Computational Methods for Design and Synthesis of Planar Mechanisms

Abstract

The objective of this research work is the study and development of techniques for the design and synthesis of planar-linkage mechanisms. The synthesis of mechanisms consists in finding the suitable mechanism for a given movement. Particularly, this thesis deals with the problem of synthesis of mechanisms starting from the initial specifications or requirements of design, that is to say, starting from zero. Consequently, it is necessary to determine the number and type of components, and the connectivity between them (type synthesis); and then to calculate the dimensions of the components, pivots positions, and the control parameters of the kinematic pairs of the input movement (dimensional synthesis). This thesis deals with the kinematic synthesis of position, whose problem consists in determining the dimensions of a mechanism that satisfies a desired set of displacements and rotations in certain points of a mechanism and for certain instants of simultaneity. This specification is called kinematic task. The allowed space –for the solution mechanism and the development of the task– is a very common requirement that restricts the solutions to obtain. The problem is highly non-linear. Besides, since it includes the selection of the topology to dimension, it constitutes a discrete problem of combinatorial complexity. In order to solve this difficult problem, it is proposed to use a representation of the mechanism based on the Finite Elements Method and Graph Theory, managing to preserve and unify both representations to integrate the synthesis into its subsequent stages of detailed analysis and optimization of the mechanism. The original theoretical aspects presented in this thesis are: The development of a new identifier of isomorphism of mechanisms and its use in the enumeration of kinematic chains and different atlases of mechanisms. The exhaustive enumeration of topologies using sub-graphs search to satisfy structural requirements from the beginning of the design process. The automatic decomposition of the closed-loop topologies into single open chains to solve their dimensional synthesis using analytical equations expressed by complex-numbers. For the dimensional synthesis, all combinations of single open chains (some of them with multiple solutions) are automatically computed. Among them, that solution which minimizes the summation of link sizes subjected to some design restrictions is retained. In the cases in which there are free parameters, a zeroorder optimization technique based on Genetic Algorithms with penalization of restrictions is applied to sweep the design space. The modifications for extending the methodology to the design of flexible mechanisms using Rigid-Body Replacement methods are developed and analyzed. As the final result of the application of this technique, it is obtained a list of alternatives that constitute good initial conditions for subsequent gradient-based optimization already available in commercial software. Throughout the thesis, various test and validation examples are provided, showing the capacity of the inventive tool developed. [Ph.D dissertation Faculta de Ingeniería y Ciencias Hídricas, Universidad Nacional del Litoral]