Week 2- 2R Robotic Arm Challenge

clear all 
close all
clc
%Inputs
l1=4;                       %Length of link 1 in metres
l2=3;                       %Length of Link 2 in metres
theta1=linspace(0,90,10);   %The values of angles theta1n2 lie from 0 to 90 degrees
theta2=linspace(0,90,10);
c=1                         %c is the counter variable here
for i=1:length(theta1);     %Initialising for loop
    THE1=theta1(i);
    for j=1:length(theta2); %Using a nested for loop to change values of arm2
        THE2=theta2(j);
        %Calculating x and y coordinates of the link arms
        x0=0;
        y0=0;
        x1=l1*cosd(THE1);   %Calculation of x n y coordinates
        y1=l1*sind(THE1);   %of the link 1

       x2=x1+l2*cosd(THE2); %Calculating x and y coordinates
   
       y2=y1+l2*sind(THE2); %of the link 2

       %Plotting
       plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],'linewidth',2);  %Ploting both the link graph at a time
       grid on
       axis([-0.1 8 -0.1 8]); %Sets max and min values for axes
       pause (0.1)            %Pausing the computation for a time 0.1sec
       m(c)=getframe(gcf)     %Frame capturing done for the plotted figures
       c=c+1;                 %counter variable incremented
    end
end
%Creating the animation for the movement of the 2R robotic arm in X-Y plane
movie(m)
videofile=VideoWriter('Forward Kinematics of a 2r robotic arm.avi','Uncompressed AVI');
open(videofile);
writeVideo(videofile,m);
close(videofile);

Explanation:- In this challenge we had to write a program in matlab in order to simulate the kinematics of a 2R Robotic Arm.As mentioned a 2R robotic arm consists of a combination of 2 links (the arms ) and 2 rotary joints. And the two arms making an angle of theta 1 and theta 2 with the x axis.

So in order to determine the position of the links in an X-Y plane we formulated an equation that gave the values of the x-y co-ordinates for both the links 1 2 using x1=L1cos(theta1) and y1=L1sin(theta1) where L1 and L2 are the lengths of link 1 and 2

Similarly for x2=x1+L2cos(theta2) and y2=y1+L2sin(theta2) for which we needed values of theta 1 and theta 2 which we odtained using the linscape function that gave us different values of theta from 0-90 degrees.

Now after computing all the x-y coordinates we neede to obtained the plot that depicted the movement of the arms in the x-y plane for which we used the plot funtion in which we gave all the values of X-Y coordinates in a set of arrays containing the values of x-y.

Here we also used a nested for loop in order to iterate the process of computing the vaues of the coordinates and to plot the that depicted a range of values of theta2(the range of motion of the second arm) for a single value of theta1(the range of motion of arm 1)

As the graphical representation involved a no.of graph at different values of theta we combined all the plots into an animation video in order for a better understanding of the motion of the robotic arm.For which we used the getframe(gcf) function that caputerd the current frame or plot and combined all the plots into a avi(video) file using the videowriter() funtion for which the counter variable was very useful. The video link for the animation is attached herewith.Video file