### MATHEMATICAL MODELING OF SOME FASTENERS ON THE BASIS OF R-FUNCTIONS

#### Abstract

The functional approach is one of the most general approaches in geometrical modeling. The functional approach describes complex geometrical objects (like engines, aircrafts, etc.) using mathematical formulas. A popular method for representation geometrical object in mathematical formulas uses implicit functions. These implicit functions can be constructed using logical operations under functions called R-functions represent logical operations (negation, conjunction, disjunction, etc) under implicit functions. A fastener is a hardware device that mechanically joins or affixes two or more objects together. In the article authors propose geometrical models based on R-functions for different fasteners (some types of bolts, nuts). In the first section of the article authors describe implicit functions for representation of basic primitives (a regular polygon, a chamfer). The next section aims to obtain of 3D models of fasteners using R-functions under primitives. Some visual examples are shown in the final section.

#### Keywords

mathematical model, R-function, nut, bolt.

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DOI: https://doi.org/10.15588/1607-3274-2012-2-20

Copyright (c) 2014 S.V. Choporov, S.I. Gomenyuk, A. A. Lisnyak, Y.V. Panasenko

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