Week 2- 2R Robotic Arm Challenge

Aim ;

To simulate the forward kinematics of a 2R Robotic arm

• Create an animation file of the plot.
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• Upload an animation on You tube and provide the You tube link for an animation in your report.
• You can also provide the google drive link.Note: Make sure that you provide the access to the video, while pasting the google drive link.

Equations used in the project ;

`y_1 = l_1 xx sintheta_1`,`x_1 = l_1 xx costheta_1` , `x_2 = x_1+l_2 xx costheta_2` , `y_2 = y_1+l_2 xx sintheta_2`

from trigonometric relations .here x1,y1,x2,y2, are x and y coordinates of the robotic arm linkages.

Objectives of the project:

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

Body of the content:

We have used Matlab to write the code to simulate the forward kinematics of a 2R robotic arm, Matlab uses C++ in its interface.

The code to simulate the forward kinematics of a 2R robotic arm is given below

% program to simulate forward kinematics of a 2R robotic arm.
clear all
close all
clc
%inputs 
l1=1;
l2=0.5;
ct=1;
%theta1 = t1
t1=linspace(0,90,10);
%theta2 = t2
t2=linspace(0,90,10);
% code to simulate the Forward kinematics of 2R robotic arm 
for i=1:length(t1)
    T1=t1(i);
    for j=1:length(t2)
        T2=t2(j);
        %x,y coordinates of the robotic arm 
        x0=0;
        y0=0;
        
        x1=l1*cosd(T1);
        y1=l1*sind(T1);
        
        x2=x1+l2*cosd(T2);
        y2=y1+l2*sind(T2);
       %ploting 
        plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],'linewidth',3)
        axis([-0.1 1.5 0 1.5])
        pause(0.03)
        M(ct)=getframe(gcf);
        ct=ct+1;
    end
end    
movie(M)
videofile=VideoWriter("forward_kinematics.avi","Uncompressed AVI");
open(videofile)
writeVideo(videofile,M)
close(videofile)


    

Explanation of the code:

• We used a “ % ” to write a comment and we used “ clear all ” command to make sure that the work space is clear and we used “ close all ” command to make sure to close all plots and figures from previous run. And “ clc ” command to make sure the command window is clean.
• We have given the inputs “ l1 , l2 , t1 , t2 , ct ” where “ l1 ” and “ l2 ” are the length of the linkages 1 and 2 of the robotic arm. “ t1 ” ,” t2 ” are the angles made by the linkages 1 and 2. And “ ct ” is the counter variable used for getting individual frames of the result.
• While assigning values for t1 and t2 we used a command called “ linspace ” which generates an array of equally spaced elements between two limits.
• We used two for loops in the code so that we can obtain : different positions of link2 for the same position of link 1.
• In the 2^nd for loops we took two temporary variables T1 and T2 to avoid confusions.
• We assigned the coordinates x0 , y0 , x1 , y1 , x2 , y2 of the linkages 1 and 2 inside the second loop.
• And we plot the positions of the two linkages by using the command “ plot ”
• The “axis” command generates an axis to the plot.
• We used pause command to delay the plot change so that it looks like an animation.
• To create an animation file we 1^st made an array of different figure frames called “M” by using “getframe” command and used a counter variable “ct” to give an increment inside the loop.
• “movie” command converts all the frames into an animation. Then we created a video file specifying the tittle of the video file and type of the video file using the command “VideoWriter”.
• Then we opened the video file using the command “open” and we wrote the “M” animation into the video file converting the animation into a video file using “writeVideo” command
• And we closed the video file using “close” command

link for result:

https://drive.google.com/file/d/1EOoRyC5cC-tcOzdHoWxqwJwuXUebmp2s/view?usp=sharing

Errors faced while programming:

• I made syntax error while using “plot” command
• I made mistake while assigning t1 and t2 values inside the loop
• I made a syntax error while using the “movie” command.

Conclusion:

• To make the animation smoother we need more number of positions or theta values.
• Matlab can be used to simulate the forward kinematics of the 2R robotic arm.
• The more number of frames involved in the video the more time it takes to generate the video.