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.
Plücker coordinates are used to locate a screw axis in space, and consist of a pair of three-dimensional vectors. The first vector identifies the direction of the axis, and the second locates its position. The special case when the first vector is zero is interpreted as a pure translation in the direction of the second vector. A screw axis is associated with each pair of vectors in the algebra of screws, also known as screw theory.
The spatial movement of a body can be represented by a continuous set of displacements. Because each of these displacements has a screw axis, the movement has an associated ruled surface known as a screw surface. This surface is not the same as the axode, which is traced by the instantaneous screw axes of the movement of a body. The instantaneous screw axis, or instantaneous helical axis (IHA), is the axis of the helicoidal field generated by the velocities of every point in a moving body.
When a spatial displacement specializes to a planar displacement, the screw axis becomes the displacement pole, and the instantaneous screw axis becomes the velocity pole, or instantaneous center of rotation, also called an instant center. The term centro is also used for a velocity pole, and the locus of these points for a planar movement is called a centrode.