Parallel Manipulators New Developments Part 1 docx
Parallel Manipulators New Developments Part 1 docx
...
yxE
∑
=
⎟
⎠
⎞
⎜
⎝
⎛
++=
j
jj
rrmIp
[
]
N
6
11 8
rp
=
[
]
kgm r
6
1
B3z9
zE
∑
=
+=
j
j
msp
[
]
-1
219
Nsm
1
rp =
[
]
kg 6
3E10
mmp
+
=
[
]
-1
220
Nsm
2
rp =
[
]
-1
2 21
Nsm
3
rp =
[
]
-1
222
Nsm
4
rp =
[
]
-1
223
Nsm ...
[
]
2
zzyyzz1
kgm
3 21
IIIp ++=
[
]
N
11
α
rp =
[
]
2
zzyyxxxx2
kgm
3232
IIIIp −−+=
[
]
N
12
β
rp
=
[
]
2
yyzz3
kgm
32
I...
Parallel Manipulators New Developments Part 14 docx
... zero, as shown in Fig. 4.
P
A
1
B
1
C
1
A
1
B
1
A
1
P
B
1
C
1
PC
1
Parallel Manipulators, New Developments
382
23456
( ) 30.496 15 4.909 311 .14 8 265.753 81. 318 stttttt=− + − +
(37)
Figure ... 5 5
M
m
g
I
=
+ (A9)
2
1 2 1 2 11 515 3 1 3
2( ) sin( )Rm g mg
ζζ
θ
ζ
θθθβ
=−+ −−
mg m g m g
ζ
ζθ
++ −+
11 2 1 2 51 1
[()]cos
(A10)
222
255...
Parallel Manipulators New Developments Part 16 pot
... uncertainties.
012 3456
-3
-2
-1
0
1
2
3
4
Roll Pitch Yaw
Angle errors [deg]
Time [sec]
012 3456
-2
-1
0
1
2
3
Surge Sway Heave
Position errors [mm]
(a) PIDE
012 3456
-3
-2
-1
0
1
2
3
4
Roll ... errors [deg]
Time [sec]
012 3456
-2
-1
0
1
2
3
Surge Sway Heave
Position errors [mm]
012 3456
-3
-2
-1
0
1
2
3
4
Roll Pitch Yaw
Angle errors [deg]
Time [sec]
0...
Parallel Manipulators New Developments Part 17 pptx
... a new
Type Design of Decoupled Parallel Manipulators with Lower Mobility
487
x
y
z
z
A
y
A
x
A
a
01
a
02
a
03
A
1
M
11
M
11
'
M
12 M
12
'
M
13
M
14
l
11
l
12
θ
1
θ
2
θ
3
M
21
M
21
'
M
22
M
22
'
l
21
l
22
M
23
M
24
M
34
A
2
A
3
M
31
M
31
'
M
32
'
M
32
M
33
l
31
l
32
z
B
x
B
p
y
B
o
...
-0 .1
0
0 .1
-0 .1
0
0 .1...
Parallel Manipulators New Developments Part 2 pot
... matrix form (1) or by twists
in
33
VV × , where addition and the Lie bracket are defined as follows:
),(=),(),(
2 211 2 211 22 211 1
bkbkkkbkbk +++
ωωωω
,
),,(=)],(),,[(
12 212 12 211
bbbb ×−××
ωωωωωω
... at time (k +1) T, where k
is discrete time index and T is sampling time, respectively.
∑
∑
∑
f
f
f
u
1
u
2
u
3
q
3
(k +1) T
b
1
1
b
2
1
b
3
1
q
2
(k +1) T
q
1
(k +1) T
z...
Parallel Manipulators New Developments Part 3 pot
... ISBN 08 218 27359, New York, Russian translation
Karger, A. (19 88). Geometry of the motion of robot manipulators. Manuscripta mathematica.
Vol. 62, No. 1, March 19 88, 1- 130, ISSN 0025-2 611
Karger, ...
i
i
r
w
1
=
(5)
Figure 11 : Two links coupled by a revolute joint
Parallel Manipulators, New Developments
52
the vector
2
m is perpendicular to the plane
ξ
....
Parallel Manipulators New Developments Part 6 pot
... 7 10 0 72 78 18 .03 22. 21 13.45
70 X 7 10 0 85 93 26.07 30 .18 15 .68
80 X 8 10 0 96 10 8 32.09 39.43 17 .13
90 X 8 10 0 11 9 13 4 39. 01 51. 19 19 .86
10 0 X 8 10 0 13 2 14 2 45 .15 63.05 18 .94
12 0 X 8 10 0 ...
60 X 7 10 0 756.4 9 21. 2 28.07 34 .15 11 .30
70 X 7 10 0 890.0 10 56.7 32. 71 44 .19 12 .47
80 X 8 10 0 10 18 .1 1263.6 39.03 48.22 15 . 21
9...
Parallel Manipulators New Developments Part 7 potx
...
()
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
⋅
=
=
⋅−=
11
22
1
223 211
12 1
,2atan
θ
θ
c
rd
b
rr
rdca
()
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
⋅
=
=
⋅−=
12
33
2
3 313 12
232
,2atan
θ
θ
c
rd
b
rr
rdca
()
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
⋅
=
=
⋅−=
13
11
3
11 211 3
313
,2atan
θ
θ
c
rd
b
rr
rdca
...
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
10 0
010
0 01
1
R
O
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
0 01
100
010
2
R
O
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
010
0 01
100
1
R...
Parallel Manipulators New Developments Part 12 ppt
...
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
+−+−
−−−−
=
11
p
13
p
10
p
13
p
11
p
12
p
14
p
8
p
9
p
13
p
10
p
12
p
14
p
7
p
9
p
12
p
14
p
13
p
12
p
11
p
12
p
10
p
12
p
9
p
12
p
7
p
14
p
8
p
12
p
7
p
13
p
14
p
13
p
12
p
2
M
0
0
Clearly ... Proceedings of 19 94 IEEE International
Parallel Manipulators, New Developments
342
−
⎡
⎤
⎢
⎥
+− −
=
⎢
⎥
−...
Parallel Manipulators New Developments Part 13 ppt
... Motions of Some
3-DOF Parallel Manipulators
355
()
Δ= =
=++−−− =
11 12 13 14
11 12 13
21 22 23 24
21 22 23
31 32 33 34
31 32 33
41 42 43 44
222
11 22 22 33 11 33 12 23 13
;
i
jj
i
cccc
ccc
cccc
Dc ... ×
5
0. 016 5256 5 .13 10 h or
−×<<−
5
5 .13 10 0.0057003h
<< ×
5
0. 013 1 215 4.28 10 h or
−×<<−
5
4.28 10 0. 016 0208h
Real ellipse...