This article proposes the use of polytopes in -description to solve tolerance analysis problems. Polytopes are defined by a finite set of half-spaces representing geometric, contact, or functional specifications. However, the list of the vertices of the polytopes is useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the -description of polytopes in from its -description. It is detailed how intersections of polytopes can be calculated by means of the truncation algorithm. Minkowski sums as well can be computed using this algorithm making use of the duality property of polytopes. Therefore, a Minkowski sum can be calculated intersecting some half-spaces in the dual space. Finally, the approach based on -polytopes is illustrated by the tolerance analysis of a real industrial case using the open source software politocat and politopix.
Tolerance Analysis With Polytopes in HV-Description
Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 4, 2016; final manuscript received April 13, 2017; published online June 16, 2017. Editor: Bahram Ravani.
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Arroyave-Tobón, S., Teissandier, D., and Delos, V. (June 16, 2017). "Tolerance Analysis With Polytopes in HV-Description." ASME. J. Comput. Inf. Sci. Eng. December 2017; 17(4): 041011. https://doi.org/10.1115/1.4036558
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