Six degrees of freedom (6-DOF) are the six independent ways an unconstrained rigid body can move in three-dimensional space: it can translate along three axes and rotate about three axes. Together, these motions describe its position and orientation—its pose.
What are the six motions?
The six motions divide into translation, which changes position, and rotation, which changes orientation.
Three translations
- Along the x-axis: movement in one of three perpendicular directions.
- Along the y-axis: movement in a second perpendicular direction.
- Along the z-axis: movement in the third perpendicular direction.
In marine and vehicle terminology, these translations are often called surge, sway, and heave. The labels depend on the coordinate convention and the body’s orientation.
Three rotations
- Roll: rotation about one axis.
- Pitch: rotation about another axis.
- Yaw: rotation about the third axis.
Roll, pitch, and yaw are common names, but the physical direction each describes depends on the axes and reference frame in use. ISO’s definition describes a degree of freedom as an independent displacement or rotation parameter by which a body or system can move; its note identifies six mechanical degrees of freedom for a rigid body in 3D. The surfaced ISO/DIS 14954 listing attributes that note to ISO 10795:2019, 3.165, as modified, and is a draft listing rather than confirmation of a final edition: ISO/DIS 14954.
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How do the six degrees describe pose?
A body’s pose combines its position and orientation relative to a reference frame. A common description gives three coordinates for translation and a representation of three-dimensional rotation. The six degrees of freedom describe the dimensionality of a free rigid body’s configuration; they are not six arbitrary labels. A Springer Nature robotics chapter uses a helicopter as an example: it can move in three spatial dimensions and rotate about three axes, giving it six degrees of freedom: Robotic Motion and Odometry.
What happens when motion is constrained?
Constraints remove available motion, so a constrained body may have fewer than six degrees of freedom. For example, a rigid body restricted to a plane can translate in two directions within that plane and rotate about the axis perpendicular to it: three degrees of freedom. Northwestern’s Modern Robotics resource explains how independent constraints reduce a spatial rigid body’s available motion: Modern Robotics.
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Does a “6-DOF” robot mean the same thing?
The phrase can describe a robot or device with six available motions, but that use is not automatically identical to saying one unconstrained rigid body has six mechanical degrees of freedom. A robot’s motion depends on its joints, constraints, and configuration. When comparing robots or devices, check which translations and rotations are available and which reference-frame convention defines them.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How to interpret roll, pitch, and yaw
Before comparing motion descriptions, establish the coordinate frame and axis convention. Ask which direction is x, y, and z, what the reference frame is, and which rotation is assigned to each axis. Without that information, the terms roll, pitch, and yaw may not identify the same physical motion across different systems.
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