eg
r
ee
o
f
f
r
ee
d
o
m
o
f
s
p
ac
e
u
tili
ze
d
f
o
r
a
m
ec
h
a
n
is
m
w
h
ile
in
o
p
er
atio
n
.
Fo
r
a
b
o
v
e
co
n
f
ig
u
r
atio
n
,
f
o
r
s
p
atial
m
o
tio
n
,
is
a
n
u
m
b
er
o
f
lin
k
s
,
is
n
u
m
b
er
o
f
j
o
in
ts
a
n
d
is
d
eg
r
ee
o
f
f
r
ee
d
o
m
f
o
r
j
o
in
ts
.
Hen
ce
,
3
-
P
R
S
m
an
ip
u
l
ato
r
h
as
th
r
ee
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
.
Gr
ü
b
ler
–
Ku
tzb
ac
h
cr
iter
i
o
n
w
a
s
s
p
ec
i
f
icall
y
u
s
ed
f
o
r
d
eter
m
i
n
i
n
g
th
e
n
u
m
b
er
o
f
d
eg
r
ee
o
f
f
r
ee
d
o
m
.
I
t
c
an
n
o
t
f
i
n
d
w
h
at
t
y
p
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o
f
d
eg
r
e
e
o
f
f
r
ee
d
o
m
p
r
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in
th
e
m
an
ip
u
lato
r
.
I
t
w
as
o
b
s
er
v
ed
t
h
at
3
DOF
m
an
ip
u
lato
r
h
as
o
n
e
tr
an
s
lat
io
n
m
o
tio
n
alo
n
g
th
e
Z
ax
i
s
an
d
t
w
o
r
o
tatio
n
al
m
o
tio
n
s
ab
o
u
t X
an
d
Y
ax
is
.
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
r
a
m
o
f
3
P
R
S p
ar
allel
m
ec
h
an
is
m
Fig
u
r
e
2
.
P
lan
n
er
v
ie
w
o
f
3
P
R
S
m
ec
h
a
n
is
m
4.
I
NVE
RS
E
K
I
NE
M
AT
I
C
A
NALYS
I
S
I
n
v
er
s
e
k
i
n
e
m
a
tic
p
r
o
b
lem
c
an
b
e
d
ef
in
ed
as
p
lace
m
e
n
t
o
f
to
o
l
f
r
a
m
e
at
d
esire
d
p
o
s
itio
n
an
d
o
r
ien
tatio
n
b
y
m
ea
n
s
o
f
ac
t
u
atio
n
.
T
h
e
p
u
r
p
o
s
e
o
f
in
v
e
r
s
e
k
in
e
m
atic
p
r
o
b
le
m
is
to
d
eter
m
i
n
e
ac
tu
ated
v
ar
iab
le
f
r
o
m
a
g
iv
e
n
p
o
s
it
io
n
o
f
en
d
e
f
f
ec
to
r
.
I
n
v
er
s
e
k
in
e
m
atic
a
n
al
y
s
i
s
w
a
s
u
s
ed
i
n
p
r
ac
tical
ap
p
licatio
n
o
f
m
an
ip
u
lato
r
.
Fi
g
u
r
e
3
,
s
h
o
w
s
p
o
s
itio
n
v
ec
to
r
s
o
f
s
p
h
er
ica
l
j
o
in
ts
w
i
th
r
esp
ec
t
to
r
e
f
er
en
c
e
f
r
a
m
e
,
,
an
d
ar
e
lin
ea
r
ac
tu
atio
n
o
f
p
r
is
m
atic
j
o
in
ts
o
f
li
m
b
s
1
,
2
an
d
3
r
esp
ec
tiv
el
y
.
is
a
d
is
t
an
ce
b
et
w
ee
n
t
w
o
lead
s
cr
e
w
,
is
a
ce
n
tr
e
to
ce
n
tr
e
d
i
s
tan
ce
b
et
w
ee
n
to
s
p
h
er
ical
j
o
in
ts
an
d
b
is
ce
n
tr
e
to
ce
n
tr
e
d
is
tan
ce
b
et
w
ee
n
p
r
is
m
atic
j
o
in
t a
n
d
r
ev
o
l
u
te
j
o
in
t.
Sp
h
er
ical
j
o
in
ts
co
o
r
d
in
ates a
r
e
ex
p
r
ess
ed
in
t
h
e
f
o
r
m
o
f
,
(
)
(
2
)
is
a
n
o
r
m
al
v
ec
to
r
p
ass
i
n
g
t
h
r
o
u
g
h
t
h
e
p
o
in
t
an
d
ce
n
tr
e
p
o
in
ts
co
o
r
d
in
ate
s
o
f
a
n
y
s
p
h
er
ic
al
j
o
in
ts
l
y
in
g
in
th
is
p
lan
e
w
i
th
co
o
r
d
in
ates
(
)
,
as sh
o
w
n
in
Fig
u
r
e
4
.
T
h
e
eq
u
atio
n
o
f
s
p
h
er
e
p
ass
i
n
g
th
r
o
u
g
h
th
r
e
e
s
p
h
er
ical
j
o
in
ts
is
ex
p
r
es
s
ed
as,
(
)
(
)
(
)
(
3
)
h
er
e
an
d
an
d
ar
e
s
p
h
er
ical
j
o
in
ts
co
o
r
d
in
ate
i
n
x
,
y
a
n
d
z
ax
is
r
esp
ec
tiv
el
y
.
[
]
Sp
h
er
ical
j
o
in
ts
an
g
le
s
ar
e
d
eter
m
in
ed
b
y
f
o
llo
w
in
g
(
4
)
,
√
√
√
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
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4856
I
n
t
J
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b
&
A
u
to
m
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
35
–
1
42
138
√
√
√
√
(
4
)
Fig
u
r
e
3
.
P
o
s
itio
n
v
ec
to
r
o
f
s
p
h
er
ical
j
o
in
t
Fig
u
r
e
4
.
No
r
m
al
v
ec
to
r
p
ass
i
n
g
t
h
r
o
u
g
h
t
h
e
p
lan
e
Ca
s
e
s
t
ud
y
1
:
Stru
ct
u
r
al
p
ar
am
eter
s
co
n
s
id
er
ed
f
o
r
3
P
R
S m
an
ip
u
lato
r
(
T
ab
le
1
an
d
Fig
u
r
e
5
)
ar
e
:
(
)
(
)
T
ab
le
1
.
J
o
in
ts
p
ar
am
e
ter
s
f
o
r
ca
s
e
s
tu
d
y
1
L
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
r
e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
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e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
r
e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
Fig
u
r
e
5
.
T
o
o
l p
o
s
itio
n
an
d
o
r
ien
tatio
n
a
f
ter
ac
t
u
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
I
n
ve
r
s
e
kin
ema
tic
a
n
a
lysi
s
o
f 3
DO
F 3
-
P
R
S
P
M fo
r
ma
ch
in
i
n
g
.
.
.
(
His
h
a
n
tku
ma
r
R
a
s
h
mika
n
tb
h
a
i P
a
tel
)
139
5.
P
O
SI
T
I
O
N
ANA
L
YSI
S O
F
M
ANIPULAT
O
R
F
O
R
DRI
L
L
I
N
G
AND
S
L
O
T
T
I
N
G
O
P
E
RAT
I
O
N
O
N
P
RIS
M
AT
I
C
SURF
A
C
E
P
lace
m
e
n
t
o
f
to
o
l
f
r
a
m
e
at
p
r
e
-
d
ef
i
n
ed
p
o
in
t
o
n
s
u
r
f
ac
e
i
s
ca
lled
p
o
s
itio
n
a
n
al
y
s
i
s
.
I
n
wh
ich
,
th
is
p
r
e
-
d
ef
in
ed
p
o
in
t
is
co
n
s
id
er
e
d
as
a
t
o
o
l
tip
.
T
h
e
to
o
l
tip
c
o
o
r
d
in
ates
ar
e
u
s
ed
to
d
ete
r
m
i
n
e
lin
ea
r
ac
tu
atio
n
s
o
f
r
ec
ir
cu
lati
n
g
b
all
s
cr
e
w
.
Fi
g
u
r
e
6
,
s
h
o
w
s
p
r
is
m
atic
p
ar
t
w
it
h
i
n
cli
n
ed
s
u
r
f
ac
e.
I
n
cli
n
at
io
n
an
g
le
o
f
in
cl
in
ed
s
u
r
f
ac
e
w
ill
b
e
v
ar
ied
as
p
er
r
eq
u
ir
e
m
en
ts
.
Selecte
d
d
i
m
e
n
s
io
n
o
f
p
r
is
m
at
ic
p
ar
t
w
a
s
lies
in
th
e
w
o
r
k
s
p
ac
e
o
f
th
e
s
a
id
m
a
n
ip
u
lato
r
.
C
o
n
s
i
d
er
o
n
e
n
e
w
co
o
r
d
in
ate
s
y
s
te
m
‗
at
o
n
e
b
o
tto
m
co
r
n
er
o
f
t
h
e
p
r
is
m
atic
p
ar
t.
T
h
is
p
r
is
m
atic
p
ar
t
w
as
p
lace
d
at
o
f
f
-
s
et
to
t
h
e
3
P
R
S
p
ar
allel
m
a
n
ip
u
lato
r
r
ef
er
en
ce
f
r
a
m
e
.
T
h
e
p
o
in
ts
r
eq
u
ir
ed
f
o
r
a
p
o
s
itio
n
an
al
y
s
is
s
h
o
u
ld
b
e
m
ea
s
u
r
e
f
r
o
m
th
e
r
ef
er
en
ce
co
o
r
d
in
ate
s
y
s
te
m
.
I
t
s
h
o
u
ld
b
e
ess
e
n
tial to
f
i
n
d
o
u
t
n
o
r
m
al
v
e
cto
r
to
th
e
in
cli
n
ed
s
u
r
f
ac
e
f
o
r
p
r
o
p
e
r
o
r
ien
tatio
n
o
f
th
e
to
o
l f
r
a
m
e.
I
n
Fi
g
u
r
e
7
s
h
o
w
n
o
r
m
al
v
e
cto
r
to
th
e
p
la
n
e
a
s
w
el
l
as
o
f
f
s
et
d
is
tan
ce
b
et
w
ee
n
t
w
o
co
o
r
d
in
ate
s
y
s
te
m
s
.
Dete
r
m
in
ed
b
y
(
4
)
.
(
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
|
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
|
)
(
5
)
(
)
(
)
Her
e,
⃗
⃗
⃗
⃗
⃗
⃗
I
s
p
o
s
itio
n
v
ec
to
r
b
et
w
ee
n
p
o
in
t 2
an
d
1
⃗
⃗
⃗
⃗
⃗
⃗
I
s
p
o
s
itio
n
v
ec
to
r
b
et
w
ee
n
p
o
in
t 3
an
d
1
T
L
is
a
to
o
l le
n
g
t
h
(
v
ec
to
r
len
g
th
)
I
s
o
f
f
s
et
d
is
ta
n
ce
b
et
w
ee
n
‗
‘
an
d
Fo
llo
w
i
n
g
s
tep
s
ar
e
f
o
llo
w
ed
i
n
p
o
s
itio
n
a
n
al
y
s
is
:
1.
Fin
d
o
u
t p
o
in
t
s
co
o
r
d
in
ate
w
i
t
h
r
esp
ec
t to
m
ec
h
a
n
i
s
m
r
e
f
er
e
n
ce
f
r
a
m
e
‗
.
(
⃗
⃗
)
(
)
2.
Dete
r
m
i
n
e
th
e
n
o
r
m
al
v
ec
to
r
to
th
e
p
lan
e
an
d
i
ts
e
n
d
p
o
in
t.
(
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
|
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
|
)
3.
C
o
m
p
u
te
m
o
v
in
g
p
lat
f
o
r
m
ce
n
tr
e
p
o
in
t (
m
cp
)
(
)
⃗
P
o
s
itio
n
an
al
y
s
is
o
f
m
a
n
ip
u
la
to
r
f
o
r
d
r
illi
n
g
a
n
d
s
lo
ttin
g
o
p
er
atio
n
o
n
i
n
cli
n
ed
s
u
r
f
ac
e
ar
e
s
h
o
w
n
i
n
ca
s
e
s
tu
d
y
2
(
a)
an
d
2
(
b
)
r
esp
ec
tiv
ely
.
Fig
u
r
e
6
.
Nu
m
b
er
o
f
p
o
in
t
s
o
n
p
r
is
m
atic
p
ar
ts
Fig
u
r
e
7
.
No
r
m
al
v
ec
to
r
an
d
it
s
en
d
p
o
in
t o
n
p
r
is
m
atic
p
ar
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
35
–
1
42
140
Ca
s
e
s
t
ud
y
2
(
a
)
C
o
n
s
id
er
a
o
n
e
p
o
in
t
o
n
in
cli
n
ed
p
r
is
m
at
ic
s
u
r
f
ac
e
Of
f
s
et
d
is
tan
ce
,
(
)
T
o
o
l tip
co
o
r
d
in
ates
(
)
(
)
No
r
m
a
l v
ec
to
r
to
th
e
p
lan
e
⃗
(
̂
̂
̂
)
Mo
v
in
g
p
latf
o
r
m
ce
n
tr
e
p
o
in
t
co
o
r
d
in
ates
⃗
(
)
(
)
(
)
An
al
y
ticall
y
,
th
r
ee
s
p
h
er
ical
j
o
in
ts
ce
n
tr
e
p
o
in
t c
o
o
r
d
in
ates
(
T
a
b
le
2
)
a
r
e
d
eter
m
in
ed
b
y
(
1
)
an
d
(
2
)
.
(
)
(
)
(
)
T
ab
le
2
.
J
o
in
t p
ar
am
eter
s
f
o
r
ca
s
e
s
t
u
d
y
2
(
a)
L
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
r
e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
r
e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
R
e
q
u
i
r
e
d
l
i
n
e
a
r
a
c
t
u
a
t
i
o
n
Fig
u
r
e
8
s
h
o
w
s
p
o
s
itio
n
an
d
o
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A
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Ka
laic
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A
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V
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Drill
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J.,
&
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.
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,
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re
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.
,
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w
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g
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.
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4
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Zh
a
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J.,
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.
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―
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5
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Zh
a
n
g
J.,
Zh
a
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Y
.
Q.,
&
Ce
c
c
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re
ll
i
M
.
,
―
El
a
sto
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a
m
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M
o
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-
Ba
se
d
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ra
ti
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C
h
a
ra
c
teristics
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re
d
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n
o
f
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T
h
re
e
P
rism
a
ti
c
–
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v
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lu
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e
,‖
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o
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.
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