Degrees of freedom (mechanics)

In physics, the number of degrees of freedom (DOF) of a mechanical system is the number of independent parameters required to completely specify its configuration or state. That number is an important property in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields.

As an example, the position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car can be completely specified by a single number expressing its distance along the track from some chosen origin. A train of rigid cars connected by hinges to an engine still has only one degree of freedom because the positions of the cars behind the engine are constrained by the shape of the track.

For a second example, an automobile with a very stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). This body has three independent degrees of freedom consisting of two components of translation (which together specify its position) and one angle of rotation (which specifies its orientation). Skidding or drifting is a good example of an automobile's three independent degrees of freedom.

The position and orientation of a rigid body in space are defined by three components of translation and three components of rotation, which means that the body has six degrees of freedom.

To ensure that a mechanical device's degrees of freedom neither underconstrain nor overconstrain it, its design can be managed using the exact constraint method.