EE 5351
UMD
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.
Find:
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
UMD
SPRING, 2014
4. FOR GRAD CREDIT:
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