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HW Assignment 6 (Total: 100 points + 20 extra credits) Z0 X0 X3 Z3 X3 Z3 Due: 9 AM, Mon
HW Assignment 6 (Total: 100 points + 20 extra credits)
Z0
X0
X3
Z3
X3
Z3
Due: 9 AM, Mon. 12/6/2021
X0
Z0
X3
Z3
L
- Find the Jacobian matrix of each robotic arm with three degrees of freedom shown below using the DH parameters and the given ?30, the transformation matrix. L and H are assumed as known parameters. (40 pts)
H
X2
Z2
X1
Z1
X2
Z2
X1, Z2
Z1
Z1
X1
X0
Z0
Z4
Z2
X2
Z3
X3,X4
Z5
X5
Z1
X1, Z2
X0
Z3
X3
Z4
X4
L
L
d2var
X2
θ2var
θ1var
θ1var
d3var
d2var
d3var
d3var
d1var
Z0, Z1
X0, X1
- Cartesian Robot (10 points)
|
Cartesian Robot |
||||
|
Joint # (i) |
ai |
αi |
di |
θi |
|
1 ( {0} -> {1} ) |
0 |
π/2 |
d1var |
0 |
|
2 ( {1} -> {2} ) |
0 |
π/2 |
d2var |
π/2 |
|
3 ( {2} -> {3} ) |
0 |
0 |
d3var+ L |
0 |
?30=[ 0010−10100?3???+?−?2????1??? 0 0 0 1]
- Cylindric Robot (15 points)
?30=[ ??1???0??1?????1???0−??1???010??1???(?3???+?)−??1???(?3???+?)?2???0 0 0 1]
|
Cylindric Robot |
||||
|
Joint # (i) |
ai |
αi |
di |
θi |
|
1 ( {0} -> {1} ) |
0 |
0 |
0 |
θ1var |
|
2 ( {1} -> {2} ) |
0 |
π/2 |
d2var |
0 |
|
3 ( {2} -> {3} ) |
0 |
0 |
d3var + L |
0 |
- Polar Robot (15 points)
?30=[ −??1?????2?????1?????1?????2???−??1?????2???−??1?????1?????2?????2???0??2?????1?????2???(?3???+?)??1?????2???(?3???+?)?+??2???(?3???+?) 0 0 01]
|
Polar Robot |
||||
|
# |
ai |
αi |
di |
θi |
|
1 |
0 |
π/2 |
H |
θ1var |
|
2 |
0 |
π/2 |
0 |
θ2var + π/2 |
|
3 |
0 |
0 |
d3var + L |
0 |
- Find the Jacobian matrix of the 4DOF manipulator on a fire truck below in a symbolic form using the given mfile (Assignment6_Fall2021.m file). D, H, L, and W are assumed as known parameters. (30 pts)
|
D-H Parameters |
||||
|
Joint # (i) |
ai |
αi |
di |
θi |
|
1 ( {0} -> {1} ) |
-D |
π/2 |
H |
θ1var |
|
2 ( {1} -> {2} ) |
0 |
π/2 |
0 |
θ2var + π/2 |
|
3 ( {2} -> {3} ) |
0 |
-π/2 |
d3var + L |
0 |
|
4 ( {3} -> {4} ) |
W |
0 |
0 |
θ4var - π/2 |
- Find the Jacobian matrix of the LabVolt robot arm below in a symbolic form using the given mfile (Assignment6_Fall2021.m file). a2, a3, d1, and d5 are assumed as known parameters. (30 pts)
(Z1, Z2, and Z3 are pointing into the page)
a3
a2
θ1var
|
LabVolt 5150 |
||||
|
Joint # (i) |
ai [mm] |
αi [° or radian] |
di [mm] |
θi [° or radian] |
|
1 ( {0} -> {1} ) |
0 |
90° or π/2 |
d1 |
θ1var |
|
2 ( {1} -> {2} ) |
a2 |
0 |
0 |
θ2var |
|
3 ( {2} -> {3} ) |
a3 |
0 |
0 |
θ3var |
|
4 ( {3} -> {4} ) |
0 |
90° or π/2 |
0 |
θ4var |
|
5 ( {4} -> {5} ) |
0 |
0 |
d5 |
θ5var |
- (Optional for Extra Credit) Describe physical meanings of the 5-th column of manipulator Jacobian from Prob. 3) as detail as possible. (20 pts)
Expert Solution
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