Project 1: Kinematics of the Stewart Platform

Garrett Lee, Aneesh Malhotra, Patrick Bishop, Jason Lasseigne

The goal for project 1 was to review material from Math 446 and learn how to do group projects within the class. To do this we learned how to work with thew Stewart Platform and learn how to manipulate robotic arms. To do so we manipulate the lengths of the struts attached to the platform, which determine the range of positions that the platform can take.

In part 1 we generated the basic function, f(theta), which was created by taking the formulas given in the problem specifications. This function would be used throughout the problem with various parameters.

In part 2 we plotted our function over the range [-pi,pi] to see the form of the function with the default parameters.

In part 3 we plotted the figures given to us in the book so that we could better understand how to do this in future parts.

Part 4 is where we really got to work with the problem. Using a set of parameters adn the bisection method we found the roots of the function which correspond to the positions of the platform. To use the bisection method we plotted the function on the range [-pi,pi] and then took a positive and negative point before and after each intersection with the x axis. This gave us the zeros / roots of the function which correspond to an angle that has a position. We then generated (x,y) values for said platforms and plotted the various structures.

Theta	X	Y	Plot
2.1159	4.5718	2.0244
-0.7208	-1.3784	4.8063
-0.3310	-0.9147	4.9156
1.1437	4.4818	2.2167

We repeat the process in part 4 but we must change the second strut length, p2, so that we wind up with 6 poses instead of 4. We chose p2 = 7.005 for our new strut length, and then followed through with the problem as before.

Theta	X	Y	Plot
-0.6587	-4.3488	2.4673
-0.3813	-4.7809	1.4637
0.0481	-4.9488	0.7134
0.4603	-0.8223	4.9319
0.9775	2.2955	4.4419
2.5144	3.2114	3.8324

Once more we repeat the process in part 4 and part 5 but this time we look for parameters that gives us only 2 roots and 2 poses. To accomplsih this we used P2 = 9 for our flexible strut and that produced two poses.

Theta	X	Y	Plot
1.5479	0.7100	4.9493
2.2989	1.3916	4.8024