Synthesis of Plane Six-Link Mechanisms Using the Monte Carlo Method

Abstract

A new method for separating independent peaks of an objective function defined in an n+1 dimensional Euclidean space composed of n decision variables and a performance index of a mechanism is developed by applying the Monte Carlo integration and its reliability is examined by numerical experiments. A method using the principle of relative peaking together with the method of reduction of the region on the basis of radii of gyration of a solid figure with respect to hyperplanes parallel to the axis of the performance index is also presented for finding the global maximum point of the objective function in each separated region. Moreover, the constants for generating the quasi-random numbers used in the Haselgrove method are extended upto the ones for the multiple integration of the 16th degree. As an example, an indicating balance with accuracy over 1/4000 is synthesized by using a Watt six-link mechanism having two prismatic pairs.