Page 1 Page 2 CompHont robotS oro o ooool oloos of TobotS. Tho

P
oc
r
e
e
d
i
ng
s of t
h
e Fi
st r
As
i
a I
n
t
e
na
r
t
i
o
na
l S
y
mp
os
i
u
m o
n Mc
c
ha
t
r
o
mc
s
(
AI
SM 2
0
0
4
)
S
e
pt
e
mb
e
r 2
7
-3
0, 20
0
4, Xi
'
a
n, Ch
i
na
Equi
l
i
br
i
um Conf
i
g
ur
a
t
i
o
ns o
f a Pl
a
na
r 3-
DOE Pa
r
a
l
l
e
l Ro
bo
t wi
t
h
Fl
exural Pi
vot
s
T
ua
n
-
J
i
e Li Xi
a
o
-
Yo
n
g Zho
u
S
c
h
o
o
l o
f El
e
c
t
r
o
me
c
h
a
n
i
c
a
l En
g
i
n
e
e
r
i
n
g
, Xi
d
i
a
n Un
i
v
e
r
s
i
t
y
, Xi
'
a
n 71
0
0
71
, Ch
i
n
a
e
-
ma
i
l
: l
i
9
6
8
6
_c
n
@s
i
na.
c
o
m
r
o
bo
t
s r
e
l
a
t
e
s t
o a
na
妙z
i
ng a
nd o
p
t
i
mi
z
i
n
g t
he ki
n
e
ma
t
i
c
h
a
v
e be
e
n s
t
u
d
i
e
d. I
n t
he l
a
t
e 8
0'
s
, a n
e
w f
i
e
l
d o
f
bo
t
h r
e
s
e
a
r
c
h a
nd a
p
p
l
i
c
a
t
i
o
n
s ha
s be
e
n o
p
e
n
e
d by
g
e
o
me
t
y r
wi
t
ho
u
t r
e
g
a
r
d t
o t
he e
q
ui
l
i
b
ium r
c
o
nf
i
gu
at
r
i
o
ns
Cl
a
v
e
l
'
t wh
o d
e
v
e
l
o
p
e
d t
h
e f
a
mo
u
s De
l
t
a
of t
he p
a
r
ll
a
e
l obo
r
t wi
t
h f
l
e
x
ur
a
l p
i
v
o
t
s o
n
c
e t
h
e e
x
t
e
r
n
a
l
r
o
o
t
s o
f t
he s
ys
t
e
m o
f t
r
an
s
c
e
nd
e
n
t
a
l e
q
u
a
t
i
on
s wi
t
h
ma
n
i
p
ul
a
t
o
r wh
i
c
h ha
s t
h
e a
bi
l
i
t
y t
o mo
ve i
n h
i
g
h
s
pe
ed. Re
c
e
n
t
l
y
, t
h
e ma
c
h
i
n
e
-
t
o
o
l i
nd
u
s
t
y
r
d
i
s
c
o
v
e
r
e
d t
h
e p
o
t
e
n
t
i
a
l a
d
v
a
n
t
a
g
e
s o
f p
a
r
a
l
l
e
l
r
o
bo
t
s a
nd mo
s
t ma
j
o
r ma
c
h
i
n
e
-
t
o
o
l c
omp
a
n
i
e
s a
r
e
i
n t
h
e p
r
o
es
c
s o
f e
x
t
e
n
s
i
v
e t
e
s
t
s a
n
d e
v
a
l
ua
t
i
o
n o
f
t
h
e
i
r p
a
r
a
l
l
e
l ma
c
h
i
n
e
s f
o
r pa
r
a
l
l
e
l k
i
n
e
ma
t
i
c
ma
c
h
i
n
e
s
t
"
t
.
I
n t
h
e ie
f
l
d o
f r
o
b
o
t
i
c
s
, t
h
e t
a
s
k r
e
q
ui
r
e
d o
f t
h
e
h
i
g
h s
p
e
e
d a
n
d a
c
c
u
r
a
c
y c
a
n b
e p
e
r
f
o
r
me
d b
y v
i
tu
r
e
o
f p
a
r
a
l
l
e
l r
o
b
o
t
s e
mp
l
o
y
i
n
g p
a
r
a
l
l
e
l me
c
h
a
n
i
s
m. A
t
r
i
g
o
n
o
me
t
ic r
f
u
nc
t
i
o
ns wi
t
h
o
u
t i
ni
t
i
a
l va
l
u
e s
e
l
e
c
t
i
o
n i
n
p
a
r
a
l
l
e
l r
o
b
o
t t
y
p
i
c
a
l
l
y c
o
n
s
i
s
t
s o
f mo
v
i
n
g p
l
a
t
f
o
r
m
t
he s
pec
i
f
i
ed i
nt
er
val
s t
o de
t
e
c
t t
he e
nt
i
r
e s
e
t of t
he i
ni
t
i
al
t
ha
t i
s c
o
n
n
e
c
t
e
d t
o a f
i
x
e
d ba
s
e b
y s
e
v
e
r
a
l l
i
mbs o
r
l
e
g
s
. T
y
p
i
c
a
l
l
y
, t
h
e l
i
mb t
h
a
t c
o
mp
o
s
e
s t
h
e pa
r
a
l
l
e
l
me
c
ha
n
i
s
m s
u
c
h a
s t
y
pe o
f t
he De
l
t
a a
n
d St
e
wa
t
r
ma
n
i
p
ul
a
t
o
r h
a
s t
h
e s
e
r
i
a
l s
t
uc
r
t
u
r
e
. Ev
e
n i
f a l
o
t o
f
pa
r
a
l
l
e
l me
c
ha
ni
s
ms ha
ve b
e
e
n p
r
o
po
s
e
氏a
l
mo
s
t t
h
e
6
-
do
f pa
r
a
l
l
e
l me
c
ha
n
i
s
ms h
a
v
e b
e
e
n s
t
u
d
i
e
d
.
Ho
we
ve
r
, i
n s
e
v
e
al r
a
p
pl
i
c
a
t
i
o
n
s
, a 6
-
do
f me
c
h
a
n
i
s
m
i
s n
o
t r
e
q
u
i
r
e
d a
n
d r
o
bo
t
s whi
c
h ha
v
e l
e
s
s t
h
a
n 6 d
o
f
Abs
t
r
a
c
t
: Al
l p
r
e
v
i
o
us r
e
s
e
a
r
c
h o
n de
s
i
g
n of pa
r
a
le
l
l
o
a
d i
s a
s
s
i
g
ne
d. Thi
s a
r
t
i
c
l
e a
d
d
r
e
s
s
e
s t
he e
q
ui
l
i
b
r
i
u
m
c
o
nf
i
gu
r
a
t
i
o
n
s of a pl
a
n
a
r 3
-
d
of pa
r
al
l
e
l ob
r
ot wi
t
h
f
l
e
x
ur
a
l p
i
vo
t
s
. A s
ys
t
e
m o
f f
o
u
r c
o
u
p
l
e
d t
r
a
ns
c
e
n
de
n
t
a
l
e
q
ua
t
i
o
ns wi
t
h t
r
i
g
o
n
o
me
t
r
i
c f
u
nc
t
i
o
ns i
n f
o
u
r u
n
kn
o
wns
i
s de
r
i
ve
d f
om r
t
h
e i
n
v
e
r
s
e s
t
a
t
i
c a
n
a
l
ys
i
s
. Th
e i
n
i
t
i
al
c
o
nf
i
g
u
at
r
i
o
ns of t
h
e p
a
r
a
le
l ob
r
o
t a
e r
d
i
s
c
u
s
s
e
d f
i
r
s
t
l
y
,
t
he
n a n
ume
r
i
c
l a
me
t
h
od i
s p
r
e
s
e
n
t
e
d b
a
s
e
d o
n t
he
Ne
wt
on
'
s i
t
e
r
a
t
i
ve me
t
ho
d, whi
c
h c
a
n f
nd i
a
l t
he ea
r
l
c
o
nf
i
gu
r
a
t
i
o
ns a
n
d t
he e
q
u
i
ib
l
ium
r
of t
he
p
a
r
a
le
l ob
r
ot wi
t
h f
l
e
x
u
r
e hi
n
ge
s
.Fi
na
l
l
y
, a nu
me
r
i
c
l
a
e
x
a
mpl
e i
s p
ov
r
i
d
e
d.
Ke
ywor
ds
: Pl
a
n
ar Pa
r
al
l
el Robot
, P
a
r
a
l
l
e
lMechani
s
m,
Pr
i
v
e
t
, I
n
ve
r
s
e S
t
at
i
c Ana
lys
i
s
,E
qui
ibr
l
ium
Conf
i
gur
a
t
i
on, Numer
i
ca
l Sol
ut
i
o
n
c
a
n b
e u
s
e
d
[
"
1 I
nt
r
oduct
i
on
F
l
e
x
u
r
e h
i
n
g
e 1
6
1 i
s a s
i
mp
l
e
, d
e
p
e
n
d
a
b
l
e a
n
d
Co
mpa
r
e
d wi
t
h s
e
r
i
a
l r
o
b
o
t
s
, pa
r
a
l
l
e
l r
o
b
o
t
s h
a
v
e
i
nge
ni
o
us mec
ha
ni
c
a
l s
t
uc
r
t
ur
e whi
c
h e
mul
a
t
es t
he
po
t
e
n
t
i
a
l
l
y h
i
gh
e
r p
r
e
c
i
s
i
o
n
, g
r
e
a
t
e
r s
t
r
u
c
t
ur
a
l
f
u
nc
t
i
on o
f a o
r
d
i
na
y r
h
i
n
g
e b
y c
on
c
e
n
t
r
a
t
i
n
g le
f
x
i
on
t
o j
u
s
t a f
e
w r
e
g
i
o
n
s
. Be
c
a
u
s
e o
f i
t
s o
u
t
s
t
a
n
d
i
n
g
pe
r
f
o
r
ma
nc
e
s
: n
o g
a
p, n
o me
c
ha
ni
c
a
l f
r
i
c
t
i
on
, no
ig
r
i
d
i
t
y
, h
i
g
h
e
r s
p
e
e
d a
n
d a
c
el
c
e
r
a
t
i
o
n
, a
n
d l
a
r
g
e
r
c
a
pa
c
i
t
y
. Th
e
r
e
f
o
r
e
, t
h
e
y ha
v
e r
e
c
e
i
ve
d i
n
c
r
e
a
s
e
d
i
nt
er
es
t f
r
om bot
h r
es
ear
cher
s a
nd i
ndus
t
ies. r
Fr
om
t
h
e f
i
r
s
t p
a
r
a
l
l
e
l r
o
b
o
t p
r
o
p
o
s
e
d b
y Go
u
g
h
l
t
t a
n
d
S
t
e
wa
tt
r
'
l
, a l
o
t o
f p
a
r
a
l
l
e
l r
o
b
o
t
s o
r d
e
s
i
g
n me
t
h
o
d
s
c
r
a
wl and no n
ee
d of l
ubr
i
ca
t
i
on whi
l
e i
n mo
t
i
o
n,
h
i
gh r
e
s
o
l
ut
i
o
n c
a
n be o
b
t
a
i
n
e
d.
一 722-
C
o
mpl
i
a
n
t r
o
bo
t
s a
r
e an
o
v
e
l c
l
a
s
s o
f r
o
bo
t
s
.
Th
e us
e o
f le
f
x
i
bl
e me
mbe
r
s t
o g
a
i
n mo
bi
l
i
t
y ha
s
br
o
u
g
h
t n
o
t
a
b
l
e a
d
va
n
c
e
s i
n t
h
e r
o
bo
t d
e
s
i
gn
Co
mp
l
e
x mo
t
i
o
n a
n
d i
n
p
u
t
/
o
u
t
p
u
t c
h
a
r
a
c
t
e
is
r
t
i
c
s
ma
y be o
b
t
a
i
n
e
d f
r
o
m c
o
mp
l
i
a
n
t r
o
bo
t
s wi
t
h f
e
we
r
pa
r
t
s t
h
a
n t
h
e
i
r r
i
g
i
d
-
b
o
d
y c
o
u
n
t
e
r
p
a
ts
r
.
Al
l pr
e
vi
o
us r
e
s
e
a
r
c
h o
n d
e
s
i
g
n o
f pa
r
a
l
l
e
l
r
o
b
o
t
s r
e
l
a
t
e
s t
o a
n
ly
a
z
i
n
g a
n
d o
p
t
i
mi
z
i
n
g t
h
e
k
i
n
e
ma
t
i
c ge
o
me
t
y r
wi
t
h
o
u
t r
e
g
a
r
d t
o t
h
e
e
q
ui
l
i
br
iu
m c
o
n
f
i
gu
r
a
t
i
o
ns o
f t
h
e pa
r
a
l
l
e
l r
o
bo
t wi
t
h
le
f
xu
r
l a
p
i
vo
t
s o
n
c
e t
h
e e
x
t
e
na
r
l l
o
a
d i
s a
s
s
i
gn
e
d.
Th
e d
e
t
er
mi
na
t
i
o
n o
f e
n
t
i
e r
e
q
ui
l
i
b
ium
r
c
o
n
f
i
g
ur
a
t
i
o
n
s i
s a mo
e r
d
i
ic
f
ul
t t
h
e
or
e
t
i
c
lp
a
r
o
bl
e
m
b
e
c
a
u
s
e i
t de
a
l
s wi
t
h in
f
di
n
g ll a
t
h
e ea
r
lr
o
o
t
s o
f t
h
e
s
ys
t
e
m o
f t
r
a
n
s
c
e
nd
e
n
t
le
a
q
ua
t
i
o
n
s d
e
iv
r
e
d f
r
o
m t
h
e
i
n
v
e
r
s
e s
t
a
t
i
c a
n
a
l
ys
i
s o
f c
o
mpl
i
a
n
t r
o
bo
t
s
.
ext
er
na
l l
oad F
B
,
1
-
\,
、
一
、
乍
G
l n
p
,
}
}
F '
X} n
I
.
,
0}
Fi
gur
e 1. The me
cha
ni
s
m ar
c
hi
t
e
ct
ur
e
2 Pl
anar Paral
l
el Robot
s wi
t
h Fl
exural Pi
vot
s
2.
1 Mec
hani
s
m archi
t
e
ct
ur
e
Th
e me
c
h
a
n
i
s
m a
r
c
h
i
t
e
c
t
u
r
e o
f t
h
e p
a
r
a
l
l
e
l r
o
b
o
t
a
n
ly
a
z
e
d i
n t
h
e pr
es
e
n
t wor
k i
s i
l
l
us
t
r
a
t
e
d i
n Fi
g
ur
e
1
. Th
e mo
vi
n
g p
l
a
t
f
o
r
m, wh
i
c
h h
a
s a r
e
gu
l
a
r
t
ia
r
n
gu
l
a
r s
ha
pe
, c
o
r
es
r
p
on
d
s t
o t
h
e e
n
d
-
e
fe
c
t
o
r
.
Th
i
s pl
a
n
a
r r
o
b
o
t i
s c
a
t
e
g
or
iz
e
d a
s a RPR t
y
pe
,
b
e
c
a
u
s
e o
n
e l
i
mb c
o
n
s
i
s
t
s o
f t
h
e p
is
r
ma
t
i
c j
o
i
n
t a
n
d
t
wo n
o
nc
o
n
s
e
c
u
t
i
v
e r
e
vo
l
u
t
ej
o
i
n
t
s
. A, B a
n
d C a
r
e
le
f
xi
b
l
e j
o
i
n
t
s
, wh
i
c
h a
r
e mo
d
e
l
e
d a
s p
i
n j
o
i
n
t
s
r
e
s
t
r
a
i
n
e
d b
y t
o
r
s
i
o
n
l a
s
pr
in
g
s
. Th
e c
o
ns
i
d
e
ed
r
me
c
h
a
ni
s
m i
s a 3
-
d
o
f pa
r
a
l
l
e
l r
o
b
o
t a
c
c
o
r
d
i
n
g t
o
F怕ur
e 2
. The c
o
nf
ig
u
r
a
t
i
o
n whe
n t
he l
i
mb
l
e
ng
t
h i
s n
e
g
a
t
i
v
e
B
t
, 0
2,B
3
-
Th
e a
n
g
u
l
a
r p
o
s
i
t
i
o
n
s o
f t
h
e
l
i
mb
s
, a
n
d a
r
e po
s
i
t
i
v
e i
n c
o
u
nt
e
r
-
c
l
oc
k
wi
s
e
di
r
ec
ti
on
B
t
u,0
2
0,0
3
0—
T
h
e i
n
i
t
i
a
l a
n
g
u
l
a
r
po
s
i
t
i
o
n
s o
f t
h
e l
i
mbs wh
e
n t
h
e s
p
r
i
n
gs a
r
e n
o
t
Li
l
'
I
. Th
e e
x
t
e
na
r
ll
o
a
d i
s a
p
p
l
i
e
d o
n t
h
e en
c
t
r
o
i
d o
f
l
oaded
t
h
e mo
vi
n
g pl
a
t
f
o
r
m. Th
e me
c
ha
n
i
s
m ma
y r
e
ma
i
n i
n
e
q
ui
l
i
b
ium r
a
s s
o
o
n a
s t
h
e t
o
r
q
u
e
s e
x
e
te
r
d by t
he
l
i
mbs u
po
n t
h
e s
pr
in
gs a
r
e e
q
ua
lt
o t
h
e mo
me
n
t
s o
f
f
o
r
c
e
s t
h
a
t t
h
e mo
vi
n
g p
l
a
t
f
o
r
m t
r
a
n
s
mi
t
s t
o t
he
k
,
, k
2, k
3
-
Th
e s
p
r
i
n
g c
o
n
s
t
a
n
t
s l
a
yi
n
g
i
n p
i
vo
t
s A,B a
n
d C r
e
s
p
e
ti
c
v
el
y
d2一 一一Th
e s
i
d
e l
e
n
g
t
h o
f t
h
e mo
v
i
n
g
l
i
mbs.
Fo
r t
h
e s
a
k
e o
f c
o
n
ve
n
i
e
nc
e, t
h
e f
o
l
l
o
wi
n
g
va
ia
r
bl
e
s a
r
e e
x
p
l
i
c
i
t
l
y d
e
f
i
n
e
d:
F -
Th
e e
x
t
e
na
r
l l
o
a
d
, a
p
p
l
i
e
d o
n t
he
c
e
n
t
r
o
i
d o
f t
h
e mo
v
i
n
g p
l
a
t
f
o
r
m.
Fi
, F
2,凡—
Th
e c
o
mp
o
n
e
n
t
s t
h
a
t t
h
e
mo
v
i
n
g pl
a
t
f
o
r
m t
r
a
n
s
mi
t
s t
o t
h
e l
i
mbs
Fx,凡—
x a
n
d y c
o
mp
o
n
e
n
t
s o
f t
h
e
pl
a
t
f
or
m
(
d, , 0 )
-
Th
e p
o
s
i
t
i
o
n o
f p
i
v
o
t B
(
a, b -
)
Th
e p
o
s
i
t
i
o
n o
f p
i
v
o
t C
1
,,1
2,1
3 -
Th
e l
i
mb l
e
n
g
t
h
s
, i
.
e
.
1
,='
A
D,1
2 =1
B
E, 1
3 =1
C
C. Re
f
e
r
r
i
n
g t
o F
i
g
u
r
e l
,
t
h
e l
i
mb l
e
ng
t
hs a
r
e r
e
ga
r
d
e
d a
s pos
i
t
i
v
e
, a
nd a
s
n
e
ga
t
i
v
e s
h
o
wn i
n Fi
gu
r
e 2.
2
.
2 I
nv
e
r
s
e s
t
a
t
i
c a
na
l
ys
i
s
Th
e me
c
h
a
n
i
s
m be
i
n
g a
n
a
l
y
z
e
d h
e
r
e h
a
s t
wo
i
nd
e
pe
nde
n
t l
oops
. The f
our s
c
al
a
r l
o
op-
cl
os
ur
e
一 723一
1
, C
O
S
0
1 +d2 C
O
S
么一1
2 c
o
s
凡一d,=0
1
1 s
i
n瑞+d2 s
i
n氏一1
2 s
i
n仇=0
1
, s
i
n B
, +d2 s
i
n
(
B
4 +;
r
/
3
)
一1
3 s
i
n 0
3一b=0
(l) (2)
equa
t
i
ons of t
h
e me
c
ha
ni
s
m a
r
e a
s f
ol
l
ows
。
+ k
, (
B
1 1
,
-
0
1
o
) s
i
n B
・
k
2 (
B
2 -
8
2
已s
i
n
1
, C
O
S
0
1 +d
2 C
o
s
(
B
4+刁3
)
一1
3 C
O
S
0
3一a=0 (
3)
凡
F2=
F3=
k3 (
B:一03
0)C
O
S
热=0(
1
4
)
1
2
1
3
k
1 (
B
1 -
0
1
0
) s
i
n
(
2
a
i
3
一
8
, +
8
4
’
十
(5)
k
2 (
B
2一0
2
0 )
s
i
n
(
B
2一04一刁3
) +
1
,
(6)
1
,
k
3 (
B
3一0
3
0
)
C
O
S 0
1一
些鱼竺业C
o
q
1
,
k
2 (
B
2一0
2
0 )
1
,
k
, (
B
,一0
1
0
)
1
1
T
h
e e
q
ui
l
i
b
iu
r
m o
f t
h
e mo
me
nt
s a
bo
u
t t
h
e
g
r
o
un
d
e
d pi
vo
t o
f e
a
c
h l
i
mb y
i
e
l
d
s
:
F,=
s
i
n仇 =0
l
2
1
, s
i
n B
, +d2 s
i
n
(
B
4 +)
r
/
3
)
一1
3 s
i
n 0
3一b二0 (
4)
k
1 (
B
1一0
1
0
)
k
3 (
B
3一0
3
0
)
k
, (
B
3一01
0 )
s
i
n
(
氏一么)=0
1
,
(7)
1
3
wh
e
r
e 1
,
,1
2 a
n
d 1
3 d
e
s
c
r
i
b
e
d b
y Eq
u
a
t
i
o
n
s (
1
1
)
,
Th
e e
q
u
i
l
i
br
i
um e
q
ua
t
i
o
n
s o
f t
he mo
v
i
n
g
pl
a
t
f
o
r
m a
r
e:
(
1
2) a
nd (
1
3
)
Th
e Eq
ua
t
i
on
s (
1
4
) d
e
s
c
r
i
b
e t
h
e s
t
a
t
i
c
s o
f t
he
凡 =F, c
o
s B
,+凡c
o
s 0
2 +F3 c
o
s t
9
3 (
9)
f
o
u
r u
n
k
n
o
wn
s〔巩,仇,仇,氏 ) W hen the
n
s
t
t
u
c
t
i
v
e p
a
r
a
me
t
e
r
s (
0
1
0, 0
2
0,0
3
0,k
,
,k
2,
(
1
0
)
棍
F
, s
i
n
(
2
,
r
/
3
一
0
1 +
0
4
)
+F
2 s
i
n
(
0
2
一
co
Fx =-F, s
i
n B
,一F, s
i
n 02一F3 s
i
n 0
3 (
8)
me
c
h
a
ni
s
m a
n
d r
e
p
r
e
s
e
n
t a c
o
u
pl
e
d s
y
s
t
e
m o
f f
o
u
r
n
o
n
-
l
i
ne
a
r eq
ua
t
i
o
n
s wi
t
h t
r
i
go
n
o
me
t
r
i
c f
un
c
t
i
o
ns i
n
氏一刁3
)
十凡s
i
n
(
氏一热)=。
S
o
l
vi
n
g Eq
ua
t
i
o
ns (
1
) a
nd (
2) s
i
mu
l
t
a
n
e
o
us
l
y,
we have
d,
,d2, a b ) a
n
d t
h
e e
x
t
e
na
r
l l
o
a
d ( Fx , F) a
r
e gi
v
e
n, t
h
e s
o
l
u
t
i
o
n
s o
f Eq
ua
t
i
o
n
s (
1
4) c
a
n
c
o
mp
l
e
t
e
l
y d
e
t
e
r
mi
n
e t
h
e e
q
u
i
l
i
b
r
i
u
m c
o
n
f
i
g
u
r
a
t
i
o
n
s
o
f t
he me
c
ha
ni
s
m.
一
-
-
-
2
了之
d, s
i
n B
,一d2 s
i
n
(
B
,一0
4
)
s
i
n
(
热一伏)
(11)
3 I
ni
t
i
a
l Co
nf
i
gu
r
a
t
i
ons
(12)
Subs
t
i
t
ut
i
ng Equa
t
i
on (
1
1
) i
nt
o Eq
ua
t
i
on (
3)
, we
ge
t
d, s
i
n 0
2一d2 s
i
n
(
B
2一04
).
c
o
s
鱼+
s
i
n
(
B
2一0
1 )
c
o
s
热
(
1
3)
d2 c
o
s
(
氏+刁3
)
一a
l
,=
Wh
e
n F二0,巩=马。,热=仇。a
n
d仇=
t
h
e me
c
ha
n
i
s
m l
i
e
s i
n i
t
s unl
o
a
d c
o
n
f
i
gu
r
a
t
i
on
t
hi
s c
a
s
e 氏。 ma
y be d
e
t
e
r
mi
n
e
d from
际Forthe
l
子.
d
, s
i
n 0
2一d
2 s
i
n
(
B
2一0
4
)
s
m(
热一风)
f
ol
l
o
wi
n
g e
q
ua
t
i
o
n d
e
r
i
v
e
d f
r
o
m t
h
e l
o
o
pequat
ions
:
C, s
i
n断 +C c
o
s
翰 +C =0
(15)
wher
e
c
os氏
S
u
bs
t
i
t
u
t
i
n
g Eq
u
a
t
i
o
ns (
5
)
, (
6
)
, (
7) i
n
t
o
Eq
u
a
t
i
o
n
s (
8
)
, (
9
) a
n
d (
1
0
)
, t
og
e
t
h
e
r wi
t
h Eq
ua
t
i
o
n
(
4
) c
o
n
s
t
i
t
u
t
e t
h
e f
o
l
l
o
wi
ng f
o
u
r c
o
u
pl
e
d e
q
u
a
t
i
o
n
s
:
一 724-
C
,
一
d
2
暗
・
零t
a
n 0
3
0
・
c
o
s O
2
0 (
s
i
n B
j
o -
c
o
s B
i
o t
a
n 0
3]
sui
t
口2
0一伪 of
石-
2
C2=
‘
合
t
a
n 0
3
,
-
F(
x
)=(
t
i (
x
)
,
几(
x
)
,
一了 =0
s
i
n 0
2
0 (
s
i
n 0
,
0 - c
o
s B
t 0 t
a
n 0
3
, ) 1
s
i
n
(
姚。一佑。)
i
n 0
2
0 (
s
i
n B
,
o -
c
o
s B
,
0 W0
3
0
) +
C3 =d,s
s
i
n
(
0
2
。一0
1
0)
a t
a
n已。一b
(
1
6)
wh
e
r
e x=(
00
2
,
二了 .T
h
e s
o
l
v
i
n
g p
r
o
c
e
s
s
p
r
e
s
e
n
t
e
d i
s o
u
t
l
i
n
e
d a
s f
ol
l
o
ws
:
(
1
) S
p
e
c
吻 t
h
e n
u
me
r
i
c
a
l p
r
e
c
i
s
i
o
n ‘,t
h
e
a
l
l
o
wa
bl
e i
t
e
r
a
t
i
o
n c
yc
l
e
s N;
Th
e
n t
he l
i
mb l
e
n
g
t
h
s c
a
n b
e o
bt
a
i
n
e
d t
h
r
o
u
gh
(
2
) Di
v
i
d
e t
h
e v
a
r
i
a
b
l
e
s x i
n
t
o s
ma
l
l s
e
g
me
n
t
s i
n
s
u
b
s
t
i
t
u
t
i
n
g B
,二0
1
0, 02 = 0
2
0, 0
3 = 0
3
0
t
h
e s
p
e
c
i
f
i
e
d i
n
t
e
r
v
a
l
s
, we g
e
t di
s
c
r
e
t
e poi
n
t
s o
f x
0,=04
, i
n
t
o Eq
ua
t
i
o
ns (
1
1
)
, (
1
2) a
nd (
1
3
)
.
a
s t
h
e i
n
i
t
i
a
l v
a
l
u
e
s o
f i
t
e
r
a
t
i
o
n x
1
0
1
;
(
3
) E
v
a
l
u
a
t
e F(
xt
k
i
), (
k=0
,
1
,
2
,
二.
).I
f
4 So
l
ut
i
on of Tr
a
ns
c
e
nd
e
nt
a
l Equa
t
i
ons
Eq
u
a
t
i
o
n
s (
1
4
) a
n
d (
1
5
) a
r
e t
h
e t
r
a
ns
c
e
nd
e
n
t
a
l
e
q
u
a
t
i
o
n
s wi
t
h t
r
i
g
on
o
me
t
r
i
c f
u
nc
t
i
o
n
s
. I
n g
e
n
e
r
a
l
,
i
t
er
a
t
i
ve met
hods ar
e us
ed t
o r
es
ol
ve t
r
ans
cende
nt
al
eq
ua
t
i
ons
. Ho
we
ve
r
, t
he i
t
er
a
t
i
ve me
t
hod n
e
ed
s t
he
i
ni
t
i
al val
ues and t
he s
el
ect
i
on of t
hos
e i
s r
a
t
her
di
f
f
i
c
ul
t
. Th
e s
ol
ut
i
on of t
he t
r
a
ns
c
e
nde
n
t
a
l
e
q
u
a
t
i
o
n
s wi
t
h t
r
i
go
n
o
me
t
r
i
c f
u
n
c
t
i
o
ns i
s r
a
t
h
e
r
t
r
o
u
bl
e
s
ome a
l
t
h
ou
g
h t
h
e d
e
gr
e
e o
f e
q
ua
t
i
o
ns i
s
l
o
we
r
. S
ome p
r
o
c
e
d
u
r
e
s o
f e
q
u
a
t
i
o
n ma
n
i
pu
l
a
t
i
o
n,
s
uc
h as t
he i
de
nt
i
c
al t
r
a
ns
f
o
r
m a
nd el
i
mi
na
t
i
o
ns
,
ma
y b
r
i
n
g a
b
o
u
t u
n
d
e
s
i
r
a
bl
e c
o
n
s
e
q
u
e
n
c
e
s
, s
i
n
c
e i
t
ma
y l
e
a
d t
o f
i
n
a
l e
q
ua
t
i
on
s t
h
a
t d
o no
t r
e
c
o
g
ni
z
e
s
o
me c
o
n
f
i
g
u
r
a
t
i
o
ns a
s s
o
l
u
t
i
o
n
s o
r r
e
ga
r
d s
ome
o
t
h
e
r
s a
s s
ol
u
t
i
o
n
s wh
i
l
e t
h
e
y a
r
e n
o
t
. So t
h
e pr
o
c
e
s
s
o
f s
ol
u
t
i
o
n t
e
s
t i
s n
e
c
e
s
s
a
y, r
a
n
d t
h
e s
ol
ut
i
o
n
pr
oc
edur
e i
s r
a
t
h
er t
i
r
es
ome.
I
n t
hi
s ar
ti
cl
e a mor
e conveni
ent met
hod i
s
pr
e
s
e
n
t
ed bas
ed on t
he Ne
wt
on'
s i
t
e
at
r
i
ve me
t
hod,
whi
c
h c
a
n wor
k o
u
t a
l
l t
h
e r
e
a
l r
o
o
t
s of t
h
e s
ys
t
e
m
o
f t
r
a
ns
c
e
n
d
e
n
t
a
l e
q
u
a
t
i
o
n
s wi
t
h t
r
i
g
o
no
me
t
ic
r
f
unct
i
ons wi
t
hout i
ni
t
i
al val
ue s
el
ect
i
on i
n t
he
s
p
e
c
i
f
i
e
d i
n
t
e
va
r
l
s t
o d
e
t
e
c
t t
h
e e
n
t
i
r
e s
e
t o
f
c
o
n
f
i
g
u
at
r
i
o
n
s o
f t
h
e r
o
bo
t
, a
n
d a
v
o
i
d pr
o
d
uc
i
n
g
I
F
(
x
(
k
'
)
N
<
二
,
d
e
t
e
c
t t
h
e s
a
m
e x
(
k
) e
x
i
s
t
s i
n t
h
e
s
e
t o
f s
o
l
u
t
i
o
n
s o
r n
o
t
. I
f n
o
t
, t
h
e
n x(
"
} i
s a n
e
w
s
ol
u
t
i
o
n a
n
d o
u
t
p
ut
t
e
d t
o t
h
e s
e
t o
f s
ol
u
t
i
o
n
s
, t
ur
n t
o
s
t
e
p (
2
)
;
(
4
) I
f t
h
e i
t
e
r
a
t
i
o
n c
yc
l
e
s n? N ,
t
u
r
n t
o s
t
e
p (
2
)
;
(
5
) I
f F'
(
x(
k
)
) i
s n
o
n
s
i
n
g
u
l
a
r
, e
v
a
l
u
a
t
e
x
(
k
.
t
)
二x (
k
)
一F(
x
(
k
)
)
一
,
F(
x (
k
) ).I
f x(
k
"
) l
i
e
s
i
n
s
i
d
e t
h
e i
n
t
e
va
r
l
s
, t
h
e
n x (
k
) =x
(
k
.
u,
t
u
r
n t
o s
t
e
p
(
3)
;
(
6
) Re
p
e
a
t s
t
e
p
s (
1
) t
h
r
o
u
g
h (
5
) u
n
t
i
l a
l
l t
h
e
d
i
s
c
r
e
t
e po
i
n
t
s o
f x h
a
ve b
e
e
n us
e
d. Th
e r
e
s
ul
t
a
n
t
s
e
t o
f s
o
l
u
t
i
o
n
s i
s r
e
g
a
r
d
e
d a
s a
l
l t
h
e r
e
a
l r
o
o
t
s o
f t
h
e
s
ys
t
e
m o
f t
r
a
ns
c
e
n
d
e
n
t
a
l e
q
u
a
t
i
o
n
s wi
t
h
t
r
i
go
no
me
t
r
i
c f
u
n
c
t
i
o
n
s i
n t
h
e s
p
e
c
i
f
i
e
d i
nt
e
va
r
l
s
.
Th
e a
b
o
v
e me
t
h
o
d i
s s
u
p
e
r
l
i
n
e
a
r c
o
nv
e
r
ge
nc
e
,
a
n
d c
a
n e
a
s
i
l
y b
e i
mpl
e
me
n
t
e
d wi
t
h c
o
mpu
t
e
r
s
. Thi
s
numer
i
cal met
hod c
an wor
k out al
l t
he r
eal r
oot
s of
t
h
e s
y
s
t
e
m o
f t
r
a
n
s
c
e
n
d
e
n
t
a
l e
q
u
a
t
i
o
ns wi
t
h
t
r
i
go
n
ome
t
r
i
c f
u
nc
t
i
o
n
s wi
t
ho
u
t i
n
i
t
i
a
l va
l
u
e
s
e
l
e
c
t
i
o
n i
n t
h
e s
p
e
c
i
f
i
e
d i
n
t
e
va
r
l
s
.
e
xt
r
a
neous or l
os
s s
ol
ut
i
ons
.
Si
n
c
e t
h
e s
o
l
u
t
i
o
ns o
f t
h
e p
r
o
bl
e
m d
e
s
c
r
i
be
d b
y
n
ec
es
s
a
y r
t
o e
s
t
a
bl
i
s
h t
he i
n
t
e
va
r
l
s i
ns
i
de whi
c
h t
he
s
ol
ut
i
on s
ear
c
h mus
t be under
taken. Consi
der t
he
p
r
o
bl
e
m o
f s
e
a
r
c
h
i
n
g a
l
l z
e
r
o
s o
f t
h
e t
r
a
n
s
c
e
n
d
e
nt
a
l
e
q
u
a
t
i
o
n
s wi
t
h t
r
i
go
n
o
me
t
r
i
c f
u
nc
t
i
o
n
s a
s f
ol
l
o
ws
As a
n e
xampl
e, a
s
s
ume f
or t
h
e pa
r
a
met
er
s t
h
e val
ue
s
= 0.
5 a=0
.
5, n=1,丸二1
d, =1
,棍 =l
,
内 氏
Equa
t
i
ons (
1
4) a
nd (1
5) a
r
e a co
un
t
a
bl
e i
nf
ni
i
t
e, i
t i
s
5 Numer
i
cal Exampl
e
k3=1
=二
a
27
r
7汇
, ana for
a
a
g
o一丁 ,U
3
0= — t
h
e e
x
t
e
na
r
l f
o
r
c
e
s F =1
,凡 二
一 725-
(
r
a
d )
1
1
] 巩 (rad) 热 (rad) 马 (rad) By }
I
.
0
4
5
7
8
4
6}
12
.
2
3
1
9
9
2
2}
12
.
3
1
4
0
6
7
6 2
] 1.652975512
.
6
6
9
4
7
7
7}
13
.
4
0
5
6
0
5
1}
11
.
9
6
5
7
8
6
4
1_
,。,
,
。
,
;}
.
4
0
9
1
6
9
0}
10
.
9
9
4
2
7
6
5}1
.
9
7
8
4
0
4
0一
口 4.4112156 10
I
1
.
1
8
4
2
7
7
3}
1一
1
.
6
8
8
9
3
0
5}
.
7
6
9
9
8
5
4}
10
.
7
1
6
0
3
8
9}1
.
4
9
3
1
4
4
5一
口 1.240044512
I-
0
.
1
1
5
5
3
5
6 1
.
0
7
1
8
9
6
1}
I
一
,
t
2
5
9
0
4
0
8
.
7
8
7
7
3
8
4}
11
.
6
5
9
2
3
4
7}1
口 4.2663029 14
.
6
3
1
4
0
0
0一
I-
1
.
9
8
7
0
2
9
8}-
2
.
2
9
8
1
8
7
3 1.0198843
.
9
9
9
6
0
9
2}
口 1.3824119 14
12
.
0
5
9
6
3
8
8}1
.
7
7
7
0
7
9
1一
I2
.
0
0
6
2
4
2
7}-
2
.
5
6
5
2
3
2
5}1
.
2
7
6
2
3
3
7
5
.
1
8
8
1
1
1
7}
口 2.3103089 I I1
.
8
5
0
8
0
8
6}1
.
5
2
1
5
3
6
1{
1
1
-
2
.
4
4
8
2
6
2
5 1
.
4
7
2
9
2
6
7}
1
-
2
.
6
4
0
5
9
6
8
门 4.4735981 1
.
7
8
8
2
9
2
5}
11
.
8
3
7
4
6
1
2}2
.
0
6
7
4
7
1
7}
1-
2
.
5
2
8
7
7
5
5}
12
.
9
6
6
4
9
4
7}
11
.
5
2
4
3
5
9
5
国 5.4744796 5
.
0
0
2
4
9
3
4}2
.
1
6
7
5
8
6
1}
14
.
1
3
2
8
2
8
0 3
.
0
1
8
0
8
9
4}
I
-
4
.
4
3
2
9
1
6
5
.
2
6
0
4
2
3
012
同 2.7956667 1
.
6
1
1
3
8
1
8},
0
3
6
8
5
5
2-
0
.
8
2
8
9
4
7
2}0
.
1
5
3
2
2
4
6}
1
-
0
.
8
4
6
1
9
0
8
.
3
4
4
9
8
2
811
.
0
0
0
9
1
9
40
.
9
4
5
8
2
1
4}0
国 2.1066861!6
.
5
7
3
0
5
3
9一
1一
。
.
1
4
4
6
2
0
1}-
0
.
5
2
6
8
8
1
9}
1
-
0
.
7
7
0
6
2
2
6
同 24161775!5
.
8
3
9
6
0
9
34
.
0
5
0
1
7
6
1}0
.
9
1
6
2
0
5
9一
}-
0
.
2
1
4
7
8
7
7}-
0
.
5
9
2
1
8
3
4 0.8629393
同 6.2491286 !1
.
1
2
2
5
5
2
6 1
.
9
9
2
6
0
8
9}
12
.
5
0
3
9
1
7
9一
I1
.
5
2
0
8
6
3
9}0
.
2
7
2
8
3
1
9}
1
一
,
.
3
7
1
0
4
5
8
国 5.5210033' 6
.
0
1
6
2
8
1
7}1
.
1
3
1
4
2
8
4}0
.
9
0
2
7
3
7
4一
I0
.
4
1
3
5
6
8
2}
}
-
0
.
4
0
5
4
7
8
7}
I
-
0
.
9
0
7
2
4
7
2
国 15.
.
2
1
5
2
9
8
1}1
.
3
8
0
3
9
2
1}
{0
.
8
3
2
1
4
4
6I 0
.
6
1
2
0
2
2
6}
10
.
1
8
6
8
5
0
6}
1
-
0
.
9
2
3
7
5
4
1
6
0
6
0
9
7
713
.一‘,
,尹-11了J }
.
Ta
bl
e 2
. So
l
ut
i
on
s o
f t
he e
qui
l
i
br
i
um c
o
nf
i
g
ur
a
t
i
o
ns
5.
1 I
ni
t
i
a
l c
o
nf
i
gur
a
t
i
o
ns o
f t
he r
o
bot
We o
b
t
a
i
n t
wo r
e
a
l r
o
o
t
s b
y s
o
l
v
i
n
g Eq
u
a
t
i
o
n (
1
5
) i
n
t
h
e i
n
t
e
r
v
a
l
s [
0
,
2
,
r
] f
o
r 0
4
,,t
h
e
n t
h
e
c
o
r
r
e
s
po
n
d
i
n
g l
i
mb l
e
n乡h
s c
a
n b
e go
te
n f
r
o
m
Eq
u
a
t
i
o
n
s (
1
1
)
, (
1
2
) a
nd (
1
3
)
, a
s l
i
s
t
e
d i
n Ta
bl
e 1
.
Th
e t
wo i
ni
t
i
a
l c
o
n
f
i
gu
r
a
t
i
o
n
s o
f t
h
e r
ob
o
t a
r
e
i
l
l
u
s
t
r
a
t
e
d i
n Fi
g
u
r
e 3.
0
,
(rod)
Sol
ut
i
on
1
Sol
ut
i
on
2
3.
6652
1
1
1
2
1.
41
42 0.
8660
c
or
r
e
s
po
n
di
n
g l
i
mb l
e
n
gt
h
s
. Re
s
ul
t
s a
r
e l
i
s
t
e
d i
n
Ta
bl
e 2. Th
e p
os
i
t
i
o
ns a
n
d o
r
i
e
n
t
a
t
i
o
n
s o
f t
h
e
mo
vi
ng pl
a
t
f
o
r
m i
n t
h
e pl
a
n
e (
x,
y) a
r
e s
h
o
wn i
n
Fi
gu
r
e 4 by t
hos
e of t
he s
i
de DE.
D,
l
,
s,
G,
0.
7071
G,
岛
5.
9378
0.
5624 0.
3953
2637 0.
及
Ta
bl
e l
. So
l
ut
i
o
ns of t
he i
ni
t
i
a
l c
o
nf
i
gu
r
a
t
i
o
ns
'
V一
一一,
-
A 0.
7
5.
2 Equi
l
i
br
i
um c
o
nf
i
g
ur
a
t
i
ons of t
he r
obot
Th
e s
ol
ut
i
o
n
s o
f Eq
ua
t
i
o
n
s (
1
4
) c
a
n c
o
mpl
e
t
e
l
y
d
e
t
e
r
mi
n
e t
h
e e
q
ui
l
i
br
i
u
m c
o
n
f
i
g
u
ra
t
i
o
ns ofthe
r
obot under t
he ext
er
nal l
oa
ds
. Sol
ut
i
ons
gh
t
son
r
n
e
dBZ
1
0
,
川 f
o
rB, a
ng t
o
[
0
,
4
z
/
3
] f
o
r B
3
,
a
n
d[
0
, v
c
] f
o
r 0
4Accordi
f
or i
n t
he i
nt
er
val
s
t
he n
umer
i
ca
l me
t
hod me
nt
i
one
d a
bo
ve
, we ob
t
ai
n
a
l
l t
h
e 1
4 r
e
a
l r
o
o
t
s o
f Eq
ua
t
i
o
n
s (
1
4) a
nd t
h
e
-
一 -一,
一一一入三一一 二
口A "j
.一
Fi
gur
e 3. The t
wo i
ni
t
i
a
l c
o
nf
i
g
ur
at
i
o
ns of t
he r
obo
t
6 Concl
us
i
ons
Co
mpl
i
a
n
t pa
r
a
l
l
el r
o
bo
t
s a
r
e a n
o
v
e
l c
l
a
s
s o
f r
o
b
o
t
s
.
Th
e u
s
e o
f le
f
x
i
bl
e me
mb
e
r
s t
o ga
i
n mo
bi
l
i
t
y h
a
s
b
r
o
u
g
ht no
t
a
bl
e a
d
va
n
c
e
s i
n t
h
e r
o
b
o
t d
e
s
i
gn
. Th
e
r
ob
o
t
s wi
t
h le
f
x
ur
al pi
vo
t
s r
e
l
y o
n t
he d
e
le
f
c
t
i
o
n o
f
一 726-
fe
l
xi
bl
e me
mb
e
r
s
, e
n
e
r
g
y i
s s
t
o
r
e
d i
n t
h
e f
o
r
m o
f
s
t
r
a
i
n e
n
e
r
g
y wi
t
hi
n t
h
e c
o
mpl
i
a
n
t me
mb
e
r
s
. Thi
s
s
t
o
r
e
d e
n
e
r
gy i
s s
i
mi
l
a
r t
o t
h
e s
t
r
a
i
n e
n
e
r
g
y i
n a
d
e
le
f
c
t
e
d s
p
r
i
n
g, a
nd t
h
e e
fe
c
t
s o
f s
p
r
i
n
g
s a
r
e
i
n
t
e
g
r
a
t
e
d i
n
t
o ac
omp
l
i
a
n
t r
o
bo
t
'
s d
e
s
i
gn. I
n t
hi
s
ma
n
n
e
r
, e
n
e
r
gy c
a
n e
a
s
i
l
y b
e s
t
o
r
e
d o
r t
r
a
ns
f
o
r
me
d,
Ac
kno
wl
e
dg
me
n
t
s
Thi
s r
e
s
e
a
r
c
h i
s s
po
n
s
o
r
e
d by t
h
e S
ha
a
n
xi Pr
o
vi
n
c
i
a
l
t
o be r
e
l
e
as
e
d i
n a di
fe
r
e
n
t ma
nne
r
. Thi
s a
ti
r
c
l
e ha
s
Re
f
e
r
ence
s
a
d
d
r
e
s
s
e
d t
h
e e
q
ui
l
i
br
i
um c
o
n
f
i
g
u
r
a
t
i
o
ns o
f t
h
e
pl
a
n
a
r pa
r
a
l
l
e
l r
o
bo
t wi
t
h le
f
x
ur
a
l pi
v
o
t
s o
n
c
e t
h
e
e
x
t
e
na
r
l l
o
a
d i
s ss
a
i
g
n
e
d. Th
e r
e
s
ul
t
s i
n
di
c
a
t
e t
h
e
e
q
ui
l
i
b
r
i
u
m c
o
n
igu
f
r
a
t
i
o
n
s o
f c
o
mpl
i
a
nt r
o
b
o
t
s a
r
e
l
. Gou
g
h V. E,Co
n
ri
t
b
ut
i
o
n t
o di
s
c
us
s
i
o
n of pa
pe
r
s o
n
mul
t
i
-
s
t
a
bl
e.
Na
t
u
ral Sc
i
e
nc
e Founda
t
i
on of Chi
na (
Gr
a
nt No
2
0
0
3
E3
4
) a
n
d s
u
p
p
o
te
r
d b
y t
h
e Yo
u
t
h S
c
i
e
n
t
i
f
i
c
Res
e
ar
c
h Wor
ks
t
a
t
i
on of Xi
di
a
n Uni
ve
r
s
i
t
y.
r
e
s
e
a
r
c
h i
n a
u
t
o
mo
t
i
v
e s
t
ab
i
l
i
t
y
, c
o
n
rol t
a
n
d t
y
r
e
p
e
r
f
or
ma
n
c
e
, I
n: Pr
oc
. Aut
o Di
v
. I
n
s
t Me
c
h
a
n
i
c
al
En
gi
ne
e
r
s
, 39
2
-
3
95
, 1
9
5
6
2. S
t
e
wa
r
t D.
, A p
l
a
t
f
o
r
m wi
t
h 6 de
g
ee
r
s of f
r
e
e
do
m, I
n:
Pr
oc
. o
f t
h
e I
n
s
t
i
t
u
t
e o
f Me
c
ha
n
i
c
a
l En
gi
ne
e
r
i
n
g, Lo
n
d
o
n
,
UK, 1
8
0
(
p
a
r
t 1
, 1
5
)
: 371
-
38
6, 1
9
6
5
y 4
、亡、见
I
n: Pr
oc
. o
f 1
8
t
h I
n
t
. S
ymp. o
n I
n
du
s
t
r
i
a
l Ro
b
o
t
, La
us
a
n
ne
,
|
乌
D
\乌
3. Cl
a
v
e
l R.
, DEL
T
A, a f
a
s
t r
o
bo
t wi
t
h p
a
r
a
l
l
e
l g
e
ome
t
r
l
91
-
1
00, 1
988-
4. Ry
u S. J
. a
n
d Ki
n J
. W. e
t a
l
, Ec
l
i
p
s
e
: a
n o
v
e
r
a
c
t
u
a
t
e
d
p
a
al
r
l
e
l me
c
ha
n
i
s
m f
or ap
r
i
d ma
c
hi
n
i
ng
, AS
ME I
n
t
.
681
-
689,1
998
5
. Ka
n
g B. a
nd Ch
u J
. e
t a
l
, De
s
i
g
n of h
i
g
h s
p
e
e
d p
l
a
na
r
p
a
r
a
l
l
e
l ma
n
i
pu
l
a
t
o
r a
n
d mul
t
i
pl
e s
i
mu
l
t
a
ne
o
u
s
! 氏
马 、、巧
-
1
Me
c
h
a
ni
c
a
l En
gi
n
e
e
r
i
n
g Con
gr
e
s
s an
d Ex
po
s
i
t
i
o
n,
s
pe
c
i
ic
f
a
t
i
o
n c
o
n
t
ol
r
, I
n: Pr
oc
. o
f t
h
e 20
01 I
EEE I
n
t
. Con
.
-
2
o
n Ro
bo
t
i
c
s &Au
t
o
mat
i
o
n, Ko
r
e
a
, 2
7
23-
2
7
28
, 2
0
01
\
DB
6
. Hi
n
kl
e
y D.
, A mu
l
t
i
f
unc
t
i
o
na
l le
f
xu
r
e b
i
n
g
e f
o
r
d
e
pl
o
yi
n
g o
mn
i
di
r
e
c
t
i
o
n
a
l s
o
l
a
r a
r
ays
r
, I
n: 4
2
n
d AI
AA
1
AS
ME/
ASCEI
AHS
I
ASC St
r
u
c
t
u
r
e
s
, S
t
r
u
c
t
u
r
a
l Dyn
ami
c
s
0 1 2 3 4
a
n
d Ma
t
e
r
i
al
s Co
n
f
e
r
e
n
c
e a
nd Ex
hi
b
i
t
, Se
a
t
t
l
e
, WA, 1
书,
2001
F
i
gur
e 4
. Th
e e
qui
l
i
br
i
um c
o
nf
i
gur
at
i
o
ns of t
he
7. LI Tu
a
n-
pe
, An
a
l
ys
i
s o
n t
he s
t
r
u
c
t
ur
a
l t
o
pol
o
gi
c
a
l
mov
i
ng pl
a
t
f
o
r
m
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s a
n
d t
he mo
bi
l
i
yo
t
f c
o
mpl
i
a
n
t me
c
h
a
n
i
s
ms
,
Me
c
h
a
ni
c
a
l Sc
i
e
n
c
e a
nd T
e
c
h
no
l
o
g
y, 22
(
1
)
: 1
0
7-
1
0
9
, 2
00
3
一 727一