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Algebraic Models of Product Assembly Process
Engineering Education # 12, December 2016
DOI: 10.7463/1216.0852565
ззю 216-232
Combinatorial Models for Assembly and Decomposition of Products
Engineering Education # 10, October 2015
DOI: 10.7463/1015.0817524
pp. 356-373
A Linearization Algorithm of the Redundant Mechanical Structures
Engineering Education # 05, May 2015
DOI: 10.7463/0515.0770391
pp. 236-250
Structural models of product assembly
Engineering Education # 10, October 2013
DOI: 10.7463/1013.0622946
In this paper the author proposes a new approach to description of mechanical linkages which determine a certain position of machine’s or device’s elements in a technical system. The location relation that exists between parts of any machine or device was considered to be many-placed and is presented as a hyper-graph. A mathematical description of the product assembly sequence was presented as a contraction of vertices of the hyper-graph. Necessary conditions of contractibility for this type of graphs were proposed. A new structure - a lattice of all s-sets - was introduced. It was shown that this lattice could be used for generation of various design decisions at the stage of technological preparation of assembly production.
Rational ordering of alternatives in a dialogue with DM
Engineering Education # 02, February 2013
DOI: 10.7463/0213.0531045
In this paper a method of selecting a rational linear order of a set of admissible alternatives is discussed. The author offers a way of representing a set of permutations of high power in a compact set of partial orders called στ-decomposition. Disparate elements of the expansion are a source of combinatorial diversity of acceptable alternatives. Additional ordinal information from the DM can reduce search space of the best linear order, and in a few iterations, get a better alternative. The proposed technique can be used to generate rational design decisions at the stage of technological preparation of production.
Rational decision-making in design of assembly diagrams
Engineering Education # 10, October 2012
DOI: 10.7463/1012.0475116
This article proposes a new approach to development of assembly diagrams and assembly structure. The authors show that the basic design properties affecting feasibility of these diagrams can be presented as a preorder relation on a set of parts of the product. The symmetrical part of the preorder is an equivalence relation describing accessory of parts to assemblies. Factorization of preorder on its symmetric part gives a partial order on the quotient set. This partial order defines a temporary ranking of parts and components during assembly. The authors propose a procedure of selection of rational assembly sequence which includes sequential afterordering of the partial order.
Modeling of geometric constraints in the process of decomposition of products into the assembly units
Engineering Education # 05, May 2012
DOI: 10.7463/0512.0415792
The problem of modeling the geometric constraints in the assembly of mechanical products is considered. This problem was reduced to a mathematical two-person game on an ordered set. The result of the game is the correct col or of the partial order that it’s necessary to obtain for the minimum number of moves by decision-maker. This paper presents a static characterization of the correct co l ored ordered sets. It was shown that any coloring of this kind could be reduced to isotone mappings of ordered set onto two-element chain.
77-30569/324631 Theoretically-lattice model of machine and mechanical device decomposition
Engineering Education # 02, February 2012
The theoretically-lattice model of product decomposition was discussed in this article; it allowed to synthesize all structurally implemented three-level schemes of machine and mechanical appliance decomposition. It was shown that the property of an independent assembly, that any candidate for the assembly unit should have, could be described as the effect of a closure operator defined on the Boolean set of parts. This set of all closed subsets was a Boolean sublattice and the scheme of decomposition could be described as a set of residue classes of top congruence relation.
Theoretical lattice structural model
Engineering Education # 09, September 2011
This article continues the series of the author's works on mechanical systems modeling during process design. It is proposed to use a lattice model describing the product’s mechanical constraints. This model is defined as a partial order on the set of contractible subgraphs. It is shown that many design and technological solutions are described in lattice terms. A set of components that are coordinated relative to each other can be described as an act of a closure operator defined on the set of parts. The images also form a lattice operator which is defined as an algebraic structure.
Collapsibility conditions. Sufficiency theorems and enumeration
Engineering Education # 07, July 2011
This article is a continuation of works devoted to the modeling of mechanical linkages machinery and mechanical appliances. To describe the positional relationships of mechanical products author is offering to use the language of hypergraphs. It is shown that this medium is an adequate model-based environment and can provide product assembly process as a sequence of normal contractibility of the hyperedges. The necessary conditions for the contractibility of the general form of hypergraphs. We prove sufficient conditions for a number of important cases. The technique of enumeration contracted hypergraph. We obtain recurrence relations that allow to find the number of such objects with n vertices.
Modeling of mechanical linkages. Contractibility conditions
Engineering Education # 05, May 2011
We consider a model describing the positional  mechanical connections of products. This model is a hypergraph. Necessary conditions for the existence of the sequence of contractions, transforming the original hypergraph in unimodal discrete state, are proved. These conditions can be used for verification of projects in the early stages of design and construction. It is shown that the violation of a linear relationship between vertices and edges of the hypergraph leads to intractable dimensional chains and the emergence of excess bases. We find all the nonisomorphic noncontractible  hypergraphs of fourth order, which remain valid for the necessary conditions
Simulation of mechanical linkage products
Engineering Education # 03, March 2011
We discuss the formalization of the mechanical linkage products. Considered mechanical system, whose elements can be considered as absolutely rigid bodies. Offered the mathematical description of the properties that deliver elements of the mechanical system a certain location in the assembly process. It is shown that an adequate description of these properties is hypernetwork model. This hypernetwork is a combination of graph and hypergraph mechanical linkage. The first describes all he connections and mechanical coupling, the second represents the full set of design bases. Hypernetwork can be used for the synthesis of product assembly sequence. Each assembly operation is represented in the form of a normal collapsing vertices of the network. Sequence of normal collapsing that transforms the network into a point, a description of the product assembly.
Structural Synthesis as discret optimization task
Engineering Education # 09, September 2010
The article is devoted to structural synthesis of technical objects. It discusses an approach based on the representation of multiple analogs and prototypes in the form of directed hypergraph. The formulation of the problem of structural synthesis in the form of discrete mathematical programming is proposed. The system of constraints, describing the restrictions on the combination and terms of coercion is introduced.
Choice of rational balance of assembly of a product
Engineering Education # 07, July 2010
The article discusses the problem of choosing a rational product assembly sequence. Means to solve this problem are focused on technical systems with a predominance of mechanical linkages: machinery and mechanical appliances.
Method of dialogue streamlining of alternatives
Engineering Education # 05, May 2010
We consider the problem of choosing the rational linear order from the original set of linearly ordered sets. A new approach to solving this problem is proposed. It is based on the representation of the set of linear orders in the form of several partial orders
Synthesis of a technological route as a decision-making problem
Engineering Education # 03, March 2010
Synthesis of a rational route of processing of a detail can be one of the most mentioned problems of area of technological preparation of machine-building manufacture. It was repeatedly discussed in works of founders of automation of technological designing and in modern works of the given subjects
Game Modelling of Geometric Accsess
Engineering Education # 12, December 2009
In article the new approach to modelling of geometrical obstacles at assemblage of mechanical products is described. Is offered the teoretiko-game model, allowing to minimise labour input of check of conditions of geometrical resolvability. Pure strategy for the linearly-ordered sets and optimum – for partial usages of a general view are formulated.

Engineering Education # 5, May 2004
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