Algorithm to Position the NIST Advanced Automated Master Angle Calibration System(AAMACS) to the Least Angular Step

摘要

An algorithm based on number theoretic arguments is given that shows how toposition the NIST Advanced Automated Master Angle Calibration System (AAMACS) to its least angular step. AAMACS consists of three stacked independently driven serrated tooth indexing tables arranged to rotate concentrically around a common vertical axis. The least angular step between nearest neighbor positions of the topmost table is delta(theta)min = 2pi/(379,080,000) rad. The problem of how to select the indexed tooth position of each of the independent tables reduces to the solution of a Diophantine equation in three unknowns. The equation is solved by use of the classic Euclidean Algorithm.