In the quest for ever finer levels of technology integration, mechanical linkages reach their precision limits at about 5 micrometers per meter of workspace. Beyond this physical limit, all six dimensional degrees of freedom need to be precisely ascertained to account for mechanical imperfections. This paper substantiates Wu’s vision of “precision machines without precision machinery.” A formulation and statistical characterization of position and orientation error propagation in rigid bodies are presented for two extreme models of measurement. It is shown that error distribution is uniquely dependent upon the design of the measurement plan. The theoretical foundations presented were evolved in the course of designing precision machinery. Other potential applications include: fixture design, metrology, and geometric tolerance verification.
Generalized Abbe Principle: Position Error Propagation in Machine Elements
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
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Pegna, J. (March 1, 1997). "Generalized Abbe Principle: Position Error Propagation in Machine Elements." ASME. J. Mech. Des. March 1997; 119(1): 1–7. https://doi.org/10.1115/1.2828783
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