19AIE201
Introduction to Robotics
Evaluation 4
19AIE201
Introduction to Robotics
Aadharsh Aadhithya - CB.EN.U4AIE20001
Anirudh Edpuganti - CB.EN.U4AIE20005
Madhav Kishor - CB.EN.U4AIE20033
Onteddu Chaitanya Reddy - CB.EN.U4AIE20045
Pillalamarri Akshaya - CB.EN.U4AIE20049
Team-1
19AIE201
Introduction to Robotics
Question 1
Elaborate and clearly explain standard DH parameters with examples of robot configurations taught in class
(i) 3R spatial Robot
(ii) SCARA Robot(4 DOF)
For the above cases do the comparison between standard DH parameters and modified DH parameters and point out the differences
19AIE201
Introduction to Robotics
Question 1
DENAVIT - HARTENBERG
(D-H) Parameters
DENAVIT - HARTENBERG
(D-H) Parameters
DENAVIT - HARTENBERG
(D-H) Parameters
θj
\theta_{j}
: angle between
zj−1
z_{j-1}
xj
x_{j}
xj−1
x_{j-1}
and
axes about the
axis
DENAVIT - HARTENBERG
(D-H) Parameters
dj
d_{j}
: distance from origin to
zj−1
z_{j-1}
xj
x_{j}
axis
along
DENAVIT - HARTENBERG
(D-H) Parameters
aj
a_{j}
: distance between
zj−1
z_{j-1}
xj
x_{j}
axis
along
and
zj
z_{j}
DENAVIT - HARTENBERG
(D-H) Parameters
αj
\alpha_{j}
: angle between
zj−1
z_{j-1}
xj
x_{j}
axis
along
and
zj
z_{j}
DENAVIT - HARTENBERG
(D-H) Parameters
The homogeneous transformation is represented as
Tjj−1=Rz(θj).Tz(dj).Tx(aj).Rx(αj)
T^{j-1}_j = R_{z}(\theta_{j}) . T_z(d_{j}) . T_x(a_{j}) . R_x(\alpha_{j})
MODIFIED DENAVIT - HARTENBERG
(MDH) Parameters
MODIFIED DENAVIT - HARTENBERG
(MDH) Parameters
Basic difference
MODIFIED DENAVIT - HARTENBERG
(MDH) Parameters
Basic difference
(αj−1,aj−1,θj,dj)
( \alpha_{j-1}, a_{j-1} ,\theta_j , d_j )
(θj,dj,aj,αj)
(\theta_j , d_j , a_j , \alpha_j)
→
\rightarrow
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
aj
a_j
θj
\theta_j
Oj
O_{j}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
aj
a_j
θj
\theta_j
Oj−1
O_{j-1}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
Oj
O_{j}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
aj
a_j
θj
\theta_j
Oj−1
O_{j-1}
zi−1
z_{i-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
αj
\alpha_j
Oj
O_{j}
zi
z_{i}
xi
x_{i}
yi
y_{i}
Oj−1
O_{j-1}
Oj
O_{j}
zi−1
z_{i-1}
zi
z_{i}
xi
x_{i}
yi
y_{i}
MDH
MDH
j
j
j+1
j+1
DH
DH
j−1
j-1
j
j
θj
\theta_j
αj−1
\alpha_{j-1}
xi−1
x_{i-1}
yi−1
y_{i-1}
dj
d_j
aj−1
a_{j-1}
aj
a_j
θj
\theta_j
Oj−1
O_{j-1}
zi−1
z_{i-1}
xi−1
x_{i-1}
dj
d_j
αj
\alpha_j
MDH
MDH
DH
DH
θj
\theta_j
αj−1
\alpha_{j-1}
dj
d_j
aj−1
a_{j-1}
aj
a_j
θj
\theta_j
dj
d_j
αj
\alpha_j
MODIFIED DENAVIT - HARTENBERG
(MDH) Parameters
Tjj−1=Rx(αj−1).Tx(aj−1).Rz(θj).Tz(dj)
T^{j-1}_j = R_x(\alpha_{j-1}) . T_x(a_{j-1}) .R_{z}(\theta_{j}) . T_z(d_{j})
The homogeneous transformation is represented as
19AIE201
Introduction to Robotics
Question 1
3R Spatial Robot
θj
\theta_j
dj
d_j
aj
a_j
αj
\alpha_j
θ1
\theta_1
θ2
\theta_2
θ3
\theta_3
0
0
0.25
0.25
0
0
0
0
0.5
0.5
0
0
−90∘
-90^{\circ}
0
0
0
0
DH
αj−1
\alpha_{j-1}
aj−1
a_{j-1}
θj
\theta_j
dj
d_j
θ1
\theta_1
θ2
\theta_2
θ3
\theta_3
0
0
0.25
0.25
0
0
0
0
0.5
0.5
0
0
−90∘
-90^{\circ}
0
0
0
0
MDH
19AIE201
Introduction to Robotics
Question 1
SCARA Robot
θj
\theta_j
dj
d_j
aj
a_j
αj
\alpha_j
θ1
\theta_1
θ2
\theta_2
θ4
\theta_4
0
0
0
0
0
0
0
0
180∘
180^{\circ}
0
0
0
0
DH
αj−1
\alpha_{j-1}
aj−1
a_{j-1}
θj
\theta_j
dj
d_j
θ1
\theta_1
θ2
\theta_2
θ4
\theta_4
0
0
d
d
0
0
1
1
0
0
180∘
180^{\circ}
0
0
0
0
MDH
0
0
1
1
0
0
0
0
0
0
d
d
1
1
1
1
1
1
0
0
0
0
0
0
0
0
19AIE201
Introduction to Robotics
Question 2
Even though obsolete, one of the famous and well-studied industrial robot arm is PUMA-560 by Unimation company. The MDH parameter calculation of PUMA-560 will be discussed in class. Calculate the standard DH parameter by hand for PUMA 560. Compare the DH and MDH parameter table with those obtained from python and matlab robotic toolbox. Do the forward kinematics operation of PUMA 560 for atleast 3 joint configurations of the robot.
19AIE201
Introduction to Robotics
Question 2
19AIE201
Introduction to Robotics
Question 2
θj
\theta_j
dj
d_j
aj
a_j
αj
\alpha_j
θ1
\theta_1
θ2
\theta_2
θ3
\theta_3
0
0
0.1
0.1
−90
-90
0
0
DH
αj−1
\alpha_{j-1}
aj−1
a_{j-1}
θj
\theta_j
dj
d_j
θ1
\theta_1
θ2
\theta_2
θ4
\theta_4
0
0
MDH
1
1
0
0
1
1
1
1
0
0
0
0
θ4
\theta_4
θ5
\theta_5
θ6
\theta_6
−0.01
-0.01
0
0
0
0
0
0
0
0
0
0
−0.01
-0.01
90
90
−90
-90
90
90
0
0
0
0
−90
-90
90
90
−90
-90
90
90
−0.01
-0.01
0
0
0
0
0
0
0.1
0.1
1
1
−0.01
-0.01
0
0
0
0
θ3
\theta_3
θ5
\theta_5
θ6
\theta_6
19AIE201
Introduction to Robotics
Question 3
Panda by Franka-Emika is a redundant (7R configuration) robot (short form for collaborative robot) like a human arm. Repeat the exercise in problem 3 for Panda robot as well.
θj
\theta_j
dj
d_j
aj
a_j
αj
\alpha_j
θ1
\theta_1
θ2
\theta_2
θ3
\theta_3
0.33
0.33
−0.825
-0.825
−90
-90
0
0
DH
αj−1
\alpha_{j-1}
aj−1
a_{j-1}
θj
\theta_j
dj
d_j
θ1
\theta_1
θ2
\theta_2
θ4
\theta_4
0
0
MDH
0
0
0
0
−0.088
-0.088
0
0
0
0
θ4
\theta_4
θ5
\theta_5
θ6
\theta_6
0.316
0.316
0.384
0.384
0
0
0
0
0.088
0.088
0
0
−0.088
-0.088
90
90
−90
-90
90
90
0
0
−90
-90
90
90
−90
-90
90
90
0.0825
0.0825
0
0
0.333
0.333
0
0
0.384
0.384
0.316
0.316
0
0
0
0
θ3
\theta_3
θ5
\theta_5
θ6
\theta_6
θ7
\theta_7
0.107
0.107
0.088
0.088
90
90
90
90
90
90
90
90
−0.0825
-0.0825
0.088
0.088
θ7
\theta_7
0.107
0.107
19AIE201
Introduction to Robotics
Question 4
- Do you think a seven axis robot like Panda is better than six axis robot like PUMA-560 in terms of operations. Do a detailed internet search and understand the advantages and disadvantages of using 6 vs 7 DOF robot. Split your group into two for the presentation of discussion of this problem, one subgroup should favour 6 DOF robot while the other should advocate for 7 DOF.
19AIE201
Introduction to Robotics
6 DOF Robots
- The robotic manipulator such as PUMA 560 which has 6of will be less Expensive when compared to 7DOF robots
- Since the number of degrees of freedom are less programming the robot becomes easy
- 6DOF robots operate faster when compared to 7DOF robots
- This kind of Robotic Manipulatore are used in assembly of automobile subcomponents
19AIE201
Introduction to Robotics
7 DOF Robots
- 7DOF Robot manipulatoire such as panda arm can do more complex moments as human arm compared 6dof manipulators
- This kind of robotic manipulators provides a narrow workspace
- It has High accurate contact recognition, interpretation and reaction
- This kind of Robotic manipulators are used for Curve welding
19AIE201 Introduction to Robotics Evaluation 4
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