# Degree of Freedom (DOF) of car suspension model

Before starting to model any type of car model like quarter car, half car or full car model there is a basic concept about that model that we need to understand.

The Degree of Freedom(DOF) of the car model.

Degree of Freedom (DOF) of car suspension model.

The Degree of Freedom is generally decided with respect to the mass and spring of the system. The basic definition of DOF is the no of independent parameter required to define the position of the system. In our first case we are considering a simple spring mass damper system.

In this system there is a mass m and a displacement x. In this case, as x is only variable, the Degree of freedom of the system is 1.
Now moving on to a quarter car model the mass will be divided into two masses. Sprung mass and Unsprung mass.

Each sprung mass and unsprung mass have their own independent displacement. So Quarter car will have two independent displacements making the degree of freedom of the quarter car model as two.
Taking step forward we will move on to half car model. When we see a half car model it can be observed that the unsprung mass is further divided into front unsprung mass and rear unprung mass.

The front and rear unsprung have there own independent displacement, in addition

The front and rear unsprung have their own independent displacement, in addition to that the sprung mass will have a vertical displacement and a rotational displacement showing the pitching of the model. All of these combined can make the half car model as a four degree of freedom system.
Finally coming to the full car model, the unsprung mass of the model will be divided into 4 wheel, two at the front of the car and two at the rear of the car.