Week 2- 2R Robotic Arm Challenge

1. Aim:

To write a program to simulate the motion of the 2R Robotic arm.

2. Governing equations:

Forward kinematics refers to process of obtaining position and velocity of end effector, for the given known joint angles and angular velocities.

The trignometric equations used are:

• `Sin(theta) = (opposite) / (hypoten use)`
• `Cos(theta) = (adjesent)/(hypoten use)`

Note:

• The length is in meters.
• The angle is in degrees.

3. Objective of the project:

1. Write to program in MATLAB to simulate the motion of the 2R robotic arm.
2. Capture all the plots as frames and convert the frame array into the video file in .avi format.
3. Save the motion in a video format.

4. Body of the content:

• Software used - MATLAB
• Language of the software - C/C++

• % Forward kinematics of 2R Robotic arm using 'for loop'
  
  clear all        % clearing all the garbage values and closing all the program/figures
  close all
  clc
  
  % Inputs
  L1 = 1;   % length of first arm (meters)
  L2 = 0.5; % length of second arm (meters)
  
  % Defining the angular range
  theta1 = linspace(0,90, 10); % Angle range for the first arm in degrees
  theta2 = linspace(0,90, 50); % Angle range for the second arm in degrees
  
  ct = 1;  % To keep track of the frames
  
  for i = 1:length(theta1)      % Looping for the length if theta1 array
      THETA1 = theta1(i)        % Assigning the values
      
      for j = 1:length(theta2)  % Looping for the length if theta2 array
          THETA2 = theta2(j)    % Assigning the values
          
          % Base co-ordinates
          X0 = 0;
          Y0 = 0;
  
          % End of link 1 & start of link 2
          X1 = L1*cosd(THETA1);
          Y1 = L1*sind(THETA1);
  
          % End of link 2
          X2 = X1 + L2*cosd(THETA2);  % using cosd because our angle is in degrees
          Y2 = Y1 + L2*sind(THETA2);  % using sind because our angle is in degrees
  
          % PLOTTING 
          plot([X0 X1],[Y0 Y1],[X1 X2],[Y1 Y2],'linewidth',3)
          
          axis([-1 2 0 2]) % Definig the axis length
          
          pause(0.0001)           % Pausing the frame for 0.1 sec
          
          M(ct) = getframe(gcf);  % Getting the current firure and saving it in an array 'M'
          ct = ct+1;
          
      end
      
  end
  
  movie(M)
  
  videofile = VideoWriter('forward_kinematics_forloop', 'Uncompressed AVI')       % Defining a video file 
  open(videofile)                                                                 % Opening the video file
  writeVideo(videofile,M)                                                         % Writing to video file with frames from M
  close(videofile)                                                                % Closing the video file
  

• First all the previous programs and variable assigned are cleared.
• Then input are defined here the length of the first and second arm is defined.
• Then angular range is defined using linspace command.
• Then using the 'for loop' to run for the length of theta1 times.
• Again using a 'for loop' to run for the length of theta2 times.
• The position of base of the first arm is defined.
• The position of the second end of the first arm is calculated by using the trignometric formulae.
• The second end of the first arm becomes the first end of second arm.
• Then the position of the second end of second arm is calculated.
• Then this data is plotted using the plot command and axis are defined for steady frame.
• Every figure of the plot is caputured in a frame and an arrray is defined to store it named 'M'.
• Then by using videowriter command the video is created named as 'forward_kinematics_forloop.avi'
  1. First step is to open the file with file id.
  2. Then frame array is written.
  3. Close the function.

4. Results and output:

• The executed progrm:

• The graphs plots array is the output containg the positon of both the arms. (single frame example)

• The output is converted from frames array to video file named 'forward_kinematics_forloop' :

5. Conclusion:

1. Successfully executed the program to simulate the motion of 2R Robotic arm.
2. The output is stored in the form of a video named 'forward_kinematics_forloop.avi'.

6. References:

1. 2 - Kinematics and Dynamics by Marko B.Popovic, Matthew P.Bowers, Worcester Polytechnic Institute, Worcester, MA, United States - https://doi.org/10.1016/B978-0-12-812939-5.00002-1