Kinematic Study

The Wild Wild West is made of a simple two-gear system. The main purpose of the gears is to change the input rotation in the vertical plane to the horizontal plane. This is accomplished by having the gears be connected at 90-degree angle (See picture below). Additionally, the input gear has 6 teeth, while the output gear has 12. This results in a gear ratio of 1/2, which increases the torque from input to output by a factor of 2. However, by conservation of energy, this also means the angular velocity decreases by a factor of 2 from input to output.

Velocity Plots

Notice in the first plot that the output angular velocity is half of the input angular velocity for all values. The velocity of the train was calculated in the second plot vs the input angular velocity.

Acceleration Plots

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)');