HW 1  

EE 5351
SPRING, 2014
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.
2w + x =1; 2x + y =1; 2y + z = 1; z=1
2. For the following matrices, calculate by hand:
a. Rank(A), Trace(A)
b. Det(A)
c. Eigenvalues(A)
d. Eigenvectors of A
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. A robotic arm moves in a 2D plane as shown below: Link A is 8 cm long and
has a Joint, a, with 160 degrees of freedom at its base. A second link, B, is 6
cm long and is attached to the end of A using Joint b, with 90 degrees of
freedom. An X-Y fixed frame of reference is established at the base of Link A.
The end of the arm is labeled point, P.
a. Calculate the maximum length of the arm in the +X direction and give
the P(x,y) coordinates of that point.
b. Calculate the maximum length of the arm in the X direction when
P(y)=0 (i.e. the end of the arm is touching the work surface)
c. Find two sets of possible joint angles (a,b) when P (x,y) = (10,9)
Scott Norr
EE 5351
SPRING, 2014
For the robotic arm described above, write a MATLAB (or other software)
script to calculate and plot the end position, P, for all possible joint values, in
½ degree increments.
Scott Norr