In my home is a common household object. I securely attached a marking pen to some point on the household object, and I placed a sheet of graph paper next to the pen, so the paper would not move. I then operated the household object in the normal manner, and it drew the pattern below. What is the household object?
Notes: My marker did not draw smoothly, but under perfect conditions, the curve would be smooth (not wavering), point A would be vertical at the end, and point B would be horizontal at the end.
The pen could have been attached to the side of the projecting footrest of a 'La-Z-boy' type recliner (on the lever side). When the lever is moved to lower the footrest, the path of the pen is like your A to B (grid in inches).
One of those oven doors that slides under the oven as you open it like the image below (without actually sliding it all the way in once it was horizontal)?
In this case the arc of the door opening would shorten in radius as the door slides under during the pivot stage. The line drawn would be that of a pen attached in line of the top edge of the oven door.
it was operated in a room, filled with a thick layer of dust. The starting position is shown by A( vertically above B, because of dust) and as the cleaning gets completed, the pen's height decreases and settles down at B.
A cake mixer. It has a rotating blade attached to a rotating disc, such that the blade focuses on a different area of the bowl each moment. The two rotations are of different radius and speeds, allowing for a spirograph like image, of which we can only see the beginnings of.