does anybody besides Audi use the trapezoidal rear suspension?

I stopped to help a little old lady with a flat tyre. She was driving an
Audi, and I found the independent rear suspension to be quite interesting.
Searching, I can only find SEAT (also part of VW) with it. But theirs
(on FWD shitbox) looks like a cheaper implementation of the Audi setup.
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There are two common types of suspension in use today, the vertical strut type and the double lateral arm type. The A4 uses a variant of the lateral arm type, also commonly called a double wishbone type. The advantage of the double lateral arm type, especially at the rear, is that it is easy to make allowance for a drive shaft and you will see that on the A4. The greatest disadvantage is that it compromises the packaging of the vehicle. In this case, the suspension intrudes into the boot space. Jaguar, with the E Type, avoided the issue by making the drive shaft the upper lateral link.
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was a very clever packaging arrangement and also avoided the need for a sliding coupling to vary driveshaft length during suspension deflection. You will also note the use of Hookes type universal joints, a pair being used to cancel cyclic speed variations. It's not a pure lateral arm suspension since it uses a trailing arm to control the fore and aft deflections of the lower link. It's a bit of a hybrid.
Another disadvantage of the standard lateral arm suspension on older RWD vehicles is that accommodation needed to be made for the drive shaft length to alter and this was done through the use of a spline connection. The disadvantage of this with a powerful engine is that the spline could lock under hard acceleration causing disastrous effects on the handling. The A4, in common with most vehicles of its ilk, avoid this through use of CV joints and, in particular, a plunge type CV on the inner end. The A4 suspension, in common with the type, has a lot of kinematic advantages. For one, it is easy to build anti dive, anti squat into the suspension. It is a trapeziod and not a parallelogram because, if the upper arm and the lower arm were the same length, the wheel track would alter on suspension deflection. With the shorter upper arm, the wheel tends to lean inward (negative camber) on suspension deflection but the tyre contact patch line never alters. Finally, because of the kinematics, a lot of suspension designs have less desirous traits when cornering and this can affect rear wheel drives. In some cases, due to suspension compliance, the rear wheels can toe out under power. That won't do a lot for your cornering line. You will find the compliance in the front bush at the inner end of the lower arm is greater than that at the rear. It is also angled differently to the rear bush. That allows a slight toe in at the rear which keeps slip angles at the rear tyres in the *comfort zone*. The A4 rear suspension has a lot of little tricks built into the design which won't be apparent to the casual observer but they make for an excellent handling vehicle.
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