Chasles' Theorem (Kinematics)

In kinematics, Chasles' theorem, also called the Mozzi-Chasles theorem, states that the most general rigid body displacement can be produced by a screw displacement, a combination of a rotation about an axis together with a translation along that same axis. A general Euclidean isometry in three dimensions involves both a translation and a rotation, and the screw displacement representation decomposes that translation into a component parallel to the rotation axis and a component perpendicular to it, with the theorem showing that the axis can always be chosen so that the perpendicular component is produced by the rotation itself.