![Page 1: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/1.jpg)
![Page 2: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/2.jpg)
n Ø Ø Ø
n Ø Ø
n
![Page 4: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/4.jpg)
![Page 5: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/5.jpg)
=
![Page 6: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/6.jpg)
n Ø
n Ø
![Page 7: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/7.jpg)
+
+
![Page 8: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/8.jpg)
: →
XYZ:
X1Y1Z1:
6 : : x y z : α β γ (X1Y1Z1→XYZ )
![Page 9: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/9.jpg)
6 → ( ) 6
6 ) →3 2 6
![Page 10: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/10.jpg)
5 6 7
?
![Page 11: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/11.jpg)
n n n
![Page 12: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/12.jpg)
n Ø
n Ø
![Page 13: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/13.jpg)
2 (q1 q2)
( )
(xd yd)
( )
![Page 14: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/14.jpg)
( )
![Page 15: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/15.jpg)
n Ø
n Ø
![Page 16: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/16.jpg)
τ(t)
(xd(t) yd(t))
( )
( ) : → :
( )
![Page 17: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/17.jpg)
![Page 18: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/18.jpg)
(q1 q2)
(xd yd) ?
![Page 19: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/19.jpg)
![Page 20: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/20.jpg)
(q1 q2)
(xd yd) ?
![Page 21: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/21.jpg)
−π ≤ q1 < +π−π ≤ q2 < +π
−qlower + nπ ≤ q < qupper + nπ
qlower ∈ 0,π[ ] qupper ∈ 0,π )⎡⎣n ( )
![Page 22: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/22.jpg)
0 ≤ cos−1 x ≤ π
−π2≤ sin−1 x ≤ π
2
− π2≤ tan−1 x ≤ π
2
cos θ
0 cos-1x π
![Page 23: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/23.jpg)
![Page 24: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/24.jpg)
![Page 25: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/25.jpg)
q2 = π −α
![Page 26: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/26.jpg)
q1 2 1
q1 = tan−1 y
x⎛⎝⎜
⎞⎠⎟ − β
![Page 27: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/27.jpg)
q2 = −(π −α )
![Page 28: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/28.jpg)
q1 = tan−1 y
x⎛⎝⎜
⎞⎠⎟ + β
![Page 29: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/29.jpg)
3
• 2 3 = 2 1 2
![Page 30: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/30.jpg)
![Page 31: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/31.jpg)
4 → : Denavit-Hartenberg
2
![Page 32: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/32.jpg)
![Page 33: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/33.jpg)
q2 = π −α
q1 = tan−1 y
x⎛⎝⎜
⎞⎠⎟ + β
![Page 34: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/34.jpg)
n Ø Ø
![Page 35: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/35.jpg)
6 → 6
![Page 36: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/36.jpg)
Q = q1,q2,q3,q4,q5,q6( )tP = x, y, z( )t
Θ = α,β,γ( )t
PΘ⎡
⎣⎢
⎤
⎦⎥ =
xyzαβγ
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥
=
fx (q1,q2,q3,q4,q5,q6 )fy (q1,q2,q3,q4,q5,q6 )
fz (q1,q2,q3,q4,q5,q6 )fα (q1,q2,q3,q4,q5,q6 )fβ (q1,q2,q3,q4,q5,q6 )
fγ (q1,q2,q3,q4,q5,q6 )
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥
= f(Q)
f* : Q
![Page 37: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/37.jpg)
t
dxdt
= ∂fx∂q1
dq1dt
+ ∂fx∂q2
dq2dt
+ ∂fx∂q3
dq3dt
+ ∂fx∂q4
dq4dt
+ ∂fx∂q5
dq5dt
+ ∂fx∂q6
dq6dt
x )
![Page 38: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/38.jpg)
f (q1,q2,q3,,qn )2
qi f qi
∂f∂qi
![Page 39: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/39.jpg)
f (q1,q2 ) = q1 + 2q2 f (q1,q2 ) = q1 ⋅q2∂f∂q1
=
∂f∂q2
=
∂f∂q1
=
∂f∂q2
=
![Page 40: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/40.jpg)
f (q1,q2 ) = cos(q1 + q2 )∂f∂q1
=
∂f∂q2
=
∂f∂q1
=
∂f∂q2
=
f (q1,q2 ) = sin(q1 + q2 )
![Page 41: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/41.jpg)
x
q1 x
dxdt
= ∂fx∂q1
dq1dt
+ ∂fx∂q2
dq2dt
+ ∂fx∂q3
dq3dt
+ ∂fx∂q4
dq4dt
+ ∂fx∂q5
dq5dt
+ ∂fx∂q6
dq6dt
![Page 42: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/42.jpg)
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
=
dxdtdydtdzdtdαdtdβdtdγdt
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
=
∂fx∂q1
∂fx∂q2
∂fx∂q3
∂fx∂q4
∂fx∂q5
∂fx∂q6
∂fy∂q1
∂fy∂q2
∂fy∂q3
∂fy∂q4
∂fy∂q5
∂fy∂q6
∂fz∂q1
∂fz∂q2
∂fz∂q3
∂fz∂q4
∂fz∂q5
∂fz∂q6
∂fα∂q1
∂fα∂q2
∂fα∂q3
∂fα∂q4
∂fα∂q5
∂fα∂q6
∂fβ∂q1
∂fβ∂q2
∂fβ∂q3
∂fβ∂q4
∂fβ∂q5
∂fβ∂q6
∂fγ∂q1
∂fγ∂q2
∂fγ∂q3
∂fγ∂q4
∂fγ∂q5
∂fγ∂q6
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
dq1dtdq2dtdq3dtdq4dtdq5dtdq6dt
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
= J dQdt
![Page 43: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/43.jpg)
→dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
= J dQdt
→
ΔPΔΘ⎡
⎣⎢
⎤
⎦⎥ = J ⋅ ΔQ
→
![Page 44: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/44.jpg)
• (x,y)
![Page 45: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/45.jpg)
dxdt
=
dydt
=
J=
![Page 46: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/46.jpg)
![Page 47: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/47.jpg)
![Page 48: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/48.jpg)
q1=q2=0
q1,q2 10 ±20 ______
![Page 49: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/49.jpg)
q1=0 q2=π/2
q1,q2 10 ±20 ______
![Page 50: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/50.jpg)
x → x ( )
x y
( )
![Page 51: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/51.jpg)
( q1, q2,qn ) ( x, y, z, α, β, γ )
![Page 52: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/52.jpg)
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
=
dxdtdydtdzdtdαdtdβdtdγdt
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
=
∂ fx∂q1
∂ fx∂q2
∂ fx∂q3
∂ fx∂qn
∂ fy∂q1
∂ fy∂q2
∂ fy∂q3
∂ fy∂qn
∂ fz∂q1
∂ fz∂q2
∂ fz∂q3
∂ fz∂qn
∂ fα∂q1
∂ fα∂q2
∂ fα∂q3
∂ fα∂qn
∂ fβ∂q1
∂ fβ∂q2
∂ fβ∂q3
∂ fβ∂qn
∂ fγ∂q1
∂ fγ∂q2
∂ fγ∂q3
∂ fγ∂qn
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
dq1dtdq2dtdq3dtdqndt
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
= J dQdt
n dQdt
?
) : n=7( 3 2 2)
![Page 53: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/53.jpg)
1: ( ) > ( )
2: ( ) = ( )
3: ( ) < ( )
![Page 54: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/54.jpg)
( ) ( )1
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
= J dQdt
dQdt
= J−1dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
dQdt
= J−1dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
ΔQΔPΔΘ⎡
⎣⎢
⎤
⎦⎥
![Page 55: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/55.jpg)
( ) ( )
: 2
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
= J dQdt
dQdt
= (JTJ)JTdPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
![Page 56: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/56.jpg)
( ) ( )
: 2
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
= J dQdt
dQdt
= JT (JJT )
dPdtdΘdt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
( 2 )
![Page 57: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/57.jpg)
dxdtdydt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
=−l1s1 − l2s12 −l2s12l1c1 + l2c12 l2c12
⎡
⎣⎢⎢
⎤
⎦⎥⎥
dq1dtdq2dt
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
1? 2? 3?
![Page 58: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/58.jpg)
J =J11 J12J21 J22
⎡
⎣⎢⎢
⎤
⎦⎥⎥ J −1 = 1
det(J )J22 −J12−J21 J11
⎡
⎣⎢⎢
⎤
⎦⎥⎥
det(J ) =J11 J12J21 J22
![Page 59: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/59.jpg)
![Page 60: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/60.jpg)
���
J
![Page 61: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/61.jpg)
L1=200mm
L2=150mm
x=200,y=150, q1=0,q2=90
x=230,y=120
q1 = tan−1 y
x⎛⎝⎜
⎞⎠⎟ − cos
−1 l12 + x2 + y2 − l2
2
2l1 x2 + y2⎛
⎝⎜
⎞
⎠⎟
q2 = π − cos−1 l12 + l2
2 − x2 − y2
2l1l2
⎛⎝⎜
⎞⎠⎟
q1= -7.6417[deg] , q2= 85.4114[deg]
[rad]
[rad]
x=230, y=120
![Page 62: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/62.jpg)
L1=200mm
L2=150mm
x=200,y=150, q1=0,q2=90
q1= -8.5944 [deg] , q2= 87.1352[deg]
J_inv
J −1 = 0.0000 0.0050−0.0067 −0.0050
⎡
⎣⎢
⎤
⎦⎥
x=230, y=120
q1q2
⎛
⎝⎜
⎞
⎠⎟ =
0π2
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟+ J −1 30
−30⎛⎝⎜
⎞⎠⎟
[rad]
[rad]
dx=30, dy=-30
![Page 63: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/63.jpg)
q1= -7.6417[deg] , q2= 85.4114[deg] q1= -8.5944[deg] , q2= 871352[deg]
![Page 64: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/64.jpg)
( )
![Page 65: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/65.jpg)
( )
det(J ) = l1l2s2 = l1l2 sinq2 = 0
q2 = nπ (n = 0,1, 2,)
q2=0q2=π
![Page 66: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/66.jpg)
→ =0
→ → →
![Page 67: ¥Ã v j l f h k z0.Mü # ý ß0.Mü " û # ý v j l L 2 [!. Iå0 Mî Mï !. l bτ(t) v j l Må0(x d(t) y d(t)) (õ)0.M ß0.M (õ)0.M: !. l b p i →å0 p i f y | f } ß0.M: !. l bϯ](https://reader033.vdocuments.mx/reader033/viewer/2022042001/5e6d9311ccc4eb77e7195af3/html5/thumbnails/67.jpg)
? ?