Forward Kinematics of 2R Robotic Arm

• Aim : Study of Kinematics of 2R Robotic Arm Using Matlab.

• Objective : Got to know algorithm for solving Basic kinematics using matlab.

• Description of Robotic Arm : 

        Robotic arm contains huge number of links , Joints etc.., They work without the help  of a human , for that we need to program them using available     

        software For the  robot to work good we should define co-ordinate positions for the required movement  to do by  the robot .we call it as a workspace.

       Workspace : set of points that can be  reached by its end-effector or in other words , it is the space in  which the robot works and can be either a 3D space

       or a 2D surface.

• Description of Robotic arm components for kinematics analysis :

      Defining the points and parameters between the links :

      `(x_0,y_0)` this is joint between base (fixed link) link-1 (blue link) ,  

      `(x_1,y_1)` this is joint between the link-1 and link-2 (red link),

      `(x_2,y_2)` this is the joint between the link-2 and manipulator.

      `theta_1` angle between the link-1 and base.

      `theta_2` angle between the link-1 and link-2.

      `L_1`length of the link-1.

      `L_2`length of the link-2.

      Robotic arm contains two links link-1 and link-2 as shown in figure and contains joints ,

      aligned with a certain angle with the horizontal axis. Parameters defined above.

     The above picture is our robotic arm but our motto is to analyse the motion of this 

     2R robotic arm , as robot is always moving to perform different tasks.

     Code for analyse using matlab :

close all  
clear  , clc 
% Initialising the required inputs to the variables.   
l1 = 1; 
l2 = 0.5; 
ct=1;  

%linspace(x,y,z) - x - start , y - end , z - no.of division between start and end.

thetha1 = linspace(0,90,10);  % creating an array of containing 10 angles values.
 
thetha2 = linspace(0,90,10);  % creating an array of containing 10 angles values. 

for i=1:length(thetha1)
    
    for j = 1:length(thetha2)
                x0 = 0;
        y0 = 0;
        
        x1 = l1*cosd(thetha1(i));
        y1 = l1*sind(thetha1(i));
        
        x2 = x1 + l2*cosd(thetha2(j));
        y2 = y1 + l2*sind(thetha2(j));
        
        
        plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],'linewidth',3);
        axis([-0.1 1.5 0 1.5]);
        %pause(0.1)
        drawnow
        
 % getframe copying the all frames of animation in array 'M'.
        M(ct) = getframe(gcf); 
        ct = ct+1;
    end
end

%VideoWriter - Creating a video file from an array
my_creator_animation = VideoWriter('M');


open(my_creator_animation)

%writeVideo - Writing the data stored in M into my_creator_animation video object.
 writeVideo(my_creator_animation,M) 

close(my_creator_animation)

Explanation of code Step-wise : 

At first using the common commands for better execution of code

close all - Clearing all existing plots and figures 

clear     - Clearing all data in the workspace.

clc        - Clearing the command window.

1. Initialising the required inputs for calculations for kinematics analysis , length of two links

   and the data of angles stored in arrays by using linspace from `0^0` to `90^0` with

   constant increment of `10^0`.

2.ct is a variable intialised to 1 , its's values increases for every iteration in the for loop.

Workflow of for loop :

The above figure describes the workflow of the loops in matlab.

3.Conditions  for loops taken  so that loops can iterate for 10 times by using (1:length(x)).

4.length(x) - returns the largest dimention of the array x . It is inbuilt function.

5.In the nested for loop declared the co-ordinate of joints as shown in code.

6.cosd() , sind() used to analysis using in terms of degrees.

7.Used 'plot' command to plot the graph. 

8.'linewidth' command define the thickness of the plots.

9.used 'axis' command to define the x-axis and y-axis limits.   'axis([x-min x-max y-min y-max]).'

10.'drawnow' - means stop the execution of code temporarily and plot the figure at current time , as matlab gives preference to the execution of code than plotting.

    so, used drawnow for to show the animation of movement of robot arm.

11.'getframe' - getframe command stores the data of all frames , and the data stored in the variable M , used ct to change the value of index or location to store data.

12.The entire required data stored in variable 'M' after completion of all iterations of for loops.

13.'VideoCreator' - creates a video file but it won't write any thing . created a Video object 'my_creator_animation' by assigning to it and it does not contain any data.

14.'open' - command used for opening the video file.

15.'writeVideo' - write a video by using the data stored in array 'M'.

16.'close' - command used for closing the video file.

video file created only after the animation completed  in the output . Can observe that in command history. By default matlab creates '.avi' files. we can convert that into  '.mp4' file . use VideoWriter('name','MPEG-4');

Animation Video Of Robotic Arm:

https://youtu.be/YnsixyUilMc