1.
Report on Project – MAE593
Fall - 2008
Serial Manipulator – PPRR
Parallel Manipulator – 4RRR
By
Hrishi Shah
Shivaswamy Anirudh
2.
ACKNOWLEDGEMENT
We extend our gratitude to Dr. Venkat Krovi. We would not have been
able to finish this project without his help and guidance.
3.
The project deals with the following manipulators:
Serial Manipulator – PPRR
The main file is “mytry1.m”. Run the file to get the GUI.
The serial manipulator is similar to a gantry crane. It is an RR manipulator on an XY plane. The
robot base can be set at any point in the axes of the GUI. Once the robot is in position, it can
trace an ellipse. The ellipse’s axes may also be rotated. The robot can be made to trace an ellipse,
with different weights given to position and orientation.
4.
The various parameters of the GUI are divided into different groups. The bottom of the GUI
contains two buttons – “Home” and “Stop”. “Home” sets the robot to the origin of the axes.
“Stop” halts the tracing of the curve.
Moving the sliders automatically changes the values in the text box adjacent to it, and vice versa.
5.
Try changing the weights for position and orientation. Begin with weight 4 for orientation and 1
for position. Then ask the GUI to trace an ellipse. You will notice that the variation in end-effector
orientation is not that much.
6.
Try tweaking time per revolution and the simulation time. These two parameters influence the
number of revolutions the manipulator makes. If the simulation time is less than the time per
revolution, then the whole ellipse is not traced. The result can be seen above.
Now ask the GUI to trace an ellipse, giving weight less for orientation than for position. It is seen
that the position variation is lesser than before, but end-effector movement is more.
Now, trace an ellipse with equal major and minor axes. This is equivalent to tracing a circle.
Change the angle of the ellipse and notice the difference – make sure that major and minor axes
are not the same.
7.
Parallel Manipulator – 4RRR with rhombus link
The parallel manipulator has been done without the GUI. The main file is parallel1.m. In this file,
we specify the various parameters, which need to be changed manually since no GUI has been
built. These are:
1. Rhombus side length (variable name – l, line 15)
2. Rhombus side angle (variable name – side_angle,line 15)
3. Ellipse angle, (variable name – ell_angle, line 12)
4. Major axis, (radiusx , line 12)
5. Minor axis, (variable name – radiusy, line 12)
6. Simulation Angle, (variable name – Sim_Angle, line 19)
8.
7. Base co-ordinates for RRR manipulators, (variable name – bases, line 18)
8. Phi – inclination of central link which is constant throughout the simulation, (variable
name – phi, line 15)
9. NULL Space correction : To disable NULL Space Correction, replace line 34 in the file
mydiff.m with the line shown below.
qidot=Ji*[xdot;ydot;0];%+NullSpace*[pi/2-x(1);pi-x(2);0-x(3)];
Initially, we specify some values like major axis = 2.5, minor axis = 1.5, ell_angle = 40 degrees. The
ellipse is then plotted as shown above. Now let us tweak the major and minor axes, and the
ellipse angle. There is a slight deviation in the ellipse.
9.
This is because we have not implemented any form of control.
We are implementing null-space in the file mydiff.m. Following code is its implementation.
J1=J*D(1:3,:);
Ji=pinv(J1);
NullSpace=eye(3)-Ji*J1;
qidot=Ji*[xdot;ydot;0]+NullSpace*[pi/2-x(1);pi-x(2);0-x(3)];
qdot=D*qidot;
This file generates the matrix qdot which has velocity values. The orthogonal or null-space
concept is used.
10.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Put equal values for radiusx and radiusy. The circle is then traced, as shown above. It is a little
flattened as scale of X and Y axes in the graph are different.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
11.
Then we change the radii so that we can trace an ellipse. There is slight deviation as we have not
implemented control. Now we trace an inclined ellipse.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
We can also tweak the simulation angle. It is changed to 3*pi/2.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
12.
Now we change the base locations to the four corners of a horizontal square.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Now we change the rhombus sides to 3 units.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
13.
Now we change the rhombus side angle to 90 degrees to make it a square link. Phi is changed to
45 degrees. The now square central link appears rectangular due to aspect ratio.
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
CONCLUSION:
The parallel and serial manipulators were implemented using the concepts taught in the course.
The problems faced in application of such concepts to real time problems were also explored and
solved. It greatly helped in improving the understanding of the theoretical concepts.
Be the first to comment