This paper proposes optimization techniques to assist in the design and evaluation of fixtures for holding prismatic workpieces. This formulation of the fixturing design problem takes into account deflection of the workpiece subjected to assembly or machining loads. Using the minimization of the workpiece deflection at selected points as the design criterion, the design problem is determining the positions of the fixture supports. The Finite Element Method is used for calculating deflections that are the basis for the design objective function, and the Broyden-Fletcher-Goldfarb-Shanno optimization algorithm is used to determine the fixture support positions. In this paper the proposed objective function is developed and the method is illustrated with three numerical examples.

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a b s t r a c tAutomotive assembly lines are often characterized by robots' failures that may result in stoppages of the lines and manual backup of tasks. The phenomena tend to impair throughput rate and products' quality. This paper presents a backup strategy in which working robots perform tasks of failed robots. The proposed Mixed-Integer LinearProgramming based approach minimizes the throughput loss by utilizing the robots' redundancy in the system. Two algorithms are developed to comply with stochastic conditions of a real-world environment. The performance of these algorithms is compared with several heuristics, and the downstream-backup based algorithm is found superior to all other methods.

In automotive manufacturing, the quality of spot welding on car bodies needs to be inspected frequently. Operators often only check different subsets of spots on different car bodies with a predetermined sequence. Currently, spot welding inspections rely on a printed drawing of the testing body, with the inspection points marked on this drawing. Operators have to locate the matching spot on the drawing and the body manually to perform the inspection. The manual inspection process suffers from inefficiencies and potential mistakes. This paper describes a system that projects visual data onto arbitrary surfaces for providing just-in-time information to a user in-situ within a physical work-cell. Spatial Augmented Reality (SAR) is the key technology utilized in our system. SAR facilitates presentation of projected digital Augmented Reality (AR) information on surfaces of car bodies. Four types of digital AR information are projected onto the surfaces of car body parts in structured work environments: 1) Location of spot welds; 2) Inspection methods; 3) Operation Description Sheet (ODS) information; 4) Visualization of weld locating methods. Various visualization methods are used to indicate the position of spot welds and the method used for spot welding inspection. Dynamical visualizations are used to assist operators to locate spot welds more easily. The SAR approach does not require additional special models in finding spot welds, but only needs knowledge of location of spot welds on the part. Our system allows operators becoming more effective and efficient to in performing proper inspections, by providing them the required information at the required time without the need to refer to paper-based manuals or computer terminals.