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The following video presentation in Figure 1 gives an overview of the project from start to finish. 

Figure 1. Project Presentation

The final assembly was successful in its attempt to recreate the motion of the PMKS simulation. As you can see from Figure 2, the joints moves smoothly with no hesitation. 

Figure 2. Final Mechanism Prototype

Once I added the motor to the mechanism, I ran it at an initially slow speed in order to place it in the correct position that would maximize the smooth mobility of the mechanism. Figure 3 shows the motor powering the mechanism. 

Figure 3. Motorized Mechanism

Once the entire mechanism and hardware was finalized, I was able to test out the actual ring toss game itself. I increased the speed of the motor to make the game challenging. I had a great time numerously attempting to land a ring on a horn of the moving longhorn. I blamed missing the target on my poor aim rather than the mechanism itself, but I was able to land a few on the horns. One of my successful landings can be seen in Figure 4.