Efficiency of programmed motion control systems

The problem of digital program control for machine tools is considered from the standpoint of efficiency and its dependence on the accuracy of scan trajectories. An overlap of neighboring scan loops will decrease the effects of trajectory inaccuracy, with three algorithms of scanning possible: (1) scan time and scan rate fixed independently of the overlap ratio, but width of sweep zone depending on the overlap ratio; (2) sweep zone and scan rate fixed, but scan time increasing with larger overlap; and (3) sweep zone and scan time fixed, but scan time increasing with larger overlap. Each algorithm yields a payoff in either detection probability or scan time. The scanning process is particularized for the two most common scan trajectories: meander and rectangular spiral in a plane with the number of loops ranging typically from 2 to 8. Calculations, with the aid of a numerical table, reveal the relation between the number of possible trajectory executions and the width (variable or uniform) of the unscanned zone for any given odd or even number loops and absolute deviation of the center of the scan pattern.