Week 3.2 - 2R Robotic Arm Challenge

Aim :

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

Objective:

• Write a program to simulate forward kinematics of a 2R Robotic Arm
• To create a Movie/Animation from the plots obtained from the program

Theory Explaination:

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 (such as in an articulated robot) or translational (linear) 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 hamd.

-In this project, we consider a 2R robotic arm. 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.

-Also, both the links are restricted to a 90° rotation with respect to the axes. Fig below shows the 2R robotic arm having many parts as described.

• Let , L1 & L2 be the lengths of the link-1 & link-2 Respectively.
• Let , θ1">θ1be the angle formed by link-1 with horizontal.
• Let , θ2">θ2 be the angle formed by link-2 with horizontal.
• Let , the starting and end co-ordinates of link-1 to be (x₀, y₀) and (x₁, y₁)
• Let , the starting and end co-ordinates of link-2 to be (x₁, y₁) and (x₂, y₂)

Coding logic and syntax explaination:

• clear all, close all, and clc: These commands respectively clear all workspace variables, close all open figures/windows, and clear the command window to ensure a clean start.

• l1 and l2: These variables represent the lengths of the two robotic arms.

• theta1 and theta2: These variables store arrays of angles in degrees. They are created using the linspace function to generate 10 equally spaced angles ranging from 0 to 90 degrees.

• ct: This variable is an index that keeps track of the frame number for creating the animation.

• The first for loop iterates through each angle in the theta1 array.

• Inside the first loop, the second for loop iterates through each angle in the theta2 array.

• Inside both loops, the current values of THETA1 and THETA2 are set to the corresponding angles from the arrays.

• The coordinates for the start point of the arms (x0 and y0) are set to (0, 0).

• The coordinates for the end point of the first arm (x1 and y1) are calculated using trigonometric functions (cosd and sind) based on l1 and THETA1.

• The coordinates for the end point of the second arm (x2 and y2) are calculated by adding the coordinates of the end point of the first arm to the position determined by l2 and THETA2.

• The plot function is used to draw the robotic arms. The plot consists of two segments: one representing the first arm and the other representing the second arm. The linewidth parameter sets the thickness of the lines.

• The axis function is used to set the limits of the plot area to ensure that the animation stays within a specific range.

• pause(0.03): This command introduces a short pause between frames, creating the appearance of animation.

• The getframe function captures the current figure as a frame and stores it in the M array. The ct index is used to keep track of which frame is being captured.

• The outer loop increments ct to prepare for the next frame.

• After both loops are completed, the movie function is used to play the animation using the frames stored in the M array.

• The animation frames are then written to a video file named 'robotic_arms.avi' using the VideoWriter object. The video format chosen is an uncompressed AVI.

• The video file is opened, the frames are written to the file using the writeVideo function, and then the file is closed.

Main code:

% kinematics of 2R Robotics Arm Manipulator
clear all
close all
clc

% Define the lengths of the two robotic arms
l1 = 1;
l2 = 0.5;

% Define an array of angles for the first and second arms
theta1 = linspace(0, 90, 10);
theta2 = linspace(0, 90, 10);

% Initialize a counter for the animation frames
ct = 1;

% Loop through each angle in the theta1 array
for i = 1:length(theta1)
    % Get the current angle for the first arm
    THETA1 = theta1(i);
    
    % Loop through each angle in the theta2 array
    for j = 1:length(theta2)
        % Get the current angle for the second arm
        THETA2 = theta2(j);
        
        % Set the starting coordinates of the arms
        x0 = 0;
        y0 = 0;
        
        % Calculate the coordinates of the end point of the first arm
        x1 = l1 * cosd(THETA1);
        y1 = l1 * sind(THETA1);
        
        % Calculate the coordinates of the end point of the second arm
        x2 = x1 + l2 * cosd(THETA2);
        y2 = y1 + l2 * sind(THETA2);
        
        % Plot the robotic arms with the calculated coordinates
        plot([x0 x1], [y0 y1], [x1 x2], [y1 y2], 'linewidth', 3);
        
        % Set the plot limits to create a consistent view
        axis([-1 1.5 0 1.5])
        
        % Pause to create an animation effect
        pause(0.03)
        
        % Capture the current frame and store it in the M array
        M(ct) = getframe(gcf);
        
        % Increment the frame counter
        ct = ct + 1;
    end
end

% Play the animation using the captured frames
movie(M)

% Create a VideoWriter object for saving the animation to a video file
videofile = VideoWriter('robotic_arms.avi', 'Uncompressed AVI');
open(videofile)

% Write the captured frames to the video file
writeVideo(videofile, M)

% Close the video file
close(videofile)

Video link:

Errors faced:

• Misplaced the code in the line of ct = ct + 1 above the line M(ct) = getframe(gcf)
• Matlab is not recognised the word of Movies(M) that can be replaced with movies(M).

Screenshot of the errors occured:

Figure - 1:

Figure - 2:

Conclusion:

We have simulated 2R robotic arm by using the matlab programming and also created a Movie/Animation from the plots obtained from the program.