Forward Kinematics of a 2R Robotic arm

Aim: To write a program in MATLAB to simulate the forward kinematics of a 2R Robotic Arm.

Objective:

a) MATLAB program for simulating forward kinematics of a 2R robotic arm.

b) Creating and saving an animation file of the plot.

Description: A 2R robotic arm contains two links (l1 , l2) and two rotational joints. If we are able to figure out how a robot is going to move we can figure out the possible location the robot can reach.

Link1 is making an angle theta1 w.r.t x-axis and Link 2 is making an angle theta2 with w.r.t y-axis.

Calculation: If θ1 and θ2 are given, we can calculate the final position of the manipulator.

calculating the position of Link1 and Link2-

x2 = (x1 + L2cosθ2)

y2 = (y1 + L2sinθ2)

With the above co-ordinates, we have our solution set-

[x0 y0] , [x1 y1] , [x2 y2]

where,

x0 yo = Fixed point of link1

x1 y1 = End point of link1

x2 y2 = End point of link2

Inputs:

Length of the link1 (l1) = 1m

Length of the link2 (l2) = 0.5m

theta1 (θ1) and theta2 (θ2) varies from 0 to 90 degrees.

Code:

%Forward Kinematics of a 2R Robotic arm manipulator
clear all
close all
clc

%Inputs
l1= 1;
l2= 0.5;
theta1= linspace(0,90,40);
theta2= linspace(0,90,40);

ct=1;
for i= 1:length(theta1)
    THETA1= theta1(i);
   for j= 1:length(theta2)
       THETA2= theta2(j);
       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 1.5 0 1.5])
       pause(0.01)
       M(ct)= getframe(gcf);
       ct=ct+1;
       
   end
end

movie(M)
videofile= VideoWriter('forward_kinematics.avi','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

Explanation of the code:

clear all, close all, clc commands used to delete the variables created in the workspace and command window.

%Inputs
l1= 1;
l2= 0.5;
theta1= linspace(0,90,40);
theta2= linspace(0,90,40);

Here,

• l1 and l2 represents the length of Link1 and Link2
• linspace command used to create arrays of theta1 and theta2 from 0 to 90 degrees with 40 values between 0 to 90.

for i= 1:length(theta1)
THETA1= theta1(i);

for j= 1:length(theta2)
THETA2= theta2(j);

Here,

• THETA1 and THETA2 is variable which contains 1 value. theta1 and theta2 is the value from 0 to 90 degrees.

• Using For loop command to repeat the value of theta1 and theta2 which has 40 values and it stores only one value. and the value of i and j is going to change from 1 to theta1 and theta2 value which is 40. And each time value changes it executes a set of commands that are present in for loop.

  Ex: when i = 1, it takes the first value of theta1 and when i = 2, it takes the second value of theta1.

x1= l1*cosd(THETA1);
y1= l1*sind(THETA1);

x2= x1+l2*cosd(THETA2);
y2= y1+l2*sind(THETA2);

Here,

• x1, y1 and x2, y2 are the starting point coordinates and endpoint coordinates of link1 respectively.

%Plotting

plot([x0 x1],[y0 y1],[x1 x2],[y1 y2], 'linewidth',3)
axis([-0.1 1.5 0 1.5])
pause(0.01)
M(ct)= getframe(gcf);
ct=ct+1;

end
end

• Using plot command to plot the graph with the given statement.
• Using axis command to set the x and y limits.
• Using pause command to set an interval at each position.
• Using an array M and adding the getframe(gcf) function to create (stitching) an animation of all the plots.

• Using Counter command (ct=ct+1) to get a single position of link2 at a time and each and every time for loop is getting executed it is going to increment 1 time.

Converting the animation plot of the above code into a movie with .avi extension with the following code.

movie(M)
videofile= VideoWriter('forward_kinematics.avi','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

Here,

• At the end of for loop MATLAB is going to make a movie with all the frames with movie(M) command.
• Creating a video with the command videofile.
  
  
• Opening a video file with open(videofile) command and then write the captured frame with writevideo command and then closing the video by close(videofile) command.

Result: