Approximate kinematic synthesis of the four-bar mechanism by two given positions of the links

Abstract

Abstract Planar four-bar linkages are widely used in various automatic devices and equipment; therefore, kinematical synthesis methods should be developed in order to reduce the amount of initial data and derived the exact solution using modern mathematical methods. The method of the best quadratic approximation of a function was applied to derive the optimality criterion through the well-known equation for closing a vector contour for four-bar linkage. The obtained mathematical model of kinematical synthesis can be used also to determine the singular positions of the mechanism that can cause a spontaneous change in the law of motion of the output link. Modeling of the proposed kinematical synthesis method using Mathcad confirmed the correctness of the mathematical model and allowed plotting the graphical diagram of connecting rod curves.