A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and SynthesisDrawing on screw theory and engineering mechanics, a mathematical theory for automatic configuration of machining fixtures for prismatic parts is developed. There are two parts in the theory: analysis and synthesis. The following functions of fixtures are analyzed: deterministic workpiece location, clamping stability, and total restraint. The synthesis of fixtures includes the determination of locating and clamping points on workpiece surface and the determination of clamping forces. The theory deals with the general case of 3-dimensionalparts, polygon support (as opposed to three-point support), and multiple machining operations.
The class of Horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time. It is shown that to every arborescence there corresponds a family of extended Horn sets, where ordinary Horn sets correspond to stars with a root at the center. These results derive from a theorem of Chandrasekaran that characterizes when an integer solution of a system of inequalities can be found by rounding a real solution ma certain way, A linear-time procedure isprovided foridentifying''hidden'' extended Horn sets (extended Horn but for complementation of variables) that correspond to a specified arborescence. Finally, a way to interpret extended Horn sets in applications N suggested.
In the 19th century, the French geometer Charles Pierre Dupin discovered a nonspherical surface with circular lines of curvature. He called it a cyclide in his book, Applications de Geometrie published in 1822. Recently, cyclides have been revived for use as surface patches in computer aided geometric design (CAGD). Other applications of cyclides in CAGD are possible (e.g., variable radius blending) and require a deep understanding of the geometry of the cyclide. We resurrect the geometric descriptions of the cyclide found in the classical papers of James Clerk Maxwell and Arthur Cayley. We present a unified perspective of their results and use them to devise effective algorithms for synthesizing cyclides. We also discuss the morphology of cyclides and present a new classification scheme.
Lagrangean techniques have had wide application to the optimization of discrete optimization problems. Inverse optimization refers to the fact that each time a Lagrangean calculation is made for a specific problem with a given resources vector, an optimal solution is obtained for a related problem with a suitably adjusted resources vector. This property is studied in depth for the capacitated plant location problem and new parametric methods for that problem are suggested. Computational experience is reported.programming: integer algorithms
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