Complex Harmonic Analysis of Plane Mechanisms. Programming on Digital Computers and Experimental Examples

Abstract

This article examines the plane hinged mechanisms with the aid of two original methods, i.e., a theoretical method and an experimental one. Each of these methods is based on the fact that the functions characterizing the motion of a large class of mechanisms are periodic functions. This fact determines the mathematical tools for the theoretical method; namely, complex Fourier series and the approximation exponential polynomial. For the experimental method this fact is of importance in the suitable choice of a system of successive derivatives of the electrical signal furnished by a polar mechanical transducer which represents the path of any point of the mechanism. The theoretical method of complex harmonic analysis represents the examination of binary structural groups with the aid of Fourier series expressed in complex form. The manner of applying this method to the investigation of plane hinged mechanisms is shown. In the case of the five-link mechanism of aspect I the method is brought to the level of a calculation algorithm which may be used on a digital computer. A numerical example is given with the aid of a CET-501 digital computer.