Week 2- 2R Robotic Arm Challenge

AIM

Program in Matlab to simulate the forward kinematics of a 2R Robotic Arm.

OBJECTIVE

• To simulate the forward kinematics of a 2R Robotic Arm.
• Animating and creating a movie from the plots obtained.

THEORY

A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm. The arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion or translational (linear) displacement. The links of the manipulator can be considered to form a kinematic chain.

GOVERNING EQUATIONS

x2 = x0 + x1 + l2*cosϴ

y2 = y0 + y1 + l2*sinϴ

x1 = x0 + l1* cosϴ

y1 = y0 + l1* sinϴ

Where,

x0, y0 = starting point of link 1

x1, y1 = ending point of link 1 / starting point of link 2

x2, y2 = ending point of link 2

l1 = length of link 1

l2 = lenth of link 2

PROGRAM

% Program for a 2R robotic arm
clear all
close all
clc
% Inputs
% Length of link 1
l1 = 1.5;
% Length of link 2
l2 = 0.75;
ct = 1;
% Set of angles for the movement of robotic arm
theta1 = linspace(0,90,20);
theta2 = linspace(0,90,20);
for i = 1 : length(theta1)   % iterating i from 1 to 20 as theta1 is having 20 values
    THETA1 = theta1(i);
    for j = 1 : length(theta2)  % iterating j from 1 to 20 as theta2 is having 20 values
        THETA2 = theta2(j);
        
        % Coordinates of starting point of first arm
        x0 = 0;
        y0 = 0;
        
        % Coordinates of starting point of second arm
        x1 = l1*cosd(THETA1);
        y1 = l1*sind(THETA1);
        
        % Coordinates of ending point of second arm
        x2 = x1 + l2*cosd(THETA2);
        y2 = y1 + l2*sind(THETA2);
        
        
        % Plotting
        
        % coordinates of arms
        plot( [x0 x1], [y0 y1],[x1 x2],[y1 y2],'linewidth',5,'marker','*')
        
        % Limits for x and y axis in the graph
        axis ([-0.5 3 0 3])
        
        title('Forward Kinematics of a 2R Robotic Arm')   
        
       % Collecting frames for making animation
        M(ct) = getframe(gcf);
        ct = ct + 1;
    end
end

% To make a movie of collected frames
movie(M)

% saving the file in avi format
videofile = VideoWriter('robotic_arm.avi','Uncompressed AVI');

% Writing the movie in videofile created
open(videofile)
writeVideo(videofile,M)
close(videofile)

EXPLANATION

1. Initially we assign the length of two links, namely l1 and l2.
2. Set of values for theta1 and theta2 are assigned as an array with the command linspace.
3. for command is used for the iteration of values for the desired variable. Again, for command is used for the movement of second robotic arm. Thus, for a particular position of link 1, we can obtain different positions of link 2.
4. Coordinates of both the arms are defined.
5. Coordinate values are plotted and commands are provided as changing the appearance of the contours.
6. All figures are assigned to a variable M, one at a time using ct followed by termination of for loop.
7. movie command is used to combine all figures saved in the M file to make an animation and there after saving it in avi format.
   

ANIMATION

The link for the animation has been mentioned.

https://youtu.be/Eaz-Nwn0XoQ

CONCLUSION

A practical scenario regarding the functioning of robotic arm and its workspace has been experienced with a program in MATLAB.