How to upgrade code for simulating a crank-shaper mechanism from a crank slider mechanism. Failing to add the crank/input disk.

This matlab code is for a simple crank slider, and i am failing to add another link to make a crank shaper mechanism(kinetic digram).

%This file calculates the position of various points on the
% basic slider-crank mechanism and animates the linkage
clear all;
close all;
clc;
r2 = 20;
r3 = 55;
theta2 = 0:2*pi/360:2*pi; %this line increments theta2 (the crank angle)
n = length(theta2);
x = r2*cos(theta2)+r3.*sqrt(1-(r2*sin(theta2)/r3).^2);
 xO2=0;
 yO2=0;
 xA = r2*cos(theta2);
 yA = r2*sin(theta2);
 xB = x;
 yB = 0;


 X = [xO2,xA(1),xB(1)]; % here we store all the x coordinates
 Y = [yO2,yA(1),0]; % here we stor all the y coordinate

 Xground = [0,2*r2+r3]; % x coordinates of two pts on the ground
 Yground = [0,0]; % y coordinates of the same two pts on the ground

 Linkage_dwg = plot(xA,yA,X,Y,Xground,Yground, 'black',xB(1),0,'-rO');
 %including xA and yA in the plot will draw a circle
 axis ([-2*r2-r3 2*r2+r3 -2*r2 2*r2]); %setting limits for the plot

 for i=1:n %we loop here to draw at incremented theta2
 delete (Linkage_dwg); %delete and redraw at every theta2

 X = [xO2,xA(i),xB(i)]; %Updated x coordinates
 Y = [yO2,yA(i),0]; %Updated y coordinates

 Linkage_dwg = plot(xA,yA,X,Y,Xground,Yground,'black', xB(i),0,'-rO',...
 'MarkerSize',12); %drawing again at the updated position

 axis ([-2*r2-r3 2*r2+r3 -2*r2 2*r2]); %chosen limits of the plot

 axis equal; %i.e. scale such that circles do not look like ellipses

 F(i) = getframe; %saving a frame at every theta2

 pause (1/30); %a small pause to allow us to see the linkage
 % befor theta2 changes

 end
 delete (Linkage_dwg); %deleting the last drawing before running
 % the movie
 movie(F,n) %running a movie of the stored frames


 % movie2avi(F,'test.avi','fps',10,'compression','None');
 %tried here to save to a file but the avi file didn't run

Answer 1

[Umang Pandey]

Hi Sydney,

I understand that you want to add an additional link to your crank-rocker mechanism to extend it to a crank-shaper mechanism.

To modify the provided MATLAB code for a basic slider-crank mechanism into a crank-shaper mechanism, we need to add an additional link and a point that represents the shaper.

The following code includes a new link (r4) and a point C that moves along a vertical line, representing the shaper motion:

% This file calculates the position of various points on the 
% crank-shaper mechanism and animates the linkage 
clear all; 
close all; 
clc; 
% Define lengths of links 
r2 = 20; % Length of crank 
r3 = 55; % Length of connecting rod 
r4 = 40; % Length of shaper link 
% Define the crank angle theta2 
theta2 = 0:2*pi/360:2*pi; % Increment theta2 (the crank angle) 
n = length(theta2); 
% Preallocate arrays for speed 
xA = zeros(1, n); 
yA = zeros(1, n); 
xB = zeros(1, n); 
yB = zeros(1, n); 
xC = zeros(1, n); 
yC = zeros(1, n); 
% Calculate positions of points A, B, and C 
for i = 1:n 
    xA(i) = r2 * cos(theta2(i)); 
    yA(i) = r2 * sin(theta2(i)); 
    xB(i) = xA(i) + r3 * sqrt(1 - (yA(i)/r3)^2); 
    yB(i) = 0; % Slider B moves horizontally 
    xC(i) = xB(i); % Point C is directly above point B 
    yC(i) = r4; % Shaper link is vertical 
end 
% Ground coordinates 
xO2 = 0; 
yO2 = 0; 
Xground = [0, 2*r2 + r3]; 
Yground = [0, 0]; 
% Set up the animation figure 
fig = figure; 
axis ([-2*r2-r3 2*r2+r3 -r4 2*r2]); 
axis equal; 
hold on; 
xlabel('X'); 
ylabel('Y'); 
title('Crank-Shaper Mechanism Animation'); 
% Animate the linkage 
for i = 1:n 
    % Check if the figure has been closed 
    if ~ishandle(fig) 
        break; % Exit the loop if the figure is closed 
    end 
    % Update the coordinates of the linkage 
    X = [xO2, xA(i), xB(i), xC(i)]; 
    Y = [yO2, yA(i), yB(i), yC(i)]; 
    % Plot the crank, connecting rod, and shaper link 
    Linkage_dwg = plot(X, Y, 'black-o', 'MarkerFaceColor', 'red', 'MarkerSize', 6); 
    % Plot the ground 
    ground_dwg = plot(Xground, Yground, 'black', 'LineWidth', 2); 
    % Draw the path of point A (circle) 
    path_dwg = plot(xA, yA, 'b:'); 
    % Draw now 
    drawnow; 
    % Capture the frame for the animation 
    F(i) = getframe; 
    % Pause for a brief moment to make the animation visible 
    pause(1/30); 
    % Delete the linkage drawing (but keep the ground and path) 
    if i < n 
        delete(Linkage_dwg); 
    end 
end 
% Play back the captured animation frames 
if ishandle(fig) 
    movie(fig, F, n); 
end 

As for saving the animation, “movie2avi” has been removed since MATLAB R2016b version. You can use the “VideoWriter” class to create video files from MATLAB animations and figures.

Here is the link to the documentation:

https://www.mathworks.com/help/matlab/ref/videowriter.html

Hope this helps.

Best,

Umang