ME 192 Exam 1 Makeup Problem
10/6/14
Name _________________________
Score ___________________
1. (6 points)
Assume that the joint-by-joint compound transformation matrices may be extracted from a six axis
robot with all rotation and translation angles and values set to zero. Show how to find 43 R , and 3 P4org
 0R
from the 01T , 02T ,......, 06T matrices. Each transformation matrix has the format: 0iT   i
0
0
4
R  30 R 43R
0
3
R 1 40 R ( 30 R 1 30 R) 43R  43R
3
4
R is found by taking out the 30 R portion of the compound rotation matrix 40 R.
0
Pi 
.
1 
0
P4org  0P3org  30R 3P4org
( 30 R 1 30 R) 3P4org  30 R 1 ( 0 P4org  0 P3org )
3
P4org  30R T ( 0P4org  0P3org )
3
P4org is found by taking the difference between the origins of frame {3} and {4} expressed in frame
{0} terms and expressing the difference in frame {3} terms.
2. (4 points)
What are the three rules the class has followed in assigning joint-by-joint frames?
1) In joint framing, always set the Z axis first coinciding with the axis of rotation or translation. Set
the X axis according to the Z axis of the succeeding frame.
2) Allow the between-frame rotation only about the X axis of the predecessor frame.
3) Allow the within-frame rotation or translation only about or in the direction of the Z axis.
3. 5 point take home extra credit (Due 10-8-14). Submit in one page, typed including a schematic.
The Denavit-Hartenberg link parameters provide a two dimensional displacement (e.g., X and Z) for
the succeeding joint. How can you incorporate a third axis displacement (e.g., Y| X and Z) in the frame
set up? How would the link offset or link length value(s) change in such set up?