Uncertainty of dimensional measurments obtained from self-initialized instruments

Precision dimensional measurement instruments often contain sensors that can only measure displacement of a moving body from some reference position. In order to measure the length of an object they often require a calibrated artifact to initialize their measurement sensors so that they may provide an absolute measurement instead of displacement. Instruments which can realize a null value, i.e. zero length, don't require one; however instruments which can't need to reference an object of known size. These calibration artifacts also serve as part of the chain of metrological traceability.;The group of instruments presented in this dissertation can self-initialize by deriving their own calibrated artifact. These instruments rely on a unique artifact geometry, which is uncalibrated, to determine a length value via a series of displacement measurements provided by the self-initializing instrument. All of the self-initializing instruments described in this dissertation rely on a precision sphere coupling with a three point kinematic seat (TPKS) as the mechanical interface between the instrument and un-calibrated artifact. The combination of the TPKS and sphere are deterministic in nature in defining a point in space, e.g. the location of the center of the sphere relative to the body of the TPKS. In practice, high precision spheres are inexpensively available, and testing has shown that the locational repeatability of the sphere/TPKS coupling to be in the range of the surface roughness of the spheres, thus allowing nanometer-level repeatability. The combination of this feature and the displacement measurement sensors in these instruments allow the instrument to directly measure length without resorting to a measure of extension.;The Laser Ball Bar instrument, an instrument which pioneered the self-initialization method for length measurement instruments, and can't realize a null value measurement for initialization, is functionally decomposed to better understand the requirements for self-initialization. Two instruments that fulfill these requirements will be presented as case studies of how a self-initialized instrument may be designed, and constructed. Measurement uncertainty with these instruments, using self-initialization, and initialization with an independently calibrated artifact will be explored. A complete uncertainty analyses are provided for both instruments using both the self-initialization mode and the calibrated artifact mastering mode of operation; and the predicted results are compared to experimental measurement data.;This dissertation: (1) Derives and/or explains the geometric conditions which enable self-initialization in an instrument (2) Describes two novel instruments that are capable of self-initialization (3) Provides an uncertainty analyses for these instruments when they are self-initialized and when they are initialized using a master artifact (4) Compares and contrasts the achievable uncertainty for each mode of use, and (5) Provides conditions under which lower uncertainty is achievable using self-initialization.