Axes of rotation standard

When building high precision piezo stages and systems, measuring the accuracy is a crucial step to verify that our products meet the specifications that our customers demand.

On this page, we discuss the terminology and various tests performed in order to specify the axis-of-rotation error motion of our piezo rotary stages before we deliver a system to our customer.

A rotary stage, consisting of a stator and a rotor, ideally has one degree of freedom, i.e. a rotation about the z-axis. However, as perfect rotary stages do not exist, any motion in the remaining five degrees of freedom is referred to as an axis-of- rotation error motion or simply error motion.


The error motion of a rotary stage is usually characterised with a displacement indicator (capacitive sensor) targeting a lapped artefact which is mounted to the rotor of the stage. The error motion of a stage is fully characterised by five error motion components, namely:

Radial error motion (x(θ), y(θ)): defined as the error motion perpendicular to the axis of rotation measured at an arbitrary axial location ‘a’. The axial location must always be specified since tilt of the rotor influences the radial error motion.

Axial error motion (z(θ)): defined as the error motion collinear with the axis of rotation.

Tilt error motion (α(θ), β(θ)): defined as the rotation of the rotor about the x- and y-axis. This error motion can be derived from two radial error motion measurements made at different axial locations ‘a’.