Simulation of the forward kinematics of a 2R Robotic Arm in MATLAB

Objective- To write a program in MATLAB to simulate the forward kinematics of a 2R Robotic Arm.

Governing equations- Robotic Arm has 2 degrees of freedom, so two coordinates need to be defined with respect to the origin.

Let, x₀=0 y₀=0, (x₀,y₀) is the origin.

L₁= length of arm 1

L₂= length of arm 2

Coordinates for arm1:

x₁ = L₁cosƟ₁ , y₁=sinƟ₁

Coordinates for arm2:

x₂= x₁+L₂cosƟ₂

y₂= y₁ + L₂sinƟ₂

where Ɵ₁ and Ɵ₂ are angles as shown in the figure.

Figure1: Robotic arm

Code

clear all

close all

clc

%inputs

l1=1.0;

l2= 0.7;

theta1=linspace(0,135,5);

theta2=linspace(0,135,5);

ct=1; % for loop for values of theta

for i = 1:length(theta1)

THETA1 = theta1(i);

for j = 1:length(theta2)

THETA2 = theta2(j);

x0 = 0;% initial postion of the arms

y0 = 0;

%Equation for first link

x1 = l1*cosd(THETA1);

y1 = l1*sind(THETA1);

%Equation for second link

x2 = x1+l2*cosd(THETA2);

y2 = y1+l2*sind(THETA2);

%plotting

plot([x0,x1],[y0,y1],[x1,x2],[y1,y2],'linewidth',4)

axis([0 2.0 0 2.0])

pause(0.08)

M(ct)=getframe(gcf);%collecting frames%

ct = ct+1;

end

end

%video generation

movie(M)

videofile= VideoWriter('robotics_Arm.avi','uncompressed avi');

open(videofile)

writeVideo(videofile,M)

Explanation of Code

1. First of all, the length of the arms is fixed.
2. Then angles Ɵ₁ and Ɵ₂ are defined with movement from 0^o to 135^o in intervals of 5⁰ .
3. For loop is used to compute the positions of arms at different angles.
4. Results are plotted and then captured frame by frame using getframe.
5. Then frames are converted into a video (AVI file).

Errors faced

1. Basic typing errors.
2. Forgot to put an apostrophe. (Figure 2)

Figure 2: error

Rectification

• Corrected the syntax.

Results

Output

Smooth animation plot

https://youtu.be/IOK9lCbHitA

Conclusion-

• The objective is achieved using MATLAB 18.0.
• The orientation of arms captured successfully