Week 2- 2R Robotic Arm Challenge

PROGRAM: Simulation of forward kinematics of a 2R Robotic Arm

AIM:

To Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm and make a video of it.

THEORY:

A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm. The links of such a manipulator are connected by joints allowing either rotational motion or translational (linear) displacement.

A 2R robotic arm represents a robotic arm with two rotations. i.e. it has two links which rotate or work over a two-dimensional plane with each of links having a single degree of freedom.

If we are able to find out how the robotic arm move, we could specify the application of a robot. That is we can find out it's workspace (The possible location the robot can reach).

For a 2R Robotic Arm, there are two links and two rotational joints. Link 1 makes an angle `theta_1`with the x-axis and link 2 makes `theta_2`with the x-axis. Let's assume the link length to be `l_1 and l_2` respectively. First we need to specify the position of the manipulator if `theta_1 and theta_2` are given/known.

The starting and end points of link 1 and 2 are marked as shown in figure.

The starting point of link 1 is marked as `(x_0, y_0)`and is taken as (0, 0). The end point of link 1 and starting point of link 2 are same, i.e. `(x_1, y_1)`. From above figure,

`x_1 = l_1*costheta_1 and y_1 = l_1*sintheta_1`.

Similarly the end point of link 2 is `(x_2, y_2)`. i.e. `x_2 = x_1+l_2*costheta_2 and y_2=y_1+l_2*sintheta_2`. With these three points we could do the program in matlab.

CODE:

% Program to simulate the forward kinematics of a 2R Robotic Arm by Matlab

 clear all
 close all
 clc

% inputs
% Lengths of Robotic arm link 1 and 2
l1 = 2;
l2 = 1;

% The angle made by link 1 and 2 with respect to x-axis
theta1 = linspace(0,90,10);
theta2 = linspace(0,90,10);

k=1;
for i=1:length(theta1)
    THETA1=theta1(i);
    for j=1:length(theta2)
        THETA2=theta2(j);

        % Assigning link coordinates
        % For link 1- starting point (x0,y0)
        x0 = 0;
        y0 = 0;

        % The end point of link 1 and starting point of link 2 are same- (x1,y1)
        x1 = l1*cosd(THETA1);
        y1 = l1*sind(THETA1);

        % The end point of link 2
        x2 = x1+l2*cosd(THETA2);
        y2 = y1+l2*sind(THETA2);

        % Plotting
        plot([x0 x1], [y0 y1], [x1 x2], [y1 y2], 'LineWidth',2.5)
        axis([-0.1 3.1 0 3.1])
        xlabel('x-axis')
        ylabel('y-axis')
        pause(0.2)
        M(k)=getframe(gcf);
        k=k+1;
    end
end
% Making the Simulation video
movie(M)
videofile= VideoWriter('forward_kinematics_2R_Robotic_Arm.avi','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

EXPLANATION:

In the above program code, first we need to specify the inputs that we need to provide. Initially we provide command to store the value of length of link 1 and 2 in `l_1 and l_2`.

Then we need the angular movements of link 1 and 2, for simulation purpose we provide ten value each for `theta_1 and theta_2` by using linspace command. i.e.,

Then the command to assign link coordinates are provided. We take the starting point of link 1 as origin, i.e.

x0 = 0;

y0 = 0;

Similarly the coordinate change of both link (due to change in `theta_1 and theta_2`) is provided in the form of equation that we derived in the theory section.

% The end point of link 1 and starting point of link 2 are same- (x1,y1)

x1 = l1*cosd(THETA1);

y1 = l1*sind(THETA1);

% The end point of link 2

x2 = x1+l2*cosd(THETA2);

y2 = y1+l2*sind(THETA2);

Then plot command is used to plot the simulation of forward kinematics of 2R robotic arm. For better understanding the command to fix the axis (By giving x limits and y limits) and to get a pause of 0.2 is also provided. The command to label axis is also given.

The command to store each frame in M is also mentioned,

M(k)=getframe(gcf);

k=k+1; (intitally k=1 is given for capturing each frame)

For making and saving the simulation video, the below command is used. By VideoWriter command the video is created in .avi format.

movie(M)

videofile= VideoWriter('forward_kinematics_2R_Robotic_Arm.avi','Uncompressed AVI');

open(videofile)

writeVideo(videofile,M)

close(videofile)

OUTPUT WINDOW:

FIGURE:

The position of link1 and link2 at particular `theta_1 and theta_2`.

SIMULATION VIDEO LINK:

https://youtu.be/T7yvyEVgsec

RESULT:

A program in Matlab to simulate the forward kinematics of a 2R Robotic Arm is made and it is saved as a simulation video.