Approximate Synthesis of Plane Four-Bar Mechanism for Rigid Body Guidance

Abstract

A new analytical method is presented for the synthesis of a plane four-bar mechanism the segment on whose coupler link may pass through five precision positions specified in a stationary co-ordinate system. The numerical procedure is established in such a concise form that consists in solving three systems of five linear equations and a quaritic equatuin. This method is extended to the synthesis of such a mechanism that the higher order differential coefficients of three position variables of the segment on the coupler link at precision positions may coincide with the specified values. Moreover, combining some calculations on the basis of the Roberts-Chebyshev theorem with the numerical procedure, this analytical method may be used as a general precision derivative approximation for designing a path generating mechanism or a function generator.