Numirecal integration for a vector

Hi everybody,

I am designing non-circular gears using MATLAB. I have designed several types. My last step is to generate the general case which starts from the speed ratio variation. I have this equation (in the photo attached).

I have the speed ratio as a vector and also I have the input angle. I need to calculate the second gear output angle. I think that I need to integrate the vector to get my goal, but how??????????

I need help in this. please.

% this program is for calculating the NCG (non-circular gear) with no approximation
clear, clc

disp('This program generates NCG depending on the imported speed ratio form Excel file')
disp('and entered center distance')

Ratio=xlsread('speed_ratio.xlsx','A:A');
Ratio=Ratio';

Center_dis=input('Enter the center distance value in mm, Center_distance= '); % use 89.305
m=input('enter the module you want to use in mm, m= '); % use 3
phi=input('enter the standard pressure angle in degrees, phi= '); % use 20
disp('*')
disp('*')
disp('The solution depends on the main equation of NCG design and geanaration')
disp('*')
disp('*')

% the input angle is equal parts since the driving gear angular velocity is
% constant, so depending on the number of the speed ratio elements, we
% can divide the one rotation (2*pi) to the same number of elements
Input_ang=0:0.0001*pi:2*pi;

% plot the speed ratio variations 
figure(1)
% plot the center
plot(0,0,'or','LineWidth',5)
hold on

plot(Input_ang,Ratio,'LineWidth',3)
title('The speed ratio variations of the NC-gearset')
xlabel('input angle')
ylabel('W_2/ W_1')
axis equal
grid on

% generating the first centrode with its evolute, base curve, tip and root curve. 
R_c1=(Center_dis.*Ratio)./(1+Ratio);
X_c1=R_c1.*cos(Input_ang);
Y_c1=R_c1.*sin(Input_ang);
       % plot it with clear zero point
       figure(2)
       % plot the center
       plot(0,0,'or','LineWidth',5)
         hold on
       plot(X_c1,Y_c1,'k')
        title('The first centrode')
        xlabel('X')
        ylabel('Y')
        axis equal
        grid on


% generating the second centrode with its evolute, base curve, tip and root curve. 
R_c2=Center_dis-R_c1;

% here I need to calcualte the second gear rotating angle but how???????? need help.

[darova]

Use diff() or gradient() to differentiate a vector

[nezir elali]

Dear Darova,

I used diff and gradient function previously,

I am looking for integrating a vector with the same way like diff.

anyway thanks for answering

Answer 1

[Steven Lord]

See the trapz or cumtrapz functions.

[nezir elali]

Thanks for answering Steven,

I tried to use cumtrapz but I don't know if I used it ok or not.

I tried to do something else.

I tried to make integration for the vector like accumlative but stil I have a problem since the Output_ang is more than 2*pi I mean th last element in the output_ang must be 2*pi not more at all.

any ideas??????????!!!!!!!!!!!!!!

% this program is for calculating the NCG (non-circular gear) with no approximation
clear, clc
disp('This program generates NCG depending on the imported speed ratio form Excel file')
disp('and entered center distance')
Ratio=xlsread('speed_ratio.xlsx','A:A');
Ratio=Ratio';
Center_dis=input('Enter the center distance value in mm, Center_distance= '); % use 89.305
m=input('enter the module you want to use in mm, m= '); % use 3
phi=input('enter the standard pressure angle in degrees, phi= '); % use 20
disp('*')
disp('*')
disp('The solution depends on the main equation of NCG design and geanaration')
disp('*')
disp('*')
% the input angle is equal parts since the driving gear angular velocity is
% constant, so depending on the number of the speed ration elements, we
% can divide the one rotation (2*pi) to the same number of elements
Input_ang=0:0.0001*pi:2*pi;

% plot the speed ratio variations 
figure(1)
% plot the center
plot(0,0,'or','LineWidth',5)
hold on

plot(Input_ang,Ratio,'LineWidth',3)
title('The speed ratio variations of the NC-gearset')
xlabel('input angle')
ylabel('W_2/ W_1')
axis equal
grid on

% generating the first centrode with its evolute, base curve, tip and root curve. 
R_c1=(Center_dis)./(1+Ratio);
X_c1=R_c1.*cos(Input_ang);
Y_c1=R_c1.*sin(Input_ang);
       % plot it with clear zero point
       figure(2)
       % plot the center
       plot(0,0,'or','LineWidth',5)
         hold on
       plot(X_c1,Y_c1,'k')
        title('The first centrode')
        xlabel('X')
        ylabel('Y')
        axis equal
        grid on

% generating the second centrode with its evolute, base curve, tip and root curve.

% R_c2=Center_dis-R_c1;                    % first choice
R_c2=(Center_dis.*Ratio)./(1+Ratio);       % second choice


% finding the rotating angle of the second gear

Output_ang=zeros(1,length(Ratio));
for i=2:length(Ratio)          % first choice to integrate the vector methodolgy to integrate like cumtrapz
Output_ang(i)=0.0001*pi.*(1./Ratio(i))+Output_ang(i-1);
end

% this method from the net as    second choice to integrate the vector
% func=0.0001*pi./Ratio;
% output_angle=cumtrapz(func);    it is not correct

Output_ang=pi-Output_ang;

X_c2=R_c2.*cos(Output_ang);
Y_c2=R_c2.*sin(Output_ang);



       % plot it with clear zero point
       figure(3)
       % plot the center
       plot(0,0,'or','LineWidth',5)
         hold on
       plot(X_c2,Y_c2,'k')
        title('The second centrode')
        xlabel('X')
        ylabel('Y')
        axis equal
        grid on