AIM:

Simulation of Forward Kinematics of a 2R Robotic Arm using MATLAB

Diagram:

The robotic arm has 2 links. Link – 1 & Link – 2.

Length of Link – 1 = L1,

Angle made by Link – 1 with base = Theta1 (with respect to the x-axis),

Length of Link – 2 = L2, and

Angle made by Link – 2 with respect to base = Theta2 (with respect to the x-axis)

First Coordinates = x0, y0 => (0, 0)

Second Coordinates = x1, y1 => (L1*cosd (theta1), L1*sind (theta1))

Third Coordinates =x2, y2 => (x1 + L2*cosd (theta2), y1 + L2*sind (theta2))

OBJECTIVE:

The main objective of this project is to write a MATLAB code for forward kinematics of the robotic arm and simulate its movement and present it through animation.

WORKFLOW OF THE PROJECT:

1. Initially, we assume the lengths of Link1 & Link2 and vary the angle between links and x-axis to different degrees.
2. Plotting the graph of individual values.
3. Merging of all the plots in one and demonstrating it with animation.

Plots:

CODE

% Forward kinematics plotting and animation

clc

clear all

close all

% Inputs for the robotic arm

L1 = 1;

L2 = 0.4;

theta1 = linspace (30, 135, 15);

theta2 = linspace (0, 360, 15);

ct = 1;

for a = 1 : length (theta1)

THETA_1 = theta1 (a);

for b = 1 : length (theta2)

THETA_2 = theta2 (b);

x0 = 0;

y0 = 0;

x1 = L1 * cosd (THETA_1);

y1 = L1 * sind (THETA_1);

x2 = x1 + L2 * cosd (THETA_2);

y2 = y1 + L2 * sind (THETA_2);

% Plotting

plot ([x0 x1], [y0 y1], [x1 x2], [y1 y2], 'linewidth', 2.5);

axis ([-1.5 1.5 -1.5 1.5])

xlabel ('x');

ylabel ('y');

grid on

pause (0.05);

M(ct) = getframe (gcf); % gets the current window figure

ct = ct + 1;

end

end

% Movie creation of the plot

movie(M)

videofile = VideoWriter ('forward_kinematicsAnimation.avi', 'uncompressed avi')

% This line will create the .avi

% file which will dump-out all the

% frames.

open (videofile)

writeVideo (videofile, M)

close (videofile)

CODE EXPLANATION:

1. Initially, lengths of links 1&2 are assigned (1, 0.4, respectively) as well the angles theta1 & theta2. The angles are varied using “LINSPACE”.
2. Using the “FOR-LOOP”, we get the different positions of the arm of the robot (Link1 & Link2). (After initially the loop counter ct.)
3. The graph is plotted and is being saved in the new variable “M”. Using the “PAUSE” command, a continuous plot is got which seems like an animation.
4. For creating the movie, ‘MOVIE’ command is used which saves all the values from the variable M. First the .avi file is created which will dump-out all the frames created. Then, it’ll open the video file, write it in M, and then it’ll close it.

CONCLUSION:

The forward kinematics of the 2R robotic arm was successfully simulated using MATLAB.

Link:

Forward Kinematics Animation of a 2R robotic arm