When designing for the mechanism, I wanted to ensure that I could manipulate the link lengths and positions so that the desired slider motion could be obtained. I used the Planer Mechanism Kinematic Simulator to recreate the 5-bar slotted slider mechanism and adjusted the layout of each pin and link. Figure 1 shows the coordinates of each pin in an X-Y coordinate system.
Figure 1. Link Positions
Figure 2 below shows the mechanism in action. As you can see, the slider varies in velocity, which is preferred in order to make the ring toss game less predictable and more of a challenge. I made the input link rotate close to the GND2 point and the coupler link very long so that when input passes GND2, the coupler links rotates very fast and changes the speed of the slider.
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Figure 2. Mechanism Animation
A more extensive analysis of each link's motion can be seen in the next section.