Although all our simulations and calculations were correct and led us to believe the design would work, we quickly learned that there is more to a mechanism than just it moving in an ideal world. The MATLAB simulation and the YouTube video exists in worlds where friction does not exist.

At the extreme ends shown on the picture above, we can see that the force exerted by the link into the bearing is almost perpendicular to the path of the guide. This is extremely ineffective because the resultant force is very small compared to the normal force which means that there would be immense mechanical disadvantage at that point which essentially rules out moving anything heavy. However, worst problem is that, due to the normal force being so high, the friction force is extremely high at this point and since the force pushing the bearing is so small due to the angle between the link and the path, there bearing could not overcome friction and got stuck at these points. We corrected our mechanism numerous times just to make sure it was not any links because slightly off their lengths or the ground joints because incorrectly distanced. However, in the end the result was the exact same, the slider completely stopped at the extreme points. It was then that we learned a great lesson: there is more to consider than just "does it theoretically move" when designing a robotic mechanism. In our case, we failed to consider immense amounts of friction and mechanical disadvantage.  Our originally laser cut guide is shown below.

Version 2

In order to solve the issue of massive friction as extreme points, we redesigned the mechanism to exert an almost perpendicular force at the points where the force would originally be almost not perpendicular. We redesigned the mechanism as such:

The issue that arrives with this design, is the limited distance you have to work with linkages and anything being picked and placed. All linkages and anything being picked or placed has to be able to fit within the box created from the ground link connected to the two sliders. If not, we learned that the collisions will simply not allow the mechanism to move.

We simulated our new design in MATLAB to ensure that the mechanism "theoretically" moves.

It was after building this model that we came to the unfortunate realization that this design, specifically the design of the guide, would not work. The points where the transition occurs from constant theta to constant radius or visa versa where points where the friction force was extremely high similar to the scenario from before. We essentially move the problem point. At this point, we came up with one final design to see if we could make this mechanism work.

Version 3 

We concluded that the main issue was the force vector being too close to perpendicular to the guide. Therefore we create a guide design to minimize this occurrence:

We learned from our mistakes and verified that this design would not encounter any friction issues. After verifying this, we built the mechanism using 3D printed shafts and cranks with the slider being locked in with a long screw to fit ball bearings at the end of the screw which made contact with the slider. We attached the crank to a 360 continuous servo and our prototype was complete.