UNIVERSITY OF MINNESOTA
DEPARTMENT OF COMPUTER SCIENCE
5551 INTRODUCTION TO INTELLIGENT ROBOTIC SYSTEMS FALL 2015
SAMPLE EXAM
100 POINTS
Problem 1 (20 points)
If axyz = (−1, 1, 1)T are the coordinates of one point with respect to the original reference coordinate
system, determine the corresponding points auvw with respect to the new OUVW coordinate system
if the frame has been rotated 30o about the OZ axis (first rotation), 60o about the OX (old) axis
(second rotation), and 90o about the OY (old) axis (third rotation). Assume that all the rotations
are counterclockwise.
Problem 2 (60 points)
For a planar PRR manipulator as defined in class, assign frames (10 points), define the DH parameters
(10 points), compute the forward kinematics (10 points), compute the inverse kinematics (20 points),
and the Jacobian with respect to the fixed base (10 points).
Problem 3 (20 points)
Prove or disprove: a translation and a rotation about the same axis are commutative. That is,
TuRu = RuTu. For simplicity, you can assume that the axis u is the x-axis (without loss of generality,
since one can choose a coordinate system however one wishes).
GOOD LUCK. NO ELECTRONIC DEVICES ARE ALLOWED. YOU HAVE 75 MIN-
UTES.