Dang it Sonny pullin out those big words! lol Its a modified Roberts lol only a straight line Roberts if the math is as follows.
This mechanism designed by Richard Robert has the proportions (a) = 1, (b) = 1.2, (c) = 2 and (d) = 1.09 any other math will create an arc.
In a sprint car we always use "(d and c)= twice as long as (b)" "(a) is = to (b)" this is done mostly because it puts the roll center near the center of the chassis.
Moving the paddle up and down on the birdcage is new the older form of adjusting the ladder was to change (c) allot of chassis still have multiple holes at (c) some ladders have diff holes in straps to change strap length. Any changes to the math will move the roll center and change the arc radius.
As for the word Jacobs ladder it came from Genesis in the bible talking about a ladder to heaven. It was later used in naming an ancient toy see photo I think this is were the simular look gave our sprint car part its nic name