Coordinate metrology uncertainty using parallel kinematic techniques

Dimensional metrology of manufactured objects is increasingly performed with coordinate measuring machines, where coordinates of surface points are recorded and fit to a model of the ideal surface. While coordinate metrology is often performed using machines with a serial Cartesian kinematic structure, the use of parallel kinematic machines has also been investigated. In this paper, we evaluate the uncertainty of trilateration measurements, which is the simplest form of parallel kinematic metrology for spatial coordinates. The instrument studied here is the laser ball bar, specifically designed for trilateration measurements. We use homogeneous transformation matrices to determine its length uncertainty. Monte Carlo simulation is then applied to model the coordinate uncertainty arising from propagation of the length uncertainty through the trilateration calculations. Simulation is compared to experimental results.