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Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies. [2] [3]
The Newton–Euler equations are used as the basis for more complicated "multi-body" formulations (screw theory) that describe the dynamics of systems of rigid bodies connected by joints and other constraints. Multi-body problems can be solved by a variety of numerical algorithms.
A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs. Chasles' theorem shows that each Euclidean displacement in three-dimensional space has a screw axis, and the displacement can be decomposed into a rotation about and a slide along this screw axis ...
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A rigid motion in three dimensions that does not necessarily fix a point is a "screw motion". This is because a composition of a rotation with a translation perpendicular to the axis is a rotation about a parallel axis, while composition with a translation parallel to the axis yields a screw motion; see screw axis. This gives rise to screw theory.
A screw axis.Mozzi–Chasles' theorem says that every Euclidean motion is a screw displacement along some screw axis.. In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a screw displacement.
By the way, a screw is defined by six parameters: four to describe a line (ISA), one to specify the pitch and one to specify the amplitude of the movement (the angle). —Preceding unsigned comment added by Lplaus ( talk • contribs ) 12:32, 11 February 2009 (UTC) [ reply ]
Leadscrew, a type of screw used to provide controlled and quantifiable movement in machine tools; Screw (motion), a description of spiral motion used in rigid body dynamics; Screw propeller; Screw, some specific pair of vectors (e.g., force+moment or linear+angular velocity); see Screw theory; Screw axis, the axis of rotation in 3D geometry