Degrees of Freedom in Robotics

Robotics
Mechanics
Geometry
Author

Ross Heaton

Published

27th April, 2025

A degree of freedom is the ability of a rigid body to move in an independent (distinct) way.

Degrees of freedom (DOF) of a rigid body is the number of independent movements it has.

A rigid body is a 3D object that is solid and does not deform or change shape.

There are six degrees of freedom in 3D space:

Figure 1. The six degrees of freedom: forward/back, up/down, left/right, yaw, pitch, roll. By GregorDS - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=38429678

Three refer to rotational movement around the x (roll), y (pitch), and z (yaw) axes.

Three refer to translational movement along the x (moving left or right; sway), y (moving forward or back; surge), and z (moving up or down; heave) axes.

Rotation is a change in orientation and translation is a change in position.