A rigid body is an idealized object whose shape and size are treated as fixed while it moves. A degree of freedom is an independent way in which such a body can change its position or orientation.

A free rigid body in three-dimensional space has six degrees of freedom:

• three translations, along independent spatial directions;
• three rotations, about independent axes.

A constraint removes one or more possible motions. For example, placing a rigid block on a perfectly supporting plane prevents motion through that plane and also prevents two rotations that would make the block penetrate it. Additional independent contacts can remove the remaining motions.

Constraints must be independent to remove additional degrees of freedom. Adding another contact that blocks a motion already prevented does not necessarily constrain a new motion; instead it can create redundant constraint or overconstraint.

This distinction matters whenever a body must be positioned reproducibly. A complete locating scheme constrains all motions that would change the required pose, while avoiding unnecessary constraints that make the system sensitive to geometric imperfections.

Degrees of freedom provide a common language for mechanisms, datum reference frames, fixturing and many other systems in which motion is progressively restricted.