Accuracy characterization and measurement point planning for workpiece localization

This paper addresses the problem of accuracy characterization and measurement point planning for 3-D workpiece localization in the presence of part surface errors and measurement errors. Two frame-invariant functions of the infinitesimal rigid body displacement are defined to quantify the localization accuracy required by manufacturing processes. Then, two kinds of frame-invariant indices are derived to characterize the sensitivities of the accuracy measures to the sampling errors at the measurement points. With a dense set of discrete points on the workpiece datum surfaces pre-defined as candidates for measurement, planning of probing points for accurate recovery of part location is modeled as a combinatorial problem focusing on minimizing the accuracy sensitivity index. Based on an interchange rule, a greedy algorithm is developed to efficiently find a near-optimal solution. It is also shown that if the number of the measurement points is sufficiently large, there is no need to optimize their positions. Example confirms the validity of the presented indices and algorithm.