This tag is for questions relating to the Degree of Freedom (DOF) of a mechanical system. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering.

Definition: The minimum number of independent coordinates required to simplify the system completely along with the constraints is called the degree of freedom of a dynamical system.

For the $N$ number of particles moving freely in $d$-dimensional space, the degrees of freedom is represented by the equation $f=Nd$. If there are constraints then $f=Nd-k$,where $k$ is the number of constraints.

For example, when a single particle moves in space, it has three degree of freedom, but if it is constrained to move along a certain space curve, it has only one.

Note: Imposing constraints is a way of simplifying the problems mathematically in that the number of equations of motion are reduced to the same number as the number of degrees of freedom.

References: https://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)