MATLAB program to simulate forward kinematics of a 2R Robotic Arm

I had tried to simulate different positions of a 2 link robotic arm in first quadrant (i.e. angle of links varies from 0 to 90 degrees), using MATLAB.

Assumptions:

1. Robotic arm is pivoted at the origin(0,0).
2. Different links are connected to each other using hinge joint.
3. Length of first link is 2 units and that of link 2 is 1.5 units.

Mathematical calculations:

The basic idea behind this is to plot both links using two end points at different angles of both links. Co-ordinates of end points can be calculated using simple trignometry at any particular angle of both links.

θ = Angle of first link with positive x-axis

ϕ = Angle of second link with positive x-axis

l1 = Length of first link

l2 = length of second link

Above image shows different dimension of robotic arm.

Co-ordinates:

x0=0

y0=0

x1 = l1*cos(θ)

y1 = l1*sin(θ)

x2 = x1 + l2*cos(ϕ)

y2 = y1 + l2*sin(ϕ )

MATLAB code:

%Program to simulate forward kinetics of a 2R robotic arm

clear all
close all
clc

% INPUT

l1 = 2;        % Length of first link
l2 = 1.5;      % Length of second link

theta = linspace(0,90,20)      % Creating 20 different values for first angle
phi = linspace(0,90,20)        % Creating 20 different values for second angle

ct = 1;                        % counter to save each figure in an array
for i = 1:length(theta)
    
   THETA = theta(i);
   for j = 1:length(phi)
       
      PHI = phi(j);
      x0 = 0;                   % x co-ordinates of first link at starting end
      y0 = 0;                   % y co-ordinates of first link at starting end
      
      x1 = l1*cosd(THETA);      % x co-ordinates of first link at other end or start of second link
      y1 = l1*sind(THETA);      % y co-ordinates of first link at other end or start of second link
      
      x2 = x1 + (l2*cosd(PHI)); % x co-ordinates of second link at other end
      y2 = y1 + (l2*sind(PHI)); % y co-ordinates of second link at other end
      
      
      %PLOT
      
      plot([x0,x1],[y0,y1],[x1,x2],[y1,y2],'linewidth',2);  %plotting both links in a single plot
      axis([-0.5,4,0,4]);        % setting visiblity limits of x and y axis
      pause(0.01);               % pause each frame of plot for 0.01 sec
      
      N(ct) = getframe(gcf);     % saving each frame in an array named as N
      ct = ct + 1; 
     
      
   end    
end

movie(N)                   % creating video file of animation
videofile = VideoWriter('Forward kinematics of 2link robotic arm','Uncompressed AVI');
open(videofile);           % opening video file
writeVideo(videofile,N);   % writing each frame in video file
close(videofile);          % close video file

Output:

Link to view video simulation of robotic arm :

https://youtu.be/h5IDjrb0hBs

Output videos shows diffrent positions of robotic arm which can be use to identify how much total space robotic arm can cover o what are the maximum and minimum length of rocotic arm at which it can be operated.