Parallel Manipulators New Developments Part 2 pot
Parallel Manipulators New Developments Part 2 pot
... are defined as follows:
),(=),(),(
22 1 122 1 122 2111
bkbkkkbkbk +++
ωωωω
,
),,(=)],(),,[(
122 121 221 1
bbbb ×−××
ωωωωωω
where
33
),( VVb
ii
×∈
ω
, Rk
i
∈ , 1 ,2= i and
×
denotes the vector product ...
a
1
) if 0=),0(),0(
322 31 323 21
mmcuummcuu ×+×−
; i.e., 0=)(
23 321
cucuu
+
−
in the case of RTT,
a
2
) if 0=),0(),0(
3 123 231 321
mmcuummcuu ×+×
; i.e., 0=...
Parallel Manipulators New Developments Part 16 pot
... S2 S3 S4 S5 Ave. Std.
Group1 97.5 92. 5 85.0 95.0 92. 5 10.7 2. 9
Group2 92. 5 100 77.5 97.5 75 13.4 4.0
Group3 62. 5 77.5 80.0 72. 5 95.0 20 .6 10.7
Table 4. Experimental Results.
Parallel Manipulators, ... that
00iiii
ls
=
+−lpse (23 )
where
0
[]
T
iiii i ixiyiz
deee=+ −=ea d b (24 )
Dot-multiplying (23 ) with itself and considering (19), (20 ) and (24 ), yields
22 222...
Parallel Manipulators New Developments Part 3 pot
... , ),(=
22
mY
ω
, ),0(=
33
mY , where 0
2
≠m and 0=
2
m⋅
ω
. Now
)0,(==
11
ω
YB
,
)=,0(==
22 122
mbYYB −
,
)=,0(==
3333
mbYB
. We know, see Remark 3 that
Parallel Manipulators, New Developments ... joint
Parallel Manipulators, New Developments
52
the vector
2
m is perpendicular to the plane
ξ
. We have ],[=],[
21 21
BBYY , ],[=],[
3131
BBYY ,
],[=],[
31...
Parallel Manipulators New Developments Part 6 pot
... 62. 22 76.39 22 . 12
170 X 8 100 189 20 2 70.56 83.55 24 .28
20 0 X 8 100 21 7 23 0 81.30 90.57 24 .88
22 0 X 8 100 23 9 25 5 92. 12 103.49 27 .35
25 0 X 8 100 26 4 29 2 1 02. 37 114. 42 29.49
300 X 8 100 28 6 ... 17.46
120 X 8 100 1 926 .2 2137.9 78.05 91.33 19.33
150 X 8 100 21 84.4 24 10.5 92. 17 1 02. 09 21 .96
170 X 8 100 24 32. 7 29 85.0 100. 02 114.43 2...
Parallel Manipulators New Developments Part 7 potx
...
admissible values for s
γ
:
()
2
2 422 222
32 2
23 211
2
11
21 10
kk k
kskkksk
kk
γγ
⎛⎞
−
++ + − − − + =
⎜⎟
⎝⎠
( 32)
For each angle
γ
that solves ( 32) , 2 different values can be found for ...
()
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
⋅
=
=
⋅−=
11
22
1
22 321 1
121
,2atan
θ
θ
c
rd
b
rr
rdca
()
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
⋅
=
=
⋅−=
12
33
2
3313 12
2 32
,2atan
θ
θ
c
rd
b
rr
rdca
()
⎪
⎪
⎪...
Parallel Manipulators New Developments Part 17 pptx
... as follows
2min
22 22
arcsin 0
()
m
eem
ρ
θ
ρρ
=
>
+−+
(25 )
22 22
2max
arctan arctan 2
me e
ρρ
θ
π
ρρ
−− −
=+< (26 )
P
R
3
R
2
R
1
e
m
q
2
θ
2
z
1
z
3
R
4
P
R
3
R
2
R
1
z
1
z
3
R
4
ρ
P
R
3
R
2
R
1
z
1
z
3
R
4
ρ
θ
2min
θ
2max
... (55)
2
2
22
22
2
11 3 3
(3)[ ()] (3)[ ()]
42 4 2
()
xy xy
z
pp dcab pp dcab
pds l
αα
α
⎧
⎫
−
⎪
⎪
⎧⎫
−− −−+ −+ −−
⎨⎬⎨ ⎬
⎩...
Parallel Manipulators New Developments Part 12 ppt
... Fang, Y. (20 02) Analysis of instantaneous motions of deficient-rank 3-
RPS parallel manipulators.
Mechanism and Machine Theory, Vol. 37, No. 2, 22 9 -24 0.
Parallel Manipulators, New Developments ... Proceedings of 1994 IEEE International
Parallel Manipulators, New Developments
3 42
−
⎡
⎤
⎢
⎥
+− −
=
⎢
⎥
−−
⎢
⎥
⎢
⎥
−−+
⎣
⎦
12
121 22
12
121 1 2
()
()
()
I
f...
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
22 2
11 22 22 33 11 33 12 23 13
;
i
jj
i
cccc
ccc
cccc
Dc ... straight
lines, the root,
()
ii
uw, of the two equations is
−
=
−
=
=− −
22 13 12 23
2
12 11 22
23 12
22 22
1 ,2, 3
i
ii
aa aa
u
aaa
i
aa
wu
aa
(13)...
Parallel Manipulators New Developments Part 14 docx
... lower
b
1
b
2
b
3
A
1
C
1
B
1
1
ρ
2
ρ
3
ρ
1
β
1
α
X
Y
A
3
A
2
C
2
C
3
B
2
B
3
e
1
e
2
e
3
P
3
α
3
β
2
β
Parallel Manipulators, New Developments
396
2. 2 Stability concept ... following form
jj
BQ
τ
=
1,2j
=
(48)
where
22
1315151
TTT
BAAA
bb
ζζ
=− −
,
22
23 2 525 2
TTT
BAAA
bb
ζζ
=− −
(49a)
Parallel Manipulators, New De...
Parallel Manipulators New Developments Part 15 pdf
... :
)sin(:
iii
s
β
α
−
=
and
)cos(:
iii
c
β
α
−
=
11
36
122
33
cos sin 0 0 0 0
00cossin 00
000 0cossin
JR
αα
αα
αα
×
Γ
⎡⎤
⎢⎥
=∈
⎢⎥
⎢⎥
⎣⎦
11
36
22 2
33
22 0000
0 02 2 00
000 022
sc
Jsc R
sc
×
Γ
⎡⎤
⎢⎥
=∈
⎢⎥
⎢⎥
⎣⎦
... ), sway ( y ), and heave
Parallel Manipulators, New Developments
438
0 123 456
-3
-2
-1
0
1
2
3
4
Roll Pitch Yaw
Angle errors [deg]
Time [sec]
0 123 456...
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