MAE 256D: Advanced Robotics
MAE256D - Midterm Exam
1) Select an industrial robotic arm form the list that is available on the class
webpage (6 DOF is preferred) that does not appear as an example or
problem in Craig, or any other books. Add a CAD drawing of the arm that is
provided by the manufacturer. The idea is that the first page can be used as a
problem by future students, so don’t draw any link frames or DH parameters
on it.
2) Use a schematic drawing or a CAD drawing of your selected arm and draw
the link frames
3) Find the DH parameters and enter them into a table. Use parameters while
avoiding numerical values.
4) Expressed all the homogeneous transformation matrixes
0
1
T ,21T ,23T ,34T ,45T ,56T
as well as the homogeneous transformation matrix 06T .
5) Solve the inverse kinematics using two methods
a) Geometric solution
b) Analytical solutions.
6) Calculate the Jacobian Matrix in the end effector frame ( 6 J ) and the base
frame ( 0 J ) Use the following methods:
a) Velocity propagation (assume that the velocity vector is defined as
v
x
vy
vz
 x  y  z T )
b) Static force propagation (assume that the force/torque vector is defined as
f
x
fy
fz
nx
ny

T
nz )
c) Direct differentiation of the kinematic equations.
7) A bonus of points will be given for
a) Simulation of the robot using MATLAB Toolbox (Please provide the Matlab
code) and verification of the analytical results with Matlab
b) Softcopy (MS Word or Latex)
1
MAE 256D: Advanced Robotics
MAE256D - Midterm Exam
Name: ___________________________
Criterion
Score
Maximum
1
Correctness of Analysis (Errors in work)
1a
Link Frame Assignments
10
1b
DH Parameters
10
1c
Forward Kinematics
15
1d
Inverse Kinematics (analytical solution)
10
1e
Inverse Kinematics (geometric solution)
10
1f
Jacobian (differentiation)
10
1g
Jacobian (propagation)
10
1h
Jacobian (force /torrque)
10
2
Thoroughness of Work (Could someone else figure out what you did?)
2a
Forward Kinematics
5
2b
Inverse Kinematics
5
2c
Jacobian
5
Total
100
Bonus MATLAB code of the manipulator
10
Bonus Word / Latex
10
2
MAE 256D: Advanced Robotics
Manipulator Schematic Illustration (CAD Drawing)
3
MAE 256D: Advanced Robotics
Link Frame Assignment
Denavit-Hartenburg Parameters
i-1
i
0
1
1
2
2
3
3
4
4
5
5
6
 i 1
ai 1
4
di
i
MAE 256D: Advanced Robotics
Forward Kinematic Equations
5
MAE 256D: Advanced Robotics
Inverse Kinematic Solutions
6
MAE 256D: Advanced Robotics
Jacobian Matrix
7
MAE 256D: Advanced Robotics
MATLAB Code
8