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Application of Dependence Graphs and Game Trees in Analysis of a Planetary Gear Modeled With a Contour Graph

Deptuła A., Drewniak J., Partyka M. A.

Machine Dynamics Research

2017

Vol. 41, No. 3

105--114

Analysis and synthesis of mechanisms are basic engineering tasks. They can suffer from errors due to versatile reasons. The graph-based methods of analysis and synthesis of planetary gears can be alternative methods for accomplishing of the afore mentioned tasks, which additionally allow for checking of their correctness. Previous applications of the graph theory concerned the modelling of gears for dynamic analysis, kinematic analysis, synthesis, structural analysis, gearshift optimization and automatic design based on so-called graph grammars. Some tasks can be performed only by using methods resulting from a graph theory, e.g. enumeration of structural solutions. The contour plot method consists in distinguishing a series of consecutive rigid units of the mechanism, forming a closed loop (so-called contour). At a later stage, it is possible to analyze the obtained contour graph as a directed graph of dependence. The work presents an example of the use of game-tree structures for describing the contour graph of a planetary gear. In addition, the complexity factor for parametric graphs was taken into account.

Game-tree structures with the complex complexity level as a tool in knowledge engineering

Deptuła A.

Information Systems in Management

2013

Vol. 2, No. 2

100--112

The paper concerns application of the dependence graphs and game- tree structures with the complex complexity level as a tool in knowledge engineering. Different graph solutions mean connections between input and output data as well as decision variables of the analyzed system. The graph distribution from any vertex in the first stage leads to a tree structure with cycles, and next to a general tree game structure. Game-tree structures from each node have different shape and properties. Algorithmic way to create graphical structures out of a mathematical model describes the optimization method of systematic exploration. Tree structure, with the lowest values of complexity level is the simplest structure.

Place/Transition Petri Net Evolutions: Recording Ways, Analysis and Synthesis

Czaja L.

Fundamenta Informaticae

2002

Vol. 51, nr 1,2

43-58

Four semantic domains for Place/Transition Petri nets and their relationships are considered. They are monoids of respectively: firing sequences, processes, traces and dependence graphs. For each of them the analysis and synthesis problem is stated and solved. The monoid of processes is defined in a non-standard way. Nets under consideration involve weights of arrows and capacities (finite or infinite) of places. However, the analysis and synthesis tasks require nets to be pure, i.e. each of their transition must have the pre-set and post-set disjoint.