Mechanical Rotation about a Virtual Axis for Robot EOAT

I am working on a robotics application where we are erecting a cardboard box and stapling the ends shut. I need control over the "top" end flap to make sure it is out of the way for the rest of the automation. I am a mechanical engineer by degree but I am now a controls/automation engineer. I cannot remember how to design the linkages to create a mechanism that rotates about a fixed virtual point. In this case, that is a location roughly at the surface of the cardboard box. The robot's end of arm tooling is ~3/8" and I assume we will be another inch higher after the real mechanism is built to account for bushings.

This is almost exactly the mechanism I need. However, try as I might, I have not figured out how to calculate the linkage lengths I need for my specific use case.

I attached a sketch of what I envision along with a screenshot from the video I mentioned.

Any help would be greatly appreciated.

• 3 points on the circumference define a circle. What does that tell you about how to work a "virtual" pivot? Why do you even care for such rather than relying on the cardboard box?
– Abel
Commented Nov 16, 2023 at 13:18
• I see the merit in your suggestion of leveraging the cardboard box's natural pivot. The real question is how we can engineer the suction cup to rotate in harmony with the box's pivot point. We're essentially looking for a mechanism that allows the suction cup to mimic the flap's rotation without a fixed joint at the pivot. It's a delicate balance between simplicity and functionality. If you have ideas on a linkage design that would facilitate this coordinated movement, it would greatly contribute to the solution. Commented Nov 28, 2023 at 0:27