A New Coupler Critical Dimensions (CCD) Method for Linkage Mechanisms Mobility Analysis

Abstract

A new Coupler Critical Dimensions (CCD) approach to define mobility criteria (crank, rocker conditions, or existence) for linkage mechanisms has been presented in this paper. The idea is to analyze the extreme lengths of a mechanism coupler link when the mechanism is on the extreme of its existence or changing its mobility condition. The method leads a set of expressions of the constant mechanism parameters that can be used to define the exact dimensional limits of the coupler link in the mechanism. These expressions present sufficient and necessary dimensional conditions for the mechanism existence and become a turning point to change its mobility from crank to a rocker and vice versa. At the boundaries of the coupler dimensions, the mechanism reaches its the change-point configuration where the mechanism may switch either from one work function to another or from existence to non-existence. The method has been successfully applied to the planar 4R, spatial RSSR, and planar multiloop linkage mechanisms. The obtained results prove the effectiveness and accuracy of the method in defining the limits of the mechanism rotatability conditions or existence in general.