Week 2- 2R Robotic Arm Challenge

Aim: Write a program in MATLAB to simulate the forward kinematics of 2R Robotic Arm.

Theory:

2R Robotic Arm:

Robotic Arm with the Degree of Freedom of 2 is called 2R Robotic arm. It consists of 2 rotating joints and 2 links with manipulator at the end of arm. In above Figure link 1 is making angle θ₁ with X-Axis and it has length of l₁, link 2 is making θ₂ with X-A xis and it has length of l₂ .

Calculation:

To find the positions of the link we follow below procedure:

Let Intial position of the link1 be (X1, Y1) = (0, 0)

Final position of the link2 be (X2, Y2)

Final position of the link3 be (X3, Y3)

Therefore,

X₂ = l₁*cos(θ₁)

Y₂ = l₁*sin(θ₁)

X₂ = X₂+l₂*cos(θ₂)

Y₂ = Y₂+l₂*sin(θ₂)

Code:

%Program to simulate 2R Robotic Arm
clear all
close all
clc
%Input
%lengths of links
l1 = input('Enter the length of 1st link(l1):');%Length of 1st link
l2 = input('Enter the length of 1st link(l2):');%Length of 2nd link
%Angles made by the links with X-axis
%her use linspace command to input angles
theta1 = linspace(0,90,10);%Input angle made by the link1 with X-axis(use linspace command)
theta2 = linspace(0,90,10);%Input angle made by the link2 with X-axis(use linspace command)
%Base position or intial position of link1
x1 = 0;
y1 = 0;
%increment value foe for loop
t = 1;
%to get the different positions of the links with respective eachoyher we
%are using for loops
for i = 1:length(theta1)
    Theta1= theta1(i);
    for j = 1:length(theta2)
        Theta2=theta2(j);
        %End position of link1 or intial position of link2
        x2 = l1*cosd(Theta1);
        y2 = l1*sind(Theta1);
        %End of link2 or position of manipulator
        x3 = x2+l2*cosd(Theta2);
        y3 = y2+l2*sind(Theta2);
        %Plotting
        plot([x1 x2],[y1 y2],[x2 x3],[y2 y3],'linewidth',5)
        axis([-0.1 2 0 2])%Axis for plot
        pause(0.07)
        M(t) = getframe(gcf);%assigning frames
        t=t+1;
    end
end
movie(M)
videofile = VideoWriter('Robotic_arm.avi','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

Procedure:

1. Input lengths of the links 1&2 using Input() command.
2. Assign the range of angles to be observed in simulation to θ₂ and θ
3. Open for loop of θ₁ and open other for loop of θ
4. Write the logic or calculation part of link positions with respective each other.
5. Plot the curve inside the for loop and use the pause () command to capture every frame or plot.
6. Assign these captured frames to different element of a matrix.
7. End the loops and create a movie.
8. Output of the Program is uploaded in Youtube and the Youtube link is given below.

Youtube link: https://youtu.be/UGP5ZJa9SWI

Errors & Corrections:

Error1:

Correction:

Here I used Input() command to give the inputs to the angles θ₂ and θ₁.Whlie doing so I accidentally given different matrix sizes which lead to this error and I rectified that in correction for next eteration.

Error2:

Here I identified two errors First is in output and Second is error in creating the movie.

Corrections:

2. Output error is due to typing (theta1,theta2) instead of (Theta1,Theta2) inside the logic.
3. Due to typing uncompressed.avi instead of Uncompress AVI inside the video file assigning command.

Result:

I uploaded the final avi also.

Conclusion:

By this we created the 2R Robotic arm Simulation and created the video file.