FORWARD KINEMATICS OF A 2R ROBOTIC ARM MANIPULATOR

FORWARD KINEMATICS OF 2R ROBOTIC ARM MANIPULATOR

AIM:

Matlab code for 2 arm robot manipulator

GOVERNING EQUATIONS: (used to obtain coordinates of the linkages)

x1 = l1*cos(θ1)

y1 = l1*sin(θ1)

x2 = x1+l2*cos(θ2)

y2= y1+l2*sin(02)

OBJECTIVES

1. in order to simulate a forward kinematics of a 2 r robotic arm whivh explores the two dimensional workspace.
2. forward kinematics refers to the use of kinematic equations of a robot to compute the position.
3. therefore it has two linkages and two rotational joints. hence it is used in various applications like welding a presision componenets.
4. the linkages has two degree of freedom in the workspace.
5. For different position of the first link, the second link is capable to at diffrent angles.
6. once the plots are generated combine them to create an animation.

code:

% forward kinematics 2R robotic arm manipulator
clear all
close all
clc
% inputs
l1 = 1; % the value of length coreesponding to link 1
l2 = 0.5; % the value of length coreesponding to link 2
theta1 = linspace(0,90,10); % value of theta1 ranging from 0 to 90 in 10 values
theta2 = linspace(0,90,10); % value of theta2 ranging from 0 to 90 in 10 values
ct = 1 % initial value of the counter
for i = 1:length(theta1) % to iterate through each loop from 1 to 10
    THETA1 = theta1(i);  % to assign the variable THETA1 to each value of i in theta 1
    for j = 1:length(theta2)% in order to create a nested for loop of each angle link 2
        THETA2 = theta2(j); % to assign the variable THETA2 to each value of j in theta 2
        x0 = 0; % these are the fixed coordinates of arm1
        y0 = 0;
        % to determine the value of coordinates in each linkages
        
        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 1.5 0 1.5]) % gives limit of x and y axis
        pause(0.03);
        M(ct) = getframe(gcf); % getting the figure and saving in an array called M
        ct = ct+1; % increment of counter value
        
    end
end
movie(M) 
videofile = VideoWriter('robotic_arm.avi','uncompressed AVI'); % format to store
open(videofile) % opens the movie file
writeVideo(videofile,M) % writes the movie file in given array
close(videofile)

output:

For the sample ouput

To refer the output in the animation:

https://drive.google.com/file/d/1uVInJvFtBoAcaXD6Ls54ayO2gSILgNPC/view?usp=sharing

https://youtu.be/v-lBhPhJplE

CONCLUSION:

• From this forward kinematics manipulator the robotic arm can perform the basic operations in the 2D workspace
• Hence its degree of freedom is restricted because it moves in a single plane.