Week 3.2 - 2R Robotic Arm Challenge

Aim:

Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm, as shown in the video.

Theory:

A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion (such as in an articulated robot) or translational (linear) displacement. The links of the manipulator can be considered to form a kinematic chain. The terminus of the kinematic chain of the manipulator is called the end effector and it is analogous to the human hand.

In this project, we consider a 2R robotic arm. A 2R robotic arm represents a robotic arm with two rotations. I.e. it has two links which rotate or work over a two-dimensional plane with each of links having a single degree of freedom.

Also, both the links are restricted to a 90° rotation with respect to the axes. Fig below shows the 2R robotic arm having many parts as described.

• Let, l1 & l2 be length of the link -1 & link-2 respectively.
• Let, theta 1 > be the angle formed by link-1 with horizontal.
• Let, theta 2 > be the angle formed by link-2 with horizontal.
• Let, the starting and end co-ordinates of link - 1 to be (x0, y0) and (x1, y1).
• Let, the starting and end co-ordinates of link - 2 to be (x1, y1) and (x2, y2).

Code explanation;

• Providing the input variables like.
• Predefining the length / values of the robotic arms.
• Providing the values for theta – 1, theta – 2 using linspace command for theta = 0 to 90 degrees for 15 values.
• Providing the cr (compression ratio) value as a specific digit.
• Now using ‘for’ command for iterating the values of the desired variable.
• Again using ‘for’ command for providing movement to the second robotic arm.
• Providing the eqn for the x1, y1, x2, y2 or say defining the co-ordinates of both the robotic arms.
• Plotting all the co-ordinates values and providing the axis no.
• Using the pause command to make the plot look realistic.
• Incrementing the cr or compression ratio value by +1 each time it executes for loop.
• All figures are assigned to a variable M, one at a time using cr.
• Enabling the ‘for’ loop twice.
• At end saving the movie in .avi format.

MATLAB Code:

% forward kinematic of a 2R robotic arm manipulator

clear all

close all

clc

% inputs

l1 = 1.5; % length of link 1

l2 = 1; % length of link 2

theta_1 = linspace(0,90,15); % create a row vector from 0 to 90 with 15 evently spacedpoints

theta_2 = linspace(0,90,15); % create a row vector from 0 to 90 with 15 evently spacedpoints

ct = 1;

% for loop

for i = 1:length(theta_1);

THETA_1 = theta_1(i); % the value theta 1 when iterated is stored in THETA 1

for j = 1:length(theta_2);

THETA_2 = theta_2(j); % the value theta when iterated is stored in THETA 1

% co-ordinates

x0 = 0; % base of link 1 is fixed at original

y0 = 0; % base of link 1 is fixed at original

x1 = l1 *cosd(THETA_1); % find the final co-cordinates of line 1

y1 = l1 *sind(THETA_1); % find the final co-cordinates of line 1

x2 = x1 + l2*cosd(THETA_2); % find the final co-cordinates of line 2

y2 = y1 + l2*sind(THETA_2); % find the final co-cordinates of line 2

% plotting

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

axis([-0.5,2.5,0,2.5]);

pause(0.03);

M(ct) = getframe(gcf);

ct = ct+1;

end

end

% Animation

movie(M)

videofile = VideoWriter('Forward_kinematic_robotic_arm.avi','Uncompressed AVI')

open(videofile)

writeVideo(videofile,M)

close(videofile)

Result:

Below is the link given for the program output for movie/animation of a 2R robotic arm

https://youtu.be/J4cJxiIpRDI

Conclusion:

Thus we have simulated 2R robotic arm by using the matlab programming and also created a Movie/Animation from the plots obtained from the program