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In this paper, an analysis is presented of the problem of characterizing the accuracy of deterministic localization of fixtures. In a statistical framework, the positioning accuracy of the workpiece localized by the locators of a fixture is described by a symmetric, positive definite accurateness matrix (or variance matrix). The accurateness (variance) matrix is identified as having similar structural properties to the stiffness (compliance) matrix of an unloaded, stable robot grasp. This connection leads us to describe a set of frame-invariant characteristic parameters with geometric interpretation. The principal translational accuratenesses and rotational variances are defined for constructions of frame-invariant quality measures for a meaningful comparison of different locating schemes. Examples are presented to illustrate the concept and usefulness of the characterizing properties in optimizing a fixture layout.