# Degrees of Freedom

## Statistics

Degrees of freedom, often represented by $v$ or $df$, 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.

## Robotics

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. $degrees of freedom=(sum of freedoms of the bodies)−(number of independent constraints)$

### Degrees of Freedom of Robot

A robot is just a combination of many rigid bodies.

- See Robot Joint

#### 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.