Synthesis of Four Bar Mechanisms as Function Generators by Freudenstein - Chebyshev

Abstract

This paper describes new method for the synthesis of four-bar linkages for generating a required input-to-output motion. The synthesis method is based on the direct application of Chebyshev’s Alternation Theorem for the Equation of Freudenstein. By this approach the maximum structural error which corresponds to the best approximation can be estimated in advance. Two comparative examples are herewith used to illustrate some of the main features of the method. The innovation in this paper is the presentation of the target function as exact satisfied equation. On substituting the solution of this equation in the Equation of Freudenstein a generalized polynomial of Chebyshev is obtained. This polynomial is minimized by the Chebyshev’s alternation theorem. This method does not require Chebyshev’s spacing of the structural error of the mechanisms. One of the advantages of the so proposed approach is the possibility to predict the peculiarities of the mechanism with respect to the synthesis problem in the beginning of the solution. The so proposed method combines the power of the Freudenstein’s equation and the Chebyshev’s theorem comprehensiveness. The method of Freudenstein-Chebyshev presented here shows that for every structural error which could be presented as generalized polynomial of Chebyshev can be found the best approximation.