Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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For the 3-DOF Industrial manipulator arm as shown in Figure 3, determine
the joint displacements for known position and orientation of the end of the
arm point.
0.
0.
Y1A
Y2 A
Y3
X2
X3
21
22
23
Yo
xo
Figure 3. 3 DOF RRR Industrial manipulator arm
The link transformation matrices are given by
C3 -S3 0 a3C3
S3 C3
1
C2 -S2 0 a,C2
C1
S1
-S1
-C1
d1
S2
C2
2T3
%3D
T2
1
1
1
1
1
S1
C\C2a3+C1a2
C1C2C3 – C1S2S3 -C¡C2S3 – C1S2S3
S,C2C3 – S1S2S3 -SĄC2S3 – S1 S2C3 -C1 SịC2a3+ Sja2
Szaz + d1
1
OT3 =
= °T, 'T2 ?T3
S½C3 + C2S3
- S2S3 + C2C3
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Transcribed Image Text:For the 3-DOF Industrial manipulator arm as shown in Figure 3, determine the joint displacements for known position and orientation of the end of the arm point. 0. 0. Y1A Y2 A Y3 X2 X3 21 22 23 Yo xo Figure 3. 3 DOF RRR Industrial manipulator arm The link transformation matrices are given by C3 -S3 0 a3C3 S3 C3 1 C2 -S2 0 a,C2 C1 S1 -S1 -C1 d1 S2 C2 2T3 %3D T2 1 1 1 1 1 S1 C\C2a3+C1a2 C1C2C3 – C1S2S3 -C¡C2S3 – C1S2S3 S,C2C3 – S1S2S3 -SĄC2S3 – S1 S2C3 -C1 SịC2a3+ Sja2 Szaz + d1 1 OT3 = = °T, 'T2 ?T3 S½C3 + C2S3 - S2S3 + C2C3
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