To set up a measuring strategy for coordinate measuring machines (CMM) is a highly complex task. It includes the selection of a sampling strategy, which is the number and distribution of touch points. In this paper a method is proposed for estimating the number of touch points for circular features required to meet a certain test objective. Thus the number of touch-points are optimized, in order not to take either too few or too many. Supported by simulations the proposed method proved to be effective in determining an equidistant sampling strategy. To explore factors that affect the sampling strategy, different CMM performances, environmental conditions and workpiece deviations are investigated.

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