This paper presents a method for determining the location of geometric elements that compose the external features of referencing fixtures. Since in most applications parts that are handled in robotic work-cells are on a worktable or a floor, this paper focuses on fixture geometries that reside on a plane of known location. The location of the unknown geometric elements are found using contacts to the geometric elements and spatial constraints between the geometric elements. Geometric equations for contacts between lines, planes, points, spheres, and cylinders are derived. Spatial constraint equations are also derived. An algorithm is given for locating the geometric elements that form the fixture. The algorithm uses the contact equations and spatial constraint equations to locate the geometric elements. To illustrate the use of this algorithm, two examples are described in detail.

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