A Graph Grammar Approach for Structure Synthesis of Mechanisms

Abstract

This paper presents a general graph grammar methodology for structure synthesis of mechanisms. Much of current mechanism design is based on a systematic method popularized by Freudenstein, Mruthyunjaya, and Tsai (among others). A graph grammar is a more natural expression for a method that relies on algebraic abstractions of graph theoretic principles. Our proposed grammar rules add vertices and loops to a start graph to obtain desired structural requirements. A grammar adaptation of an existing linear time algorithm for the detection of isomorphism is presented. Also presented is a specialized grammar for the structure synthesis of Epicyclic Gear Trains. A valid graph grammar for structure synthesis of mechanisms enables both the eventual automation of general atlas construction and atlas construction for customized mechanism classes. [S1050-0472(00)01904-8]

Addition method with 2 links and 3 pairs of type synthesis to planar closed kinematic chains

“…And they can be summarized into four main kinds: addition method with 2 pairs, transformation of binary chains, superposition of kinematic chains and algebraic method of matrix. Schmidt [1] applied a general graph grammar methodology for the synthesis of kinematic mechanisms. Rao and Deshmukh [2] introduced a method based on loop formation for structural synthesis which eliminates explicit isomorphism detection.…”

Comparing a Graph-Grammar Approach to Genetic Algorithms for Computational Synthesis of PV Arrays

“…the synthesis of mechanisms and epicyclic gear trains [5], the automated synthesis of gear boxes [6] and sheet metal design [7]. Besides assisting synthesis, graph grammars allow the support of the whole design process, e.g.…”

A Method for Design of Modular Reconfigurable Machine Tools

“…Therefore, isomorphism detection is performed during solution generation. There are several methods proposed in the literature for isomorphism detection [23][24][25][26][27][28]. The isomorphism detection algorithm presented in this paper is based on the tree method [23], which requires examining if the tree is rooted or not first.…”

“…For this purpose, tree graph enumeration algorithms are adopted and the interested reader can refer to [23][24][25][26][27][28] for details. Steps are provided here: the first step is to enumerate all the generalized layouts by defining enumeration constraints, performing enumeration, and checking isomorphism.…”