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.
Facts
StatementThe most general rigid body displacement can be produced by a screw displacement, that is, a rotation about an axis combined with a translation along that same axis. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Chasles' theorem (kinematics), Wikipedia
Introduction section
the most general rigid body displacement can be produced by a screw displacement or screw motion.
History section
most textbooks refer to a subsequent similar work by Michel Chasles dating from 1830.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.