Simulating Forward Kinematics of a 2R Robotic Arm using MATLAB program.

AIM:

Simulating Forward Kinematics of a 2R Robotic Arm using MATLAB program.

OBJECTIVES:

1. Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm.
2. Creating an animation from the plots obtained in the program.
3. Understand the movement of an 2R Robotic in 2D workspace.

THEORY:

A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion or translational displacement. The links of the manipulator can be considered to form a kinematic chain. The terminus of the kinematic chain of the manipulator is called the end effector and it is analogous to the human hand.

Forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters.

Robotic arms used in various industrial applications such as drilling, welding, metal cutting , painting etc.

Here we have a 2R Robotic arm as shown in the figure:

The link-1 is attached to the base and end of link one is connected to link-2. And end of link-2 is connected to the end effector which performs the desired operation. In this project we will restrict the movement of the links in a 2D plane.

PROGRAM:

Programming language used is MATLAB.

% A program to simulate the forward kinematics of a 2R Robotic Arm

clear all
close all
clc

% Taking inputs
% Length of link-1 (L1) and link-2 (L2) in meter
L1=1;
L2=0.5;

% Angle traced by link-1 in degrees (theta_1)
theta_1=linspace(0,90,11);

% Angle traced by link-2 in degrees (theta_2)
theta_2=linspace(0,90,21);

% Initialising base coordinates of link-1
x_0=0;
y_0=0;

ct=1;

for i=1:length(theta_1)
    THETA_1 = theta_1(i);    %taking particular values of angle traced by link-1 in order.
    for j = 1:length(theta_2) % Iterating all values of theta_2 for particular value of theta_1
        THETA_2=theta_2(j);   %taking particular values of angle traced by link-2 in order.
        
        % Calculating the coordinates of end point of link-1
        x_1=x_0+L1*cosd(THETA_1);
        y_1=y_0+L1*sind(THETA_1);
        
        % Calculating the coordinates of the end of link-2
        % End coordinates for link-1 are the start coordinates for link-2
        x_2=x_1+L2*cosd(THETA_2);
        y_2=y_1+L2*sind(THETA_2);
        
        % Plotting the robotic arm for simulation
        plot([x_0 x_1],[y_0 y_1],[x_1 x_2],[y_1 y_2], "linewidth",2);
        axis([-0.1 1.5 0 1.5]);
        
        % Pausing the current plot for a while before movoing to the next
        % plot
        pause(0.03);
        
        % Capturing the current plot to combine later
        M(ct) = getframe(gcf);
        
        % Incrementing ct so that each frame is captured in M
        ct=ct+1;
        
    end
end

% Making a movie from collected frames
movie(M);

% Creating a video file of '.avi' format to save the animation
videofile=VideoWriter('forward_kinematics_of_2R_robotic_arm.avi','Uncompressed AVI');
open(videofile);

% Writing the movie in the videofile created
writeVideo(videofile, M);
close(videofile);

EXPLANATION OF THE PROGRAM:

1. Lengths of both the links are taken as input. Length of link-1 (L1) is taken as 1m and length of link-2 (L2) is taken as 0.5m.
2. Angles traced by both the links, for link-1 and for link-2 is taken as input. The angles traced are varied over a range to simulate the movement of the robotic arm.
3. Base position of link-1 (`x_0,y_0`)is considered as origin (0,0).
4. Then two for loops are used to iterate over the range of angles traced by both the links. For each particular angle of link-1 , link-2 is moved over its entire range , to obtain different positions of end effector at that angle of link-1.
5. For a particular value of `θ_1` and `θ_2` , the end position of link-1 is calculated by these equations.

`x_1=x_0+L_1*cos(θ_1 )`

`y_1=y_0+L_1*sin(θ_1 )`

The end position of link-1 is also the start position of link two. The end position for link-2 is calculated by these equations.

`x_2=x_1+L_2*cos(θ_2 )`

`y_2=y_1+L_2*sin(θ_2 )`

6. Then for each particular position of lin-1 and link-2 , a plot is made which is then captured frame by frame to make a movie.
7. A video file of '.avi' format is made to save the movie.
8. The movie is then written into the videofile and the final animation is thus created.

OUTPUT:

The output is obtained in form of an animated video clip. This animation can be viewed by visiting the link mentioned below.

https://youtu.be/9QOsVcTAxNM

CONCLUSION:

A simulation of the forward kinematics of a 2R Robotic Arm in 2D workspace was created using MATLAB program.