How a wheel actually moves

Linkage geometry from first principles: the two views, the points that aren't there, and every angle that changes while you aren't looking.

1. Your suspension has exactly one job (and it isn't comfort)Ride quality is a side effect. The actual job is keeping four contact patches loaded and square to the road — and your linkage is quietly changing the angles the whole time you're driving.
2. The instant center: the pivot that isn't thereYour wheel pivots around a point that has no bearing, no bracket and no bolt — and is often several meters outside the car. Find it and most of suspension geometry stops being mysterious.
3. Camber curve: how much lean, and where it comes fromCamber gain is one divide away from the swing-arm length you found last chapter. Here's the equation, why it lands within a few percent of the solver, and how to work out how much you actually need.
4. Roll center: the most abused point in vehicle dynamicsIt has no bearing, it moves constantly, and half of what's said about it on forums is wrong. It also decides how hard your springs have to work — so here's what it actually is, and the one number you get from it.
5. Roll center migration: the number that won't sit stillYour roll center is a design value at exactly one ride height. Drive the car and it moves — on one Mini, by 186 mm across travel, straight through ground level. Here's how to measure the envelope and how much is too much.
6. Bump steer: your suspension is steering without youThe tie rod swings on a different arc than the control arms, so the wheel steers itself over every bump. Here's the construction that kills it at the front — and why the rear deliberately keeps some.
7. Kingpin axis, part 1: KPI, scrub radius, and why your steering fights backThe wheel steers about a line through two joints — not through the middle of the tire. Where that line hits the ground decides steering weight, kickback, and what happens when one front tire finds ice.
8. Kingpin axis, part 2: caster, trail, and free camberCaster is why the wheel comes back to center, why steering loads up, and — the part people miss — how the outside front tire gets negative camber exactly when it needs it, without any camber gain at all.
9. Anti-dive and anti-squat: side-view geometry earns its keepYou can stop a car diving under braking without a single extra newton of spring — by tilting the arms in side view. Here's where the percentage comes from, and why 100% is almost always the wrong answer.
10. Motion ratio: the lever between the spring and the roadYour spring rate is not your wheel rate. The linkage sits in between as a lever, and because the effect goes as the square, a small ratio change makes a big difference — 400 lb/in can arrive as 196.
11. Ackermann, and whether you actually want itThe inside wheel is on a tighter circle, so it should turn more. That's been the textbook answer since 1817 — and most race cars deliberately ignore it. Here's the geometry, and the slip-angle argument that overrules it.