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Joints orientation of the robot

   

Added on  2022-11-25

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QN 1: Joints orientation of the robot
Firstly, we fill table1: Robotics and Automation
Axis (i) α i-1 di θ
1 70 352 0
2 360 0 90
3 0 0 0
4 0 380 0
5 0 0 0
6 0 0 0
Then table 2: for Cθi and Sθi
C S
Θ1 (0) 0 -1
Θ2 (90) 1 0
Θ3 (0) 0 -1
Θ4 (0) 0 -1
Θ5 (0) 0 -1
Θ6 (0) 0 -1
Then table 3: for Cάi and Sάi
C S
Θ1 (0) 0 -1
Θ2 (90) 1 0
Θ3 (0) 0 -1
Θ4 (90) 1 0
Θ5 (90) 1 0
Θ6 (0) 0 -1
For table 2 and 3 values, we use the following equations:
S= Sin (θ-90) and C= Cos(θ-90)
If θ= 0, then S= Sin(-90)= -1
And C= Cos(-90) = 0
And if θ=90, S= Sin(90-90) = 0 and C= Cos0 = 1

The homogenous transform is obtained from tables 1,2,3 and the given
matrix below:
i-1T = Cθi -Sθi 0 ai-1
SθiCά-1 CθiCά-1 -Sά-1 -diSά-1
SΘiSά-1 CθiSά-1 Cά-1 diCά-1
0 0 0 1
0 1 0 0
1T = 0 0 0 0
0 0 0 0
0 0 0 1
2T = 1 0 0 70
0 0 1 0
0 -1 0 0
0 0 0 1
0 1 0 360
3T = -1 0 0 0
0 0 1 0
0 0 0 1

0 1 0 0
4T = 0 0 1 -380
1 0 0 0
0 0 0 1
0 1 0 0
5T = -1 0 0 0
0 0 1 0
0 0 0 1
6T = 0 -1 0 0
0 0 0 0
0 0 1 0
0 0 0 1
QN2: And lastly, we can determine the overall transformation which is given
by:
6T = 1[T] 2[T] 3 [T] 4[T] 5[T] 6[T]

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