FORWARD KINEMATICS OF A 2-R ROBOTIC ARM

Program Explaination-

Define the program objective by comment

Define Inputs-

1. length of link 1(AB) = L1, length of link 2(BC) = L2.
2. Angle made by link 1 with x-axis = theta1, Angle made by link 2 with x-axis = theta2 .
3. To define angles, we use linspace command because for a particular range of motion links angles vary w.r.t x-axis.
4. To create animation we req. n frames. So, in order to create a frame we define ct.

Now, as we want to lift our robotic arm from 0 drgree to 90 degrees. It could be accomplished in n steps & for each step we want same set of instructions to be performed, therefore we use 'for loop'.

for loop-

1. i- defines the total range of steps in which link1 moves from initial position(0 degree) to final position (90 degree).
2. IN 1:length(theta1), 1 means step1 & length (theta1) means value of i upto total values of theta1 (in our case 10).
3. For each step, value of theta1 changes & to store it we create another variable 'alpha1'.
4. For link2 we create another 'for loop' with variable j to store steps.
5. For each step, value of theta2 also changes & to store it we create another variable 'alpha2'.
6. Now, we define the coordinates of link1 as [A(x0,y0) & B(x1,y1) and the coordinates of link2 as [(x1,y1)& C (x2,y2)].
7. As we want each & every position of the link to be in the frames, therefore we use plot command inside the for loop.

Plotting-

1. Both the links are plotted under single plot command with desired line (link) width.
2. Now we adjust the plot-axis, so that we get sufficient space to make the whole link visible.
3. To see the each frame of motion from 0 to 90 degree, we use pause command, to pause the program (for desired time).

To create the animation-

1. To save these n frames, we define a variable M(ct) and get the current fig. into the frame by using getframe(gcf) command. Here ct shows the nth frame.
2. Every time link approches to new position, we req. new frame to capture it. Therefore, no. of frames increases one by one. (ct=ct+1).

Here, our for loop completes, Therefore we use end commond two times for two for loops each.

Saving the animation-

1. To play the animation in matlab itself we use movie function along with the variable in which all frames are saved, "movie(M)".
2. To create a video file that can be accessed outside the MATLAB, we create an empty videofile and save it in a variable.
3. Empty videofile can be created by using VideoWriter command followed by videofile name with format extension & its type under single quote in paranthesis.
4. Robotic_arms = VideoWriter ('Forward_Kinematics.avi' , 'uncompressed AVI').
5. Now, we will open the empty video file by open command.
6. open (Robotic_arms)
7. Now, we will write the previously created animation into this videofile by writeVideo command.
8. writeVideo (Robotic_arms,M)
9. Now, to close the videowriter we use close command.
10. close (Robotics_arms)

Error solutions-

error1 = In movie function 'm' should be of lower-case.

error2 = In VideoWriter function 'v' & 'W' should be of upper-case.

error3 = In writeVideo function 'w' should be of lower-case and 'V' should be of upper-case.

Video_link-https://youtu.be/Ay5KBRIkiFo

%To animate the 2-R robotic arm
clear all
close all
clc

%Inputs

L1 = 2;
L2 = 1;
theta1 = linspace(0,90,10);
theta2 = linspace(0,90,10);
ct = 1;
for i= 1:length(theta1)
    alpha1 = theta1(i);

for j= 1:length(theta2)
        alpha2 = theta2(j);
        
        x0 = 0;
        y0 = 0;

        x1 = L1*cosd(alpha1);
        y1 = L1*sind(alpha1);

        x2 = x1 + L2*cosd(alpha2);
        y2 = y1 + L2*sind(alpha2);

        %Plotting

       plot([x0 x1], [y0 y1],[x1 x2], [y1 y2], 'linewidth',3)
       axis ([-1 4 0 4])
       pause (0.03)
       M(ct) = getframe (gcf);
       ct = ct+1;
  
    end
end
     % To_create & save videofile.
      movie (M)
      Robotic_arms = VideoWriter ('forward_kinematics.avi','uncompressed AVI')
      open (Robotic_arms)
      writeVideo (Robotic_arms,M)
      close (Robotic_arms)