EE 5351
UMD
SPRING 2016
HW 1: 25 Points (You may use the software of your choice)
1. For the following system of equations, calculate by hand, showing your work:
a. The A matrix for Ax=B form
b. The B matrix
c. Form the augmented 4x5 A|B matrix, and use Gaussian operations to produce the RREF of
the augmented matrix.
d. Use MATLAB (or other software) to check part c.
i. 2w + x =1; 2x + y =1; 2y + z = 1; z=1
2. For the following three matrices, calculate by hand:
a. Rank, Trace
b. Det
c. Eigenvalues (if you can ‘guess’ them using trace and det, do so!)
d. Eigenvectors
e. Check a-d with MATLAB (or other software)
A = [-10 -7 ; 14 11]
B = [2 16 8 ; 4 14 8 ; -8 -32 -18]
C = [3 -2 5 ; 0 1 4 ; 0 -1 5]
3. For the planar figure shown below, and using MATLAB (or other software):
a. Form each homogeneous matrix, Hi, based on Denavit-Hartenberg criteria, for each
link/joint of the robotic arm shown below.
b. Use P = H1*H2* … *Hi to calculate the position vector from the origin to point P if the joint
angles are a1 = 30 degrees, a2 = -15 degrees and a3 = 60 degrees.
4. For the figure shown below, and using MATLAB (or other software):
a. Form each homogeneous matrix, Hi, based on Denavit-Hartenberg criteria, for each
link/joint of the planar robotic arm shown below.
S.Norr
EE 5351
UMD
SPRING 2016
b. Use P = H1*H2* … *Hi to calculate the position vector from the origin to point P if the
rotational joint angle is at 60 degrees, and the linear joint is at 50%.
5. For the 3-D figure shown below, and using MATLAB (or other software):
a. Form each homogeneous matrix, Hi, based on Denavit-Hartenberg criteria, for each
link/joint of the robotic arm shown below.
b. Use P = H1*H2* … *Hi to calculate the position vector from the origin to point P if the joint
angles are a1 = 30 degrees, a2 = 60 degrees.
6. (FOR GRAD CREDIT): For the robotic arm described in Problem 5 above, write a MATLAB (or
other software) script to calculate and PLOT the end position, P, for all possible joint values, in
1-degree increments.
S.Norr