Analyses

The above figures shows a schematic of the mechanism. Input rotation is applied to the crank at point p1. The crank is connected directly via a shaft to gear 2 which has 6 teeth. Gear 2 meshes with gear 3 which has 12 teeth. This causes a gear ratio of 0.5 and a torque amplification (mechanical advantage) of 2. Gear 3 is directly connected to the output turntable via a shaft. The center of the train is located at point p2 on the turntable. 

Due to the difference in teeth between the two gears, the output turntable only rotates 180 degrees with every full turn of the input crank (see figure bellow). 

The figures bellow show the position, velocity, and acceleration of point p1 as a function of input crank angle. We can assume that the user provides a constant input velocity of 10 RPM. Therefore, there is no tangential acceleration. The position of this point is located 1 in. from the center of the crank wheel. The velocity of p1 is a constant 1.047 in./sec and acceleration is 1.097 in./sec^2. 

The figure bellow shows similar position, velocity, and acceleration analyses of point p2 as a function of input crank angle. Here, the input crank has to make two full rotations before the train makes one rotation. The point p2 is located 2.75 in. from the center of the turntable. The velocity of p2 is a constant 1.440 in./sec and acceleration is 0.754 in./sec^2. Also bellow is a plot of position of p2 showing the circular trajectory around the track. 

Finally, the relationship between input and output force can be defined by the following equation: