Program to simulate forward kinematics of a 2R robotics arm Using MATLAB

AIM :

       To simulated the forward kinematics of a 2R robotics arm

INTRODUCTION :

       2R robotics arm contains 2 links and 2 rotational joints, link 1 is connected to the base and makes angle theta1 with respect to X-axis and link 2 connected to link 1 makes angle theta 2 with respect to the same X-axis and manipulator connect to link 2.

THEORY : 

         kinematics : the branch of mechanics concern with the motion of the object body without reference to the force which causes the motion, here we need geometric property such as length and degree of freedom of the manipulator bodies.

         Forward kinematics : refer to the use of kinematics of the equation of robot to compute the position of end-effector from specified value fro the joint parameter.

         A robotics arm is a mechanical arm usually a programable, a similar function of the human arm. the link which is a manipulator is connected by joints allowing either by rotation motion or translational displacement. this link considers forming a kinematics chain. the terminus of the kinematics chain of the manipulator is called end effector.

         If we know the geometry of the robot and all its joint points, we can do the math and figure out the position and orientation of any point on the robot. i.e if we can able to figure out how the robot is going to move then we can figure out its workspace {wrokspace refer to maximum position robot can move or reach}.

        APPLICATION :

• wielding is automobile nad aerospace industry 
• material handling
• assembly operation 
• machine loading and unloading
• spray painting in automobile and aerospace industry and ETC   

PROJECT-SETUP :

EQUATIONS :

      length of link 1 = l1

      length of kink 2 = l2

we will take the fix link at base as origin

Co-Oridinates of link 1

(X0,Y0) = (0,0)

(X1,Y1) = (l1*costheta1,l1*costheta1)

Co-Oridinates of link 2  

 the end point of link 1 is the start point of link 2

(x1,y1) = (l1*cosdtheta1,l1*cosdtheta1)

x2 =x1 +l2*cosdtheta2

y2 = y1 +l2*sindtheta2

With the above co-ordinate we can describe the position of the robotics manipulatior

%  a program to simulate forward kinematics of 2R robotic Arm 
clear all
close all
clc
  

%input
l1 = 1;
l2 = 0.5;

theta1 = linspace(0,90,10);
theta2 = linspace(0,90,10);

ct=1;
for  i=1length(theta1)
    THETA1 = theta1(i);
    
for  j = 1:length(theta2)
       THETA2 = theta2(j);
       x0 = 0;
       y0 = 0;  
       
       x1 = l1*cosd(THETA1);
       y1 = l1*sind(THETA1);
       
       x2 = x1 + l2*cosd(THETA2);
       y2 = y1 + 12*sind(THETA2);
       
       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 = VideoWritter('forward_kinematics.avi','uncompressed avi');
open(vediofile)
writeVideo(videofile,M)
close(vediofile)

RESULT :

The final result as animated vedio are mention below {link}.

  https://www.youtube.com/watch?v=KSU19i7sSYs