Suspension is pretty cool. It makes cars not awful on roads that are awful. (That's the layman's explanation, anyway.) Hell, even good roads have bumps and imperfect textures that you won't necessarily want to feel in minute detail with your butt and spine. Suspension helps ease those bumps out, and that's why we love it. Of course, a ton of permutations have been developed over the years, and these are the major ones.
Solid Beam Axle
We've all seen this one before, it's what was featured on the 1913 Everything, Pharaoh Ramses' chariot, and the back of the 2014 Mustang. It's quite good at putting power to the ground when going in a straight line on a perfectly flat surface, but the fact that a bump on one wheel can upset the other means both handling and ride quality suffer greatly on any road that isn't a drag strip. The Egyptians' chariots were both terrible and dangerous off-road because of this.
Swing-Axle
The first attempt at rectifying the issues of a solid axle was the swing-axle. It did help with ride smoothness and rough roads, but under heavy cornering a sad thing called “jacking” happens. Jacking is when the lateral load on the suspension pushes the tops of both wheels inward. This, of course, messes up the camber, and hurts traction.
Trailing-Link
In trailing-link set-ups, the wheels trail behind an arm that help support the unsprung weight. This kind of suspension can fit in smaller spaces than earlier designs, but the wheels tend to vibrate under heavy lateral loads and and those arms add a lot of weight to the car.
MacPherson Struts
The MacPherson strut debuted in the '70s and is still very common. It's extremely compact and very effective for front-wheel drive cars. It's good suspension, but it is difficult to fit wider tires to a MacPherson strut and the wheels don't gain much camber during upward travel.
Double Wishbone
The double wishbone is better known as A-arm suspension setups, and it comes in equal length and unequal length. Double wishbone suspension offers the same advantages as other independent suspension, but to a greater degree. Ride quality and handling are very good, and the added rigidity of the two A-arms greatly reduces deflection in heavy cornering. Like MacPherson struts, however, there is a lack of camber gaining equal length A-arms, which can be useful, in upward wheel travel. Shortening the upper arm increases camber gain during upward travel.
Pushrod
The pushrod isn't used, with the exception of the Lamborghini Aventador, in road cars, but it certainly is interesting. Most of the elements of the suspension are moved in towards the center line of the car, reducing the polar moment of inertia, reducing weight, and greatly helping aerodynamics in open wheeled cars. They're also very adaptable, allowing team mechanics to tune cars for specific tasks. Durability can be an issue, and the ride is harsh.
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