As it pivots up and down, the main bar changes slope. The resulting lines orient to a remote vanishing point that would be otherwise difficult to establish.
E.G. Lutz’s book Practical Drawing includes the diagram above.
Concept artist and illustrator Craig Elliott discovered an antique centrolinead dating from around 1890 (below). Note how the Y-legs branch from a point along the top line of the ruler. He reports:
“I did a little building facade and some windows to test out the Centrolineaid. It is such a breeze, even better than using a long ruler! I set the map pins at 3 inches from the HL and the blades at 30 degrees.
I did the verticals with a t-square and the 30-60 triangle shown. I think two or three of these would make darn quick work of a two- or three-point perspective drawing on a quite small drawing board. This board is about 24 x 32. Another benefit of this tool seems to be that it doesn't pop off the pin all the time like a regular ruler would- it is very steady on the 2 pins.
For the pins or nails, I used a paper clip with one end bent up, or even an upside down flat headed thumbtack taped to the board or paper. This is good for balancing a ruler on for perspective points on the board or for this operation.
You could also use a sheet of metal to draw on, even with a Borco cover, and Neodymium magnets about 1/2 cube size for the pins. They are so strong they won't shift.”
Check the comments for a lot more links and tips. Below is a scanned version of Craig's antique model, with measurements.
Craig Elliott’s blog post about his centrolinead