Forward Kinematics of 2R Robotic Arm

Introduction -

Robot is a machine that collects the information about the environment using some sensors and makes a decision automatically. People prefers it to use different field, such as industry, some dangerous jobs including radioactive effects.

In this point, robots are regarded as a server. They can be managed easily and provides many advantages.

A robot arm is known manipulator. It is composed of a set of jonts seperated in space by tha arm links. The joints are where the motion in th arm occurs. In basic, a robot arm consists of the parts: base, joints, links, and a grapper. The base is the basic part over the arm, It may be fix or active. The joint is flexible and joins two seperated links. The link is fix and supports the grapper. The last part is a grapper. The grapper is used to hold 2 and move the objects. Figure shows these parts. In the report, the manipulator types are defined in details. Figure Basic robot arm.

1. Base, 2. joint, 3. link grapper.

Homogeneous transformation is used to solve kinematic problems. This transformation specifies the location (position and orientation) of the hand in space with respect to the base of the robot, but it does not tell us which configuration of the arm is required to achieve this location. It is often possible to achieve the same hand position with many arm configurations

Objective - Validating the MATLAB programing for the forward kinematics of a 2R robotic Arm;

Some definitions regarding robotic arm :

Workplace - It is that maximum area or a plane in which the manipulator can reach freely and can execute its operation.

Links - Link are the connecting hands of robot which makes an arm functional.

Manipulator - It is a grabing component of robot which holds the object and comes directly into the contact of assigned target.

INPUTS -

Length of Link 1 - 1m

Length of Link 2 - 0.5 m

Angle of link1 with base theta1 = varies from 0 to 90 (degree)

Angle of link2

clear all
close all
clc

% Inputs 
l1 = 1;
l2 = 0.5;

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 = l2*sind(THETA1);

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 1.5 0 1.5])
pause(0.03)
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)

theta2 = varies from 0 to 90 (degree)

Problem - If theta1 and theta2 are given then what will be the postion of manipulator?

Solution - X0 = 0 , Y0 = 0

X₁ = l₁COSθ₁

Y1 = l₁Sinθ_2;

X₂ = X₁ + l₂COSθ₂

Y₂ = Y₁ + l₂Sinθ₂

_{Further , the work has been done on the arm length by changing alternatively with both the links (L1 and L2).}