On the application of Chebyshev's methods to the problem of balancing mechanisms

Abstract

The aim of this book is to present the theory of the best approximation of functions in an engineering context. While the detailed presentation and application of the best uniform approximation theory of P.L. Chebyshev is its primary direction, considerable effort is made to present the best average approximation theory for comparison. Application of these theories is centered about the balancing of mechanisms. The excerpts presented here start with the mathematical criteria of Chebyshev's theory. They continue with discussions of the best average and best uniform approximations to a unit circle by means of a constant. Furthermore, iterative and graphical approximation methods for the determination of the first order harmonic which deviates least from a given function in the sense of Chebyshev are shown. Finally, each of the theoretical results is applied to a specific problem of mechanism balancing.