Degrees of Freedom


Degrees of freedom, often represented by or , is the number of independent pieces of information used to calculate a statistic.

DOF is calculated as the sample size minus the number of restrictions.


DOFs describe how something is free to move in space. It is equal to the dimension of the Configuration Space.

Intuitively, the degrees of freedom of a robot typically refer to the number of movable joints of a robot. A robot with three movable joints will have three axis and three degrees of freedom, a four-axis robot will have four movable joints and four axis, and so on.

Degrees of Freedom of Rigid body

A rigid body in three-dimensional space has six freedoms, which can be described by the three coordinates parametrizing point A, the two angles parametrizing point B, and one angle parametrizing point C, provided A, B, and C are noncollinear.

Degrees of Freedom of Robot

A robot is just a combination of many rigid bodies.

Types of mechanisms

Open-chain mechanisms and closed-chain mechanisms. A closed-chain mechanism = a mechanism with a closed loop. Ex: A person standing with both feet on the ground

An open-chain mechanism = any mechanism without a closed loop Ex: your arm when your hand is allowed to move freely in space.

We use Grubler’s Formula to figure out how many degrees of freedom a robot has.