Week 3.2 - 2R Robotic Arm Challenge

R Robotic Arm Challenge:

Aim:

To write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm, as shown in the video and upload simulation video on google drive.

 

Solution:

 

• In this challenge we need to find the position of manipulator.
• Step 1:
• For that we need to calculate position of link 1
• Step 2:
• Then we need to calculate the position of link 2
• Step 3:
• By above mentioned diagrams we need to define [X0,Y0],[X1,Y1] and [X2,Y2].And execute the given below expression to find the position of the links.
• X0 = 0;
  Y0 = 0;
  X1 = l1 * cosd (THETA1);
  Y1 = l1 * sind (THETA1);
  X2 = X1 + l2 * cosd (THETA2);
  Y2 = Y1 + l2 * sind (THETA2);

 

Pseudocode for 2R Robotic arm challenge:

• First we need to get l1 and l2 input from the user,here l1,l2 is link 1 and link 2.
• Then assign the theta arrays like theta1 and theta2 which is starts from 0 deg and end with 90 deg with 10 intervals by using linspace logic.
• Then assign ct=1 it is used for increment process at the plotting area for simulation.
• Using 'for' operator for assigning theta values at number of intervals with using of Variable called THETA1 and THETA2.
• X0 = 0; Y0 = 0;
• X1 = l1 * cosd (THETA1);
• Y1 = l1 * sind (THETA1);
• X2 = X1 + l2 * cosd (THETA2);
• Y2 = Y1 + l2 * sind (THETA2);
• Then come into plotting area for theta 1 and theta 2 we get the values from for loop and that is converterted into graph with line width of 3mm for that we do the expression in single line that  plot ([X0 X1],[Y0 Y1],[X1 X2],[Y1 Y2],LineWidth=3).
• Then assign the coordinate axis for graph starts from -0.1 to  1.5 and 0 to 1.5.
• And end the for loop.
• Then assigning the link coordinates starting from X0,Y0 and X1,Y1.
• Then give the input of our mathematical expression for link movement,That
• Then we slow the motion in the graph video for that we use the pause for 0.3 sec.
• Then by using gcf function we get the current figure that for plotting the graph.
• Then increment that ct values for collecting current figure.
• Then using movie function we create the avi formate of that video of the simulation,during this time we can adjust the speed and interval of the plot movement.

CODE:

 

%Forward Kinematics of 2R Robotic arm

close all

clc

%INPUT

l1 = 1;     

l2 = 0.5;

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 1.5 0 1.5])

pause (0.03)

m(ct) = getframe (gcf);

ct = ct + 1 ;

end

end

movie (m)

videofile = VideoWriter ('forward_kinematics.avi' , 'uncompressed AVI');

open (videofile)

writeVideo(videofile,m)

close (videofile)

%Forward Kinematics of 2R Robotic arm

close all

 

clc

Code line by line explaination:

%INPUT

l1 = 1; // Get l1 input

l2 = 0.5; // Get l2 input

theta1 = linspace (0,90,10); //Assign the array theta 1

theta2 = linspace (0,90,10); //Assign the array theta 1

ct=1; //Assign the Ct value as 1.

for i = 1 : length (theta1) //using for loop give i = 1 and assign the theta 1 length

THETA1 = theta1 (i);//Then give the THETA Variable for save the length of theta 1.

for j = 1:length(theta2) //same as assign j = 1 and get the length of theta 2 array.

THETA2 = theta2(j); // Then save the values inside the THETA2 Variable.

X0 = 0;//Then come to mathematical expression first assign x0 =0.

Y0 = 0; //Assign Y0 = 0,These are starting values of the link

X1 = l1 * cosd (THETA1); //Then find the angle of x1 by using this expression,by this we find horizontal angle of theta 1

Y1 = l1 * sind (THETA1);// same as to find the angle of Y1 by using this expression,by this we find Vertical angle of theta 1

X2 = X1 + l2 * cosd (THETA2);//This expression for X2 Angle.

Y2 = Y1 + l2 * sind (THETA2);//This is for Y2 Angle

%plotting

plot ([X0 X1],[Y0 Y1],[X1 X2],[Y1 Y2],LineWidth=3) //This line is used for plot the x0,y0 and x1,y1 links.

axis ([ -0.1 1.5 0 1.5])//This is for making the coordinate axis

pause (0.03)// This is used for slow the speed of video

m(ct) = getframe (gcf);//By this expression we can get the current figure.

ct = ct + 1 ; //By this line we are increament the ct value.

end //This is for end the j for loop

end //This is for end the i for loop

movie (m) //This is used for get the movie output of the plot.

videofile = VideoWriter ('forward_kinematics.avi' , 'uncompressed AVI'); //This is used for save the file formate in .avi

open (videofile) //This is for open the video file

writeVideo(videofile,m) //This for save the file

 

close (videofile) // This is for close the file

Conclusion:

      From this challenge I learned about mechanism of 2R robotic arm and how to program for that using matlab.

https://drive.google.com/file/d/1JPeeZ4Mp_elL-R6jGWq1mSgQWjWAHIMu/view?usp=sharing