movingaxis

Moving axis is a concept in physics and engineering referring to an axis of rotation or reference frame that is not fixed in space but moves with time or with a body. In many analyses, a distinction is made between a fixed, world-axis and a body-fixed axis that translates and rotates with the object. When a rigid body undergoes general motion, the observable rotation can be described about an axis that itself moves; in three dimensions such a motion is often modeled as a screw motion about a line, known as the screw axis.

For planar motion, at any instant the velocity pattern is equivalent to a rotation about an instantaneous axis perpendicular to the plane; that axis is typically moving as the body continues to move. In 3D, the instantaneous axis of rotation, or instantaneous screw axis, is the line about which rotation occurs at that instant.

Practical use and calculations: An axis that moves complicates kinematic and dynamic equations. Transformations between moving and fixed axes use standard results such as the parallel axis theorem for moments of inertia when translating the axis, and more generally rigid-body kinematics tools to relate angular velocity and translational velocity. In robotics and computer graphics, moving axes attached to mechanisms or models simplify control and animation by keeping the reference frame aligned with the moving parts.

Applications and related concepts: Moving axes appear in mechanical design, ballistics, aerospace, and robotics. Related ideas include instantaneous axis of rotation, screw theory, and rigid-body motion.