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The normal acceleration of the train is plotted on the left, while the tangential acceleration is on the right. Notice that the tangential acceleration does not depend on the input angular velocity, but rather the input angular acceleration.
MATLAB Code
% Wild Wild West Train
% Paramters
N1 = 6; % Teeth on the first gear
N2 = 12; % Teeth on the second gear
R = 2.75; % Turn-Table Radius (in)
% Analyis
GR = N1/N2; % Gear Ratio
omega1 = [0:.1:20]; % Input Angular Velocity (RPM)
alpha1 = [0:.1:20]; % Input Angular Acceleration (RPM/s)
for i = 1:length(omega1)
omega2(i) = omega1(i)*GR; % Output Angular Velocity (RPM)
vel(i) = omega2(i)*(2*pi/60)*R; % Velocity of Train (in/s)
an(i) = (vel(i)^2)/R; % Normal Acceleration of Train (in/s)
at(i) = alpha1(i)*(2*pi/60)*R; % Normal Acceleration of Train (in/s)'
end
figure(1)
plot (omega1,omega2,'k','LineWidth',2)
title('Output Angular Velocity Vs. Input Angular Velocity');
xlabel('Omega1 (RPM)');
ylabel('Omega2 (RPM)');
figure(2)
plot (omega1,vel,'k','LineWidth',2)
title('Train Tangential Velocity Vs. Input Angular Velocity');
xlabel('Omega1 (RPM)');
ylabel('Velocity (in/s)');
figure(3)
plot (omega1,an,'k','LineWidth',2)
title('Train Normal Acceleration Vs. Input Angular Velocity');
xlabel('Omega1 (RPM)');
ylabel('Normal Acceleration (in/s^2)');
figure(4)
plot (alpha1,at,'k','LineWidth',2)
title('Train Tangential Acceleration Vs. Input Angular Velocity');
xlabel('Alpha1 (RPM/s)');