Machine Kinematics
solved, then drawn
Concept

Suspension — where it appears

The linkage between a vehicle's body and one of its wheels, which is a four-bar in a front view with the wheel bolted to its coupler. Its geometry decides how the wheel leans, steers and moves sideways as it rises, and every one of those is a property of the coupler's motion rather than of the spring.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The wheel is the coupler — double wishbone. The suspension solved at 0 mm of bump, with the whole travel ghosted behind it. The two arms are the cranks and the upright between them is the coupler; the wheel is bolted to that coupler, so camber is the coupler's rotation and nothing else. Camber here is 0.00° and the contact patch has moved 0.0 mm across the road. The cross is the instantaneous centre of the upright, found from the solved velocity field; the roll centre is where the line from it to the contact patch crosses the car's centreline, and it is at 73 mm here.

The wheel is the coupler

A double wishbone is a four-bar standing on end whose coupler carries a wheel, so camber is coupler rotation and scrub is a coupler point's path. Both are computable, and the second one comes out with the opposite sign from the model every suspension book uses — by more than the whole scrub.

applied · Fourbar The roll centre through the travel — double wishbone. The roll centre is a construction: the instantaneous centre of the upright, joined to the contact patch, extended to the car's centreline. It is quoted as a height. Over 160 mm of travel it moves 54 mm — 52 mm to 106 mm — The number in a specification is the value at one position of a curve, and the curve is steeper than the thing it is a property of.

A roll centre is not a point

The roll centre is a construction on the instantaneous centre of the wheel's upright, and every step of it is exact. What it is not is a height: over eighty millimetres of bump and droop it moves 54 mm on a wishbone and 131 mm on a strut, and on the strut it goes below the road.

applied · Fourbar Two ways to stop an axle moving sideways. A Panhard rod is one link from the body to the axle, so the axle's end follows an arc and the whole car shifts sideways as the suspension moves: 3.56 mm at 80 mm of travel, and always in the same direction, so it happens twice per bounce. A Watt's linkage keeps the same point on a path that is straight to 33.7 µm — 106 times better, and it is drawn on the same axis, which is why it looks like the zero line.

Holding an axle still

A Panhard rod moves the axle 3.56 mm sideways over 80 mm of travel and a Watt's linkage moves it 34 microns — a hundred times better, and by a higher power. The Panhard's error is quadratic in the travel and the Watt's is fifth order, which is a much stronger statement than "the Watt is better" because it says how the comparison changes with the suspension.

applied · Coupler

Named alongside it

The objects these essays reach for when they reach for this one.

CouplerCamberConstraintCoupler curveFour-barScrubApproximationDerivativeInstantaneous centreInversionKennedy's theoremPin in slot

All concepts