Week 2- 2R Robotic Arm Challenge

Aim of the project

1.To write a program in Matlab and python to simulate the forward kinematics of a 2R Robotic Arm.

2. Create an animation file of the plot

Introduction

• Kinematics :is the study of motion of a system of bodies without directly considering the forces or potential fields affecting the motion
• Forward kinematics: forward kinematics refers to process of obtaining Position and velocity of end effector
• Robotic Arm: Robotic arm are machines that are programmed to execute a specific task robotic joint provides relative motion between two link
• 

Link-joint numbering

The robotic base and its connection to the first joint are referred to as link 0. The first joint in the sequence is joint 1. Link 0 is the input link for joint 1, while the output link from joint 1 is link 1 which leads to joint 2. Thus link 1 is, simultaneously, the output link for joint 1 and the input link for joint 2. This joint-link-numbering scheme is followed for all joints and links in the robotic system

MATLAB Program

% Forward kinematics of a 2R Robotic Arm
clear all
close all
clc
%inputs

l1=1.5 % lenth of 1st arm

l2=0.5 % lenth of 2nd arm 

theta1= linspace(0,90,10)%angle of 1st arm 

theta2= linspace(0,90,10)%angle of 2nd arm

ct=1;% initial counter value

for i=1:length(theta1)

    Theta1=theta1(i);

    for j=1:length(theta2)

        Theta2=theta2(j);
        
        x0=0;
        y0=0;              % co-ordinate of link 1 at fix support

        x1=l1*cosd(Theta1);
        y1=l1*sind(Theta1); %co-ordinate of link 1 at point joint

        x2=x1+l2*cosd(Theta2);
        y2=y1+l2*sind(Theta2);%co-ordinate of link 2 at free end

        %plotting
       
        
        plot([x0 x1],[y0 y1],'linewidth',3,'Color','r')
        hold on
        plot([x1 x2],[y1 y2],'linewidth',3,'color','g')
        axis([-0.1 3 -0.1 3])
        hold off
  
        pause(0.03)
        M(ct)=getframe(gcf)
         ct=ct+1;
         
    end
end
%conversion of plot into video
movie(M)
videofile=VideoWriter('rc1program.m','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)       

Inputs

L1-Link1=1.5 Length of link1

L2-Link2=0.5 Length of link2

(X0,y0) = starting point of link1

(X1,Y1)= ending point of link1/starting point of link2

(X2,Y2)=ending point of link2

Step-wise explanation of your code

1.Clear Screen

• 1^st start writing the code it is important to start wirh clear all,close all,and clc
• Clear all-remove the data from workplace and freeing up system memory
• Close all-deletes the current figure or the specified fig
• Clc =clears all input and output from the command window display

2.Inputs

• Assign l1=1.5 and l2=0.5 (length of link )
• Assign theta1 & theta 2(0 to 90) here we use the linspace command

0 to 90 there are infinite position are develop but we plot only 10 position therefore we use linspace command (theta1=10pos,theta2=10pos)

3.For loop which allows code to be executed repeatedly

• for loop operated as 100 times therefore assign ct=1 after evey for loop ct increment by 1 till the 100
• For plotting link 1 wrt theta1 & link 2 wrt theta2 Assign ‘I’ as variable for theta1 and ‘j’ for theta2 to calculating theta1 & theta2
• Calculating the position of co-ordinates using the value of theta1 & theta2
• X0=0

Y0=0 (fix point co-ordinate)

x1=l1*cosd(Theta1);

y1=l1*sind(Theta1); (1^st point co-ordinate)

x2=x1+l2*cosd(Theta2);

y2=y1+l2*sind(Theta2); (2^nd point co-ordinate)

4.Plotting

• Writing the plot command we plot the position for link 1[(x0,x1),(y0,y1)] & link2([x1 x2],[y1 y2]

plot([x0 x1],[y0 y1],'linewidth',3,'Color','r')

• plot([x1 x2],[y1 y2],'linewidth',3,'color','g')
• to adjust the width of plot we use line width taking as 3 and selecting red colour
• hold on to display all result on one plot we use hold on command
• axis([-0.1 3 -0.1 3]) to arrange the axis point on plot as (x=-0.1,3) and y=(-0.1,3)
• hold off to sets the hold state to off so that new plot added
• pause(0.03) time to hold state between 2 plot
• M(ct)=getframe(gcf) to display all output state in one frame
• ct=ct+1;ct=count increasing by 1 for next for loop

5.Create an animation file

Converting all position of output into video format using mat lab command

• movie(M)
• videofile=VideoWriter('rc1program.m','Uncompressed AVI');
• open(videofile)
• writeVideo(videofile,M)
• close(videofile)

Errors faced while programming.

At time of practicing the program lots of errors happens with me here i am presenting 2 Majar errors

Error1. in formula of y2 y2=y1+l2sind(Theta2); at place of y1 is replace by x1

x2=x1+l2*cosd(Theta2);

y2=x1+l2*sind(Theta2);

my program runing without any error but output of animation not getting exact position after reading program 2 times then i realizing my mistakein place of y1 i write x1

Error2 Forget to mention M(ct)=getframe(gcf) in for loop

to conversion of plot into video format writing the movie(M) correctly and run the program then program runing correctly error 1 also solved but after runing the program at the end getting a error messag in command window after watching video from dashboard i realizing my mistake forget to mention m (M(ct)=getframe(gcf)in for loop

Animation video:- Here is the link for the video of the animation

https://youtu.be/VfEb7r0jcbo