Challenge

Week 2- 2R Robotic Arm Challenge

SSkill-Lync learner6 Jun 2022

MATLAB

AIM: To simulate the forward kinematics of a 2R Robotic Arm using MATLAB.

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.

As shown in figure here are the inputs that will be used in writing the matlab program

(x0 y0) = starting point of link1 / base

(x1 y1) = ending point of link1/ starting point of link2.

(x2 y2) = ending point of link2/ starting point of simulator.

L1 = Length of link1

L2 = Length of link 2

theta1 = Angle made by link 1 with the base along x-axis

theta2 = Angle made by link 2 with LINK1 along x-axis

Following values are assigned while writing the code

Co- ordinates of (x0 y0) = (0,0)

L1 = 1 metre

L2 = 0.5 metre

Co-ordinates of (x1 y1) and (x2 y2) can be computed by using simple mathematics and resolving the links with respect to the angles.
x1 = L1*cos(THETA1)
y1 = L1*sin(THETA1)
x2 = x1+l2*cosd(THETA2);
y2 = y1+l2*sind(THETA2);

CODE

clear all
close all
clc

% Program for simulating forward kinematics of 2R robotic arm challenge
% using MATLAB
%INPUTS
l1 =1;      %length of link 1 in meters
l2 =0.5;    %length of link 2 in meters
%theta1 is the angle made by link 1 with  origin/starting point along x
%axis
theta1 = linspace(0,90,10);  %taking value for theta 1 starting from 0 to 90 degress in the intervals of 10
%theta2 is the angle made by link 2 with end point of link 1 along x axis           
theta2 = linspace(0,90,10);

 ct = 1;  %counter with starting value as 1

 for i= 1: length(theta1) %length of theta(1) is 10, for loop from i= 1 to 10
THETA1 = theta1(i);
for j = 1:length (theta2)
THETA2 = theta2(j);

%co-ordinates of starting point/origin
x0 = 0;
y0=0;


%co-ordinates of link1 end point/ link2 start point
x1 = l1*cosd(THETA1);
 y1 = l1*sind(THETA1);
 
%co-ordinates of link2 end point/ manipulator start point 
x2 = x1+l2*cosd(THETA2);
y2 = y1+l2*sind(THETA2);

%plotting
%plotting x co-ordinates and y co-ordinates

plot([x0 x1], [y0 y1], [x1 x2], [y1 y2], 'linewidth',3)

%assigning limits for x-axis and y-axis
axis([-0.1 1.5 0 1.5])

%to pause the animation for small intervals to see the animation properly
 pause (0.03)
 
 %Collecting all the frame to create a movie
 M (ct) = getframe(gcf);
 ct =ct+1; %increasing counter value in intervals of 1
end
 end
 
 %creating movie
 movie (M)
 
 %saving ,ovie in .AVI FORMAT
 videofile =VideoWriter ('robotic_arm.avi', 'uncompressed AVI');
 open(videofile)

 %Writing the videofile
 writeVideo(videofile, M)
 close (videofile)

CODE EXPLANATION:

It is recommended to start the code by following these 3 commands
close all = closes all previous figures and plots.

clear all = clears data stored in workspace.

clc = clears all data in command window.
Always include comments in your code for better understanding, comments can be added by using % command
Assign the input values for L1 and L2
As theta1 and theta2 angles can vary so we use linspace command for printing theta1 and theta2 values from (0,90) in intervals of 10.
As theta2 value depends on theta1 i.e for each value of theta1 there can be different values of theta2, hence we use 2 for loops to compute theta2 values for variation in theta1 values and vice versa
Assigning intial values for (x0 yo) co-ordinates
Plotting the co-ordinates and assigning limits for x-axis and y-axis.
To get clear and smooth animation use pause command to pause the frames at small intervals.
All frames are captured in single variable M and for every increment in counter frames get captured.
Movie command is used to create a movie/animation by combining all frames