2.3. Degrees of Freedom

Degrees of Freedom

The degrees of freedom (DoFs) of a system are the minimum number of independent parameters required to uniquely specify its configuration.

• A point in ${\mathbb{R}}^3$ has 3 DoFs.
• A rigid body in ${\mathbb{R}}^3$ has 6 DoFs (three translational and three rotational).
• A serial robot with $n$ independent joints has $n$ internal DoFs.

The robot’s configuration space therefore has dimension $n$, whereas its workspace has dimension at most 6. When $n>6$, the robot is redundant: internal DoFs exceed task-space DoFs.

In dynamic models, the number of state variables is typically twice the number of DoFs, since both configuration variables and their associated velocities must be represented.