A sedan steers its front wheels; a forklift steers its rear wheels. Give both the same wheelbase, the same maximum steering angle, and both gears, forward and reverse. Is there any path one can trace that the other cannot? And as each begins a left turn while rolling forward, which way does each body first swing?
Solution
No path separates them — the immediate motion does: the forklift begins its left turn by throwing its tail, and with it most of its body, to the right.
Rolling without slipping pins each axle’s midpoint to move only along its wheels’ heading — one nonholonomic constraint per axle — and the car’s instantaneous center of rotation sits where the two axles’ perpendiculars cross. Steer the front and that center slides along the rear axle’s line; steer the rear and it slides along the front’s. The two machines are therefore the same linkage read in opposite orders: a forklift rolling forward is a sedan rolling backward with nose and tail relabeled. Since both have both gears, every curve the one can trace the other traces by swapping which end leads — same minimum turning circle, same reachable configurations, and even the parallel-parking wiggle, the trick of composing two constrained motions into the sideways displacement each alone forbids, is available to both.
What differs is where the pivot sits while the maneuver happens. The sedan turns about a point on its rear axle: the nose swings into the corner and the rear wheels track a tighter arc inside the front’s — the familiar corner-cutting that clips curbs. The forklift pivots about its front axle: to point its forks left it must first sweep everything behind that axle to the right. The body’s initial sideways velocity is opposite to the commanded turn, and that tail swing is why forklift training drills one rule above all — keep clearance on the side you are turning away from, because a forklift hugging a wall cannot turn away from the wall without striking it.
The unsteered axle is a trailer, and which end of the vehicle it occupies decides who won the road. Trailing behind the steered end — the sedan rolling forward — its heading errors die out on their own, the rear pursuing the front the way a towed dolly straightens behind a hand truck. Leading trailer-first — the forklift at speed, or any sedan in reverse — the same geometry amplifies every error, and the driver must supply the missing stability by hand. That is why rear steering lives at walking pace among the pallets, appears on highway cars only as a few assistive degrees on the rear axle, and why backing down a long straight driveway feels like balancing a broom.
Deeper in the notebook: the Classical Mechanics shelf — still being bound; rolling constraints and the geometry of nonholonomy will live there.