2R Robotic Arm Challenge

AIM: To simulate the forward kinematics of a 2R Robotic Arm

GOVERNING EQUATIONS:

for First Arm:

`x1 = l1*cos(theta1)`

`y1 = l1 * sin(theta1)`

For Second Arm:

`x2 = x1 + l2*cos(theta2)`

`y2 = y1 + l2*sin(theta2)`

Where,

`(x1,y1) implies` end points of First Arm

`(x2,y2) implies` end points of Second Arm

`l1` is the length of First Arm in 'm'

`l2` is the length of Second Arm in 'm'

`theta1` is the angle made by First Arm with horizontal in degree

`theta2` is the angle made by Second Arm with horizontal in degree

OBJECTIVE:

1. To write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm.

2. Create an animation file of the plot

MATLAB CODE:

% Forward Kinematics of a 2R Robotics Manipulator
clear all
close all
clc

% Inputs
l1 = 1;
l2 = 0.7;
theta1 = linspace(0,90,30);
theta2 = linspace(0,90,30);

ct = 1;
for i = 1:length(theta1)
    Theta1 = theta1(i);
    for j= 1:length(theta2)
        Theta2 = theta2(j);
        % Coordinates
        x0 = 0;
        y0 = 0;
        
        x1 = l1*cosd(Theta1);
        y1 = l1*sind(Theta1);
        
        x2 = x1 + l2*cosd(Theta2);
        y2 = y1 + l2*sind(Theta2);
        
        % Plotting
        plot([x0 x1],[y0 y1],[x1 x2],[y1 y2], 'linewidth', 3);
        axis([-0.1 2 0 2]);
        xlabel('x-axis');
        ylabel('y-axis');
        title('Forward Kinematics of a 2R Robotic Arm');
        grid on;
        pause(0.03)
        M(ct) = getframe(gcf);
        ct = ct +1;  
    end
end

%Animation Recording
movie(M)
videofile = VideoWriter('robotics.mp4', 'MPEG-4');
open(videofile);
writeVideo(videofile,M);
close(videofile);

1. linspace() is used to create an array of `theta1 and theta2` having equal intervals in its elements.

2. sind() and cosd() are used instead of sin() and cos() as `theta` values are in degree.

3. getframe(), captures the current axes as it appears on the screen as a movie frame.

4. movie(), plays the movie defined by a matrix whose columns are movie frames produced by getframe().

5. VideoWritter(), creates a video file.

6. open(), opens a specified file.

7. writeVideo(), writes video in the specified file.

8. close(), closes a specified file.

ERROR ENCOUNTERED:

This error is encountered because I did not initialize ct.

Steps were taken to overcome the error: Initialized ct = 1 at line number 12.

ANIMATION:

2R Robotic Arm Animation