Simulation of forward kinematics of a 2R robotic arm

Aim:

To simulate the forward kinematics of a 2R robotic arm.

Objective:

To animate and simulate the motion of the 2R robotic arm in the given workspace.

Theory:

Forward kinematics means the use of kinematic equations of a robot to compute the position of the arm of the robot from specified values for the joint parameters.

A robotic arm is a usually a programmable robot manipulator having similar functions as a human arm. In our robotic arm there are 2 links forming a kinematic chain which allows for both rotational and translational motion. These types of robots are vastly used in industries such as automobile, electronics, welding etc.

Input Parameters:

L1=length of link 1

L2=length of link 2

Theta1=angle made by link 1 w.r.t x-axis

Theta2=angle made by link 2 w.r.t x-axis

(X0, Y0) = starting point of link 1

(X1, Y1) = ending point of link 1 and starting point of link 2

(X2, Y2) = ending point of link 2

Explanation of code:

• Length of first link is assumed to be 1 m
• Length of second link is assumed to be 0.5 m
• Theta1 and Theta2 varies from 0 to 90 degree in 4 partitions
• The value of counter is set to 1 which increases by 1 for every iteration of loop
• Double for loops are used for iteration of the robotic arm position
• First for loop is for link 1 and second for loop is for link 2
• The positions of link 1 and link 2 is itearted and plotted in a graph
• saveas and sprintf command were used to save each iteration.
• ImageMagick was used to create the animation in gif file.

Code:

Programming language used=MATLAB

Software used=Octave

%Stimulate the forward kinematics of 2R robotic arm
clear all
close all
clc

%length of first link in metre
l1=1;
%length of second link in metre
l2=0.5;

%Angle made by the first link wrt x-axis
theta1=linspace(0,90,4);
%angle made by the second link wrt x-axis
theta2=linspace(0,90,4);

%counter pointer
ct=1;
%for creating animation of 2R robotic arm
for i=1:length(theta1)
  for j=1:length(theta2)
    THETA1=theta1(i);
    THETA2=theta2(j);
    %Staring coordinates of link 1
    X0=0;
    Y0=0;
    %Ending coordinates of link 1 and starting coordinates of link 2
    X1=l1*cosd(THETA1);
    Y1=l1*sind(THETA1);
    %Ending coordinates of linl 2
    X2=X1+l2*cosd(THETA2);
    Y2=Y1+l2*sind(THETA2);
    %plotting
    plot([X0,X1],[Y0,Y1],[X1,X2],[Y1,Y2],'linewidth',3)
    axis([0 1.5 0 1.5])
    pause(0.1)
    file_text=sprintf("robotic_arm%d.png",ct)
    saveas(gca,file_text);
    ct=ct+1;
  endfor
endfor

Output:

As the animation is a gif file, you can view or download it from the below google drive link:

https://drive.google.com/open?id=1kojNhibKSsuH-2wlrXgtL1UO9sD0Y6Gp