ME 581 – H04
Name ________________________
1) A machined block is resting on a ramp feeder on a small table in a robot work cell as shown
below. Determine the location and attitude of block 8 with respect to global coordinate frame 1.
Ensure that your attitude matrix is positive orthonormal.
__________ 
r8   __________ 
__________ 


 __________
A 8    __________
 __________
__________ 
__________ 
__________ 
__________
__________
0
z 8’
Block 8 (not to scale)
y8’
y1’
x8’
x8’
y8’
x8’
z 8’
30 cm
TABLE
RAMP
20 cm
RAMP
x4’
y4’
60°
45°
15 cm
90 cm
60 cm
TABLE
z 4’
z1’ OUT
out
x4’
x1’
100 cm
Top view of workcell (not to scale)
Side view of table (not to scale)
2) Extract Euler parameters from
A = [
0.6538
-0.7507
0.0944
0.3609
0.1998
-0.9109
p  _______________
0.6650 ;
0.6297 ;
0.4016 ];
_______________
_______________
_______________
T
ME 581 – H04
Name ________________________
3) Three beverage cans are placed on a ramp as shown below and allowed to roll to the bottom.
All cans are the same size. Assume pure rolling with no sliding.
Rate the cans in order from fastest 1 to slowest 3. Show your work. (Try it experimentally?)
____________________ can A empty
____________________ can B full
____________________ can C full but frozen
can
ramp