The kinematic analysis of the volumetric error measurement of a prismatic guideway based on six optical sensors and three diffraction gratings

A six degree of freedom encoder based on 3 optical gratings and six sensing elements was developed to measure the position as well as the volumetric deviations of a linear motion axis. In order to evaluate the performance of the device and in order to create a mathematical representation a kinematic model was developed. The kinematic models as well as the influence of geometric errors due to manufacturing and assembly are discussed.