Week 2- 2R Robotic Arm Challenge

Aim: To simulate forward kinematic of a 2R-Robotic Arm using MATLAB.

Objective:

• To create a MATLAB program for the movement of 2R-Robotic arm having an end manipulator. 
• Animating and creating a movie from the obtained program in MATLAB.

Theory:

A robotic arm is 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 hand.

 

                                      Figure of 2R robotic arm

Inputs: 

1. The above figure represents the fig of 2R- Robotic arm.

2. There are two links,

• Link1 (l1) = length of link attached to base.
• Link2 (l2) = length of link between the first link and the manipulator

3. The coordinates of link1 (l1) are,

• (x0 y0) = starting point of l1.
• (x1 y1) = end point of l1/ starting point of l2.

4. The coordinates of link2 (l2) are,

•  (x1 y1) = starting point of l2.
• (x2 y2) = end point of l2.

5. Two angles are made which are,

• theta1 = angle made by l1 with x-axis.
• theta2 = angle  made by l2 with x-axis.

Code:

  % Forward Kinematic of a 2r Robotic Arm Manipulator
    clear all
    close all
    clc
    
    % Inputs
    l1 = 2; 
    l2 = 1;
    
    theta1 = linspace(0,90,10);
    theta2 = linspace(0,90,10);
    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 3.5 0 3.5])
              pause(0.03)
              M(ct) = getframe(gcf);
              ct = ct+1;
                
         end
    end
    
    movie(M)
    videofile = VideoWriter('Forward_kinematic.avi','Uncompressed AVI');
    open(videofile)
    writeVideo(videofile,M)
    close(videofile)

Explanation of the above code and output:

1. Clear & Close command
   • Clear all - used to clear all the workspace variable.
   • Close all - used to close all the plot output window.
   • Clc - used to clear the command window.
2. Length of link’s
   • l1 = 2; - the length of link one with 2meter.
   • l2 = 1; - the length of link tow with 1meter.
3. Angle of the link’s
   • theta1 = linspace(0,90,10); - the value of angle of l1.
   • theta2 = linspace(0,90,10); - the value of angle of l2.
4. Linspace command
   • linspace command is used for equal interval array.
5. For loop
   • For loop is used to repeat a specific number of times.
6. For loop for link length
   • i = 1: length(theta1); for loop between length of theta range.
   • THETA1 = theta(i); initialized value of different value in THETA1.
   • for j = 1: length(theta2); - for loop between length of theta range.
   • THETA2 = theta2(j); initialized value of different value in THEAT2.
7. Coordinates
   • x0 = 0
   • y0 = 0
   • x1 = l1*cosd(THETA1); - cosd gives the value of THETA1 in degree.
   • y1 = l1*sind (THETA1); - sind gives the value of THETA1 in degree.
   • x2 = x1+l2*cosd(THETA2); - x2 coordinates value.
   • y2 = x1+l2*sind(THETA2); - y2 coordinates value.
8. Plot
   • plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],’linewidth’,3); -plot command is used to generate x-axis & y-axis plot. Linewidth command was used to give width to the line in the plot.
9. Axis
   • axis([-0.1 3.5 0 3.5]) – used to set the range, (-0.1to3)for x-axis and (0to3.5)for y-axis.
10. Pause
    • pause(0.03) – used to pause video for smoother animations.
    • M(ct) = getframe(gcf) – get a frame from plot.
11. End
    • end – used to close the loop command.
12. Movie
    • movie(m) – plays the movie in matrix ones.
13. Videofile
    • Videofile = videoWrit(‘forward_kinematics.avi’,‘Uncompressed AVI’) – is used for uncompressed avi properties to this video data on avi file.
    • Open(videofile) – is used to open videofile from writing video data.
    • writeVideo(videifile,M) – toweite video data to file.
14. Close
    • Close(videofile) – is used to close file for writing video data.

The errors faced while programming:

• Error 1

•  The error I faced was 'invalid expression' {theta1 = (0,90,10)} I had not mentioned the linspace command. The correct command is {theta1 = linspace(0,90,10)}.

• Error 2

• The error I faced was 'error of line 27' {plot([x0 x0]' [y0 y1], [x1 x2], [y1 y2], 'LineWidth',3)}. I had misspelt the y coordinate to yo (leter O) instead of zero.

Result:

Click on the link below to view the Simulation of the 2R Robotic Arm

Youtube link for an animation: https://youtu.be/DJiJPiPesH4

Conclusion:

The results show the maximum reach of the robotic arm used to perform the different applications. The workspace has been experienced by simulating the forward kinematics with a program in MATLAB.