Week 2- 2R Robotic Arm Challenge

AIM-

*MATLAB program for simulated the forward kinematics of a 2R robotic arm

INTRODUCTION-

*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

*In industries like automobile industries and aviation all the processes are now days automatically done by robot. So, at the design stage of robot designer need to know the workspace of the robot for particular operation, so by software like MATLAB designer can easily know range of robot by inserting different size of robotic arm and different angles of robotics arm with reference surface

GOVERNING EQUATION-

As per the image mention above L1(1m) & L2(0.5m) are two links of the arm which makes θ1& θ2 angle with horizontal axis respectively

*Co-ordinates of link1

Starting point = [X0 ,Y0]=[0,0]

Ending point =[X1 , Y1] = [L1Cosdθ1,L1Sind θ2]

*Co-ordinates of Link2

Starting point=[X1,Y1] = [L1Cosd θ1,L1Sind θ1]

Ending point= [X2,Y2] = [X1+L2Cosd θ2, Y1+L2 θ2]

OBJECTIVE

We will take multiple values of θ1 & θ2 range from 0 to 90 and by all different combination of those values and plots will be created and at the end of stitching all the plots together to make a animation

Program

clear all
close all
clc

%inputs
l1=1;
l2=0.5;

%angle of both links with horizontal axis
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);
    
    plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],'linewidth',3,'color','g');
    axis([-0.1 1.5 0 1.5])
    title('kinematic of 2R robotics arm')
    xlabel('arm movement in xaxis');
    ylabel('arm movement in yaxis');
    grid on
    pause(0.1)
    file_text=sprintf('robotics_animation%d.png',ct);
    saveas(gca,file_text);
    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)

First of all the inputs should be provided

% Length of link

l1=1

l2=0.5

% Angle of both links with horizontal axis

Theta1=linspace(0,90,10)

Theta2=linspace(0,90,10)

By using the command 10 values for theta will be calculated which is starting from 0 up to 90 degree

For i = length (theta1);

Values of i will change from 1 to the lenth (theta10 , length(theta1) is nothing but all the 10theta values between 0to 90 , which is generated by linspace command

THETA1=theta1(i);

THETA1 is a variable where theta1 is a array, i is loop counter which determine how many times forloop get executed

For each value of theta1 theta 2 has to change 10 values

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)

plot ([x0 x1],[y0 y1],[x1 x2],[y1 y2],’linewidth’,3,'color','g');

By this command plot will be generated, in which linewidth and color is specified

Axis ([-1.5 1.5 0 1.5])

Pause(0.3)

Grid on

File_text=sprint(‘robotics_animation%d.png’,ct)

Saveas(gca,file_text);

Print f command to change the file name

Tis will result in saving the entire output file in the present

Ct=ct+1

Increment forloop execution

Error

1^st Error—we had to write clear all starting with small c and not with capital C

2^nd Error—missing the theta 1 in the i loop,due to which plots wew generated for final position.

3rd Error—missing to add for loop for the j loop due to which robotics arm made in multiple form in the plot

4^th Error—Adding 2 end command in the program for the i and j loop for closing both the loop

The video file has been uploaded to YouTube link is given below

https://youtu.be/ftVJ8Vevw7U

Conclusion—

*After generating animation by examine closely we can understand the workspace of the robotics arm which is our main purpose.

*By changing length & angle of the links different combination are possible , plotting graphs for all those different combination robot design can be done