Type Synthesis and Initial Sizing of Planar Linkages using Graph Theory and Classic Genetic Algorithms starting from Parts Prescribed by User

MARTÍN PUCHETA; ALBERTO CARDONA

Madrid

Congreso; ECCOMAS Thematic Conference Multibody Dynamics 2005; 2005

European Community in Computational Methods in Applied Sciences ECCOMAS

We present a methodology for generating planar mechanisms with rotoidal and prismatic joints to fulfill a given planar kinematic task like path, motion and function generation subject to space restrictions. We use the graph representation of mechanisms, the enumeration of kinematic structures, and Degree Code identification techniques to solve the type synthesis problem. We take into account parts of mechanisms prescribed by the user to construct an initial graph that is searched in an atlas as a subgraph. For an abstract mechanism manipulation, we use combinatorial algorithms detecting, in an increasing order of complexity, non-isomorphic subgraph occurrences. The kinematic chain associated to each feasible topology is automatically decomposed into open-chains. Then, dimensions for each open-chain with unknown dimensions are computed using Analytical Synthesis Methods. If an open-chain has infinities of solutions we use classical Genetic Algorithms to determine which free parameters set are the most appropriate. Combinations of computed open-chains are assembled to build feasible kinematic chains. This methodology has the advantage of producing several kinematically feasible alternatives with minimal human intervention. Depending on how they fulfill the task, they are used directly for detailed design or as initial guess for optimization based on gradient techniques. Masses, inertias, weight and forces are not considered at this stage. However, they are taken into account in subsequent detailed designs using classical analysis tools. This module was written in language C++ under the OOFELIE environment. Solutions for typical aeronautical problems will be shown.C++ under the OOFELIE environment. Solutions for typical aeronautical problems will be shown.