| The doctoral research reported in this dissertation was designed to investigate rigid body position error distribution and sensing for machine elements in nominal translation. To this end, this research integrated state of the art contributions from various related fields.; To understand position error distribution in the workspace of a machine, the Generalized Abbe Principle was applied to the design of measurement plan that is kinematically invariant under translation. Thus, it leads to a sensor design capable of deriving five degrees of freedom position information from three two-degrees of freedom straightness error measurements.; Concurrent straightness error measurements constitute the centerpiece of the sensor and build upon prior works by Hilaire (36). Fundamental contribution added to Hilaire's work draw from state of the art phase shifting interferometry and computational geometry. The phase shifting interferometry was used to interpret fringe pattern, yielding results that were significantly more robust than those of Hilaire (36). Computational geometry principles were critical to circle metrology, specifically for the purpose of concentricity, center, and circularity measurements. These measurements were in turn applied for novel interferometric measurements of two degrees of angles for parallelism, and two degrees of straightness measurements.; Central to the concentricity measurement is a circle fitting problem known as the Chebyshev fit. A novel algorithm is developed in this research to measure the concentricity of the fringes based on the Chebyshev fit. Resolution of this algorithm is five times better than that of alternative approaches. Furthermore, its running time represents 1-2 order of magnitude improvement. Application to parallelism adjustment results in a resolution of 0.1 pixel (0.0055{dollar}spcirc{dollar}).; With the parallelism adjusted interferometer, resolution of the straightness measurement has been improved to 40 nanometers (previously 80 nanometers) over a depth of field up to one meter. |
