2R ROBOTIC ARM USING MATLAB

AIM

Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm, as shown in the video. Also create an animation file of the plot.

PRE-REQUISITES

RESOLUTION OF VECTORS - Vector resolution is a process where one vector is broken down into two or more smaller vectors.

MATLAB FUNCTIONS USED

• linspace(x,y,z)
• plot()
• title()
• xlabel() & ylabel()
• axis()
• pause()
• getframe()
• VideoWriter('filename','format')
• open() & close()
• writeVideo()
• movie()

PROCEDURE

1. The inputs like length, angle of inclination, rectangular coordinatesof origin & the joint of both the the link 1 & link 2.
2. The angle of inclination is defined as an array using linspace().
3. The for loop is defined with iteration from 1 to the array length of angle of inclination of the link 1.
4. Since the link one is fixed to the origin, for each orientation of link 1, link 2 will can execute its every orientation. So we will define another for loop inside the 1st for loop with iteration from 1 to the array length of angle of inclination of the link 2.
5. NOTE: In both the for loops the first statement will be a variable to assign the array value of the angle of inclination corresponding to the iteration (.i.e. THETA1 and THETA2 for the 1st & 2nd for loops)
6. Inside the 2nd for lop, we will define the rectangular coordinates of the origin (X1,Y1), joint (X2,Y2) & manipulator (X3,Y3).
7. The values of (X2,Y2) & (X3,Y3) are defined by the resolution of vector principle.
8. Now inside the 2nd for loop itself, we will define the plotting statements.
9. the plot is given the required title and axes are labelled.
10. As the orientation of the two links changes the axes also changes, and hence for consistency, we will difine a common axis for orientation of the links using the axis(). Also a pause().
11. for making the animation, we will store all the frames obtain from each orientation into an array M. Also for knowing the iterations, we will define a counter variable (.i.e. ct=1).
12. Atlast, we will define the function movie outside the 1st for loop to create a movie filr by the matlab using the frames of plots obtained from the above for loops.
13. to create the movie, the matalab requires a variable to store the file name and file format(.i.e. videofile).
14. This variable is opened using open() and the frames are converted into video format using the movie().
15. Atlast the file is closed to make it saved in the destination folder.

CODE:-

% MATLAB PROGRAM FOR 2R ROBOTIC ARM

% REQUIRED INPUTS

% LINK1 INPUTS
L1=4;
theta1 = linspace(0,360,10);
X1=0;
Y1=0;
A=0.33;
B=0.66;

% LINK2 INPUTS
L2=4;
theta2 = linspace(360,0,10);
% X2 and Y2 ARE DEFINED IN THE FOR LOOP

ct=1;

for i=1:length(theta1)
    THETA1 = theta1(i);
    
    for j=1:length(theta2)
        THETA2 = theta2(j);
        
        X1 = 0;
        Y1 = 0;
        
        X2 = (-L1/3)*cosd(THETA2);
        Y2 = (-L1/3)*sind(THETA2);
        
        X3 = (0.66*L1)*cosd(THETA1);
        Y3 = (0.66*L1)*sind(THETA1);
        
        X4 = X2+(0.5*L2)*cosd(THETA1);
        Y4 = Y2+(0.5*L2)*sind(THETA1);
        
        X5 = X2+(0.5*L2)*cosd(THETA2);
        Y5 = Y2+(0.5*L2)*sind(THETA2);
      
        
        % PLOTTING
        plot([X1 X2],[Y1 Y2],[X2 X3],[Y2 Y3],'linewidth',3)
        title('Forward Kinematics of 2R Robotic Arm');
        xlabel('X-axis');
        ylabel('Y-axis');
        axis([-3 3 -3 3])
        pause(0.03)
        M(ct) = getframe(gcf);      
        ct = ct+1;
   end
end
movie(M)
videofile = VideoWriter('Forward_kinematics','MPEG-4');
open(videofile)
writeVideo(videofile,M)
close(videofile)

ERRORS

(NOTE: The screenshots of all the errors are attached below)

1. the graph was plotted using the line() for each link separately.
2. The axis was not consistent hence, for each orientation the plot was changing.
3. the icremented counter value was defined before defining the array variable for storing the plot frames (.i.e. M).
4. the VideoWriter() & writeVideo() was wrongly execute.

CORRECTION CARRIED OUT

1. the graph is plotted using the plot().
   
2. The axis() was introduced.
3. the icremented counter value is defined after defining the array variable for storing the plot frames (.i.e. M).
4. the VideoWriter() & writeVideo() was executeD, correctly.

IMPORTANT LINKS

youtube link - https://youtu.be/Rq3EbcuxNgg

google drive link - https://drive.google.com/file/d/1b9kpSwa9a392xg6UZ5n4uQC6uH47niCj/view?usp=sharing