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MEM455 HW02
MATLAB FORWARD AND REVERSE DISPLACEMENT ANALYSIS
HW01 uses the RobotSketch toolbox to move the robot from pose1 to pose 2 using joint interpolation.
For this assignment the robot also moves from pose1 to pose2 but uses end-effector or Cartesian
interpolation. A different method has to be used for a second path where the end-effector rotates in a
circle. a
1
= 9.3cm, a
2
= 9.3cm, a
3
= 10.2cm.
1.
Make a copy of
demo_robot_serial.m
and rename it to
demo_robot_serial_HW02.m
and similarly make a copy of
demo_robot_serial_movie.m
and rename it to
demo_robot_serial_movie_HW02.m
(a)
The data files you will need should be referenced as:
dh_robot_data = ’data_RRR_lab_HW02’;
dh_movie_data = ’data_path12_movie_HW02’;
2.
Pose1 and pose2 (from HW01) are:
dh.t = [nan, 30, 45, 15, 0]*pi/180; %pose1
dh.t = [nan, 105, 45, -60, 0]*pi/180; %pose2
and all other parameters are the same as in
data_RRR_lab.m
3.
Write the Matlab function
dh = RRR_FDA(dh)
that calculates the end-effector location
dh.Xe_FDA=[x
e
y
e
φ
e
].
This is the Forward Displacement Analysis.
•
Test with the pose1 joint angles. Before proceeding visually check the results by
comparing with a pose1 figure.
4.
Write the Matlab function
dh = RRR_RDA(dh)
that calculates the joint angles
dh.t_RDA
= [nan,
θ
1
,
θ
2
,
θ
3
, 0]
using the end-effector location
dh.Xe
. This is the Reverse
Displacement Analysis.
•
Test by setting
dh.Xe
to
dh.Xe_FDA
found in 3.,
dh.elbowplus=1 (true)
, and
the same
dh.a
(link lengths). The values of
dh.t_RDA
should be the same (to within
roundoff) as the original pose1 joint angles
dh.Xe_FDA
. If not, you have an error
somewhere and need to fix before proceeding.
5.
It is desired to move the robot from pose1 to pose2 by simultaneously moving all joints to keep
the end- effector on a straight path with a constant orientation. Write a script
data_path12_movie_HW02.m
to generate the end-effector locations that move the robot
from [x
e
y
e
φ
e
]
0
to [x
e
y
e
φ
e
]
n
in n equal end-effector steps (giving n + 1 locations),
[࠵?
!
࠵?
!
∅
!
] = [࠵?
!
࠵?
!
∅
!
]
"
+
#
$
([࠵?
!
࠵?
!
∅
!
]
$
− [࠵?
!
࠵?
!
∅
!
]
"
), ࠵? = 0,1, … , ࠵?
• Use this script with
demo_robot_serial_movie_HW02.m
to animate the path. With the
trace on, export a copy of the trajectory as
path12.png
. For visual clarity you may want to
limit n to about 10. Also suggest you use an x − y view for to aid in analysis.
6.
Repeat for a second path by writing the script
data_circle_movie_HW02.m
where the
robot moves on a circle of radius r = 3 , always points to the center (x
c
,y
c
) = (3,3), has the starting
end-effector angle 0
◦
, and uses
dh.elbowplus=1
.
[࠵?
!
࠵?
!
∅
!
]
#
= 1࠵?
%
− ࠵? cos
2࠵?࠵?
࠵?
,
࠵?
%
− ࠵? sin
2࠵?࠵?
࠵?
,
2࠵?࠵?
࠵?
: , ࠵? = 0,1, … , ࠵?
7.
Submit the following:
(a) Program listings(MATLAB code).
RRR_FDA
,
RRR_RDA
,
data_path12_movie_HW02.m
and data_circle_movie_HW02.m.
Be sure to comment your work.
(b) Printout of the paths generated in 5 and 6. (Use x − y view.)
(c) A short explanation comparing the results with the corresponding ones of HW1.
Serial robot displacement analysis
1. For the RRP serial robot in the figure:
(a) Solve the forward displacement analysis
(b) Sketch another solution to the reverse displacement analysis.
2. The RPR serial robot in the figure has a
1
=a
3
=2. The end-effector location is x=2,y=4, and φ
e
=90
◦
.
(a) Determine the required joint configurations (revolute and prismatic) and show them on the figure.
(b) Sketch an alternative solution to the reverse displacement analysis and the actuator displacements
on your sketch.
(c) Determine condition(s) for a displacement singularity. If they do not exist, explain why.
3. In the study of planar robot types, why was the PPP serial robot was not studied.
4. It
is physically possible for a RRR serial robot to have 360
◦
rotation of all joints without the links
interfering. Sketch a figure that illustrates this and include any constraints on the dimensions if
necessary.
5. Sketch an RRR serial robot in a configuration where the reverse displacement analysis yields an
indeterminate joint angle solution. What special dimensions and/or joint angles are necessary? Hint:
think about displacement singularities.
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17
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Wind Farms
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turbine C is in the wakes of turbines A and B.
Given the following:
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A
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- z = 60 m
- Zo = 0.3 m
U.
-r, = 20 m
B
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