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You can get oversteer and oversteer regardless of where the wheels are driven - it's about weight transfer and slip angles although granted it is easier to create the necessary slip angles depending on which wheels are driven.
Understeer is effectively a yaw movement where the forward portion of the vehicle is propelled away from the corner axis relative to the intended arc ie what is called "pushing." This is generally when the slip angles on the front wheels exceed those of the arc around the corner.
Oversteer is effectively a yaw movement where the nose of the vehicle is propelled toward the corner axis relative to the intended arc ie it begins to get "taily" alternatively it can be described as the condition where the rear wheels have slip angles exceeding those of the arc around the corner.
Most passenger vehicles usually are intended to provide understeer as it is thought this is more benign and easy to recover for most drivers than oversteer. Why? I'll try to explain...
The first thing to consider is weight transfer - under acceleration, the car tends to "squat" (ie weight is transferred to the rear) and under braking the car tends to "dive" as weight is transferred to the front. This weight transfer has the same effect as lift and downforce - when you have lift your mechanical grip to the road is reduced and when you have downforce mechanical grip is increased.
You usually get understeer (particularly plough-on understeer) where the grip of the steering wheels is exceeded by the sideways cornering forces ie you are cornering too fast for the mechanical grip of the car. This causes the vehicle nose to push wide of the apex of the corner. To alleviate this you can apply more steering lock (ie turn the wheels toward the axis of the corner) but at some point the yaw force (understeer) will be to great to compensate. To alleviate this, you can reduce the throttle gently this reduces the cornering forces and reduces the slip angles bringing the car back to neutral and also subtly transfers weight over the front wheels adding to grip. This is accepted to be easier to control for most drivers.
However, sudden lifting off of the throttle and/or braking when experiencing understeer can cause what is termed "snap-oversteer." This is because weight is sudden transferred to the front of the vehicle (ie pitch) which reduces the weight on the rear of the car. This weight transfer reduces the downward force on the rear which reduced grip. The cornering forces which were held equal at the rear of the car now exceed the grip of the rear tires. This causes the rear of the car to be pushed outside the intended arc (ie oversteer) in a very rapid transition.
This rapid transition is often difficult to control as it must be compensated rapidly by a reduction in steering lock or alternatively to a steering angle OUTSIDE the intended arc ie the steering wheels are pointed AWAY from the apex of the corner! This is called 'opposite lock' and must be applied as rapidly as the transition to oversteer to be corrected successfully. This is generally accepted to be outside the skill levels of most drivers of passenger vehicles.
Front Wheel drive cars are inherently more likely to understeer because the steering wheels are also charged with the job of applying drive so acceleration forces as well as the bulk of braking forces are applied to this end of the vehicle as well as having the job of steering. However, with sudden weight transitions or differences in front-rear grip (eg worn tires on the rear and grippy tyres on the front) oversteer is still possible. Weight distribution front to rear can also affect the tendency to under/oversteer eg unladen forward control front wheel drive vans.
Rear-wheel drive cars are inherently more likely to oversteer than FWD as the rear wheels have acceleration forces to contend with. Again weight transfer/distribution is significant. High powered RWD pickup trucks can produce oversteer due to the unladen rear end having less weight over the driven axle.
Finally, polarity of inertia is also a major factor. Rear-engine Beetles and Porsches inherently have oversteer characteristics as the weight of the vehicle is skewed behind the rear axle which creates inertia towards the oversteer yaw movement. Front Engine and in particular FWD cars tend to understeer for similar reasons as weight is skewed over the front axle.
On the other hand, mid-engine vehicles have a low polarity of inertia as the weight is centred between the axles. While improving weight distribution and reducing the tendency to produce yaw movements, this does have the disadvantage of having a higher propensity to spin on the axis of the engine location.
Phew...
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