Additive manufacturing (AM) comprises a range of deposition processes which include, but are not limited to, direct metal laser sintering (DMLS), electron beam melting, direct metal deposition, photo polymerization, stereo-lithography, and fused deposition modeling. While rapid prototyping techniques have been available for more than two decades [1, 2], AM has experienced phenomenal growth in recent years driven by new applications and processes associated with design, prototyping, limited quantity production, tooling and fixturing, and repair or modification of existing parts. The advantages of additive manufacturing include reduced setup costs, fast turnaround, and the ease of fabricating designs that lack symmetry, that include arbitrary freeform geometries, and/or that include complex internal geometries. While metrology tools exist that are useful for additive parts and processes, AM provides challenges which have not yet been addressed by industry or the research communities. Any designer has in mind functional requirements, and through the design, satisfies these functional requirements. While design parameters include material properties and geometry, the current work is limited to how additive manufacturing technologies meet geometry requirements such as part dimensions, surface form, and surface finish or texture. "Traditional" subtractive manufacturing methods (i.e. machining) generate a desired geometry through removal of stock material using a cutting tool whose location is controlled by the machine's motion platform. To first order, dimensional geometry errors are driven by the accuracy of the machine tool, while tool interactions with the workpiece tend to control the surface finish generated by machining. The location of the tool can be predicted through machine modeling [3,4]. We can express the actual location of the tool as a vector function: r_(act) = r_(nom)+δ (1) δ=f(x,y,z) where r and δ are vectors, and the subscripts denote actual position or nominal position. The generated part geometry is generally considered to be deterministic based on the tool location.
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