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 concept is critical to design and analyze the extreme lengths of a mechanism coupler link when the mechanism is at the extreme of its existence or changing its mobility condition. The method leads a set of expressions of the constant mechanism parameters that can define the mechanism's coupler link's exact dimensional limits. These expressions present sufficient and necessary dimensional conditions for the mechanism's existence and become a turning point to change mobility from a crank to a rocker and vice versa. The mechanism reaches its changepoint configuration at the boundaries of the coupler dimensions. The mechanism may switch 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. The crank condition is essential to couple it with the motor or engine. If the mechanism input link is not a crank (i.e., it has a possibility of full rotation), the motor may crash the entire mechanism. Rotatabilty of the input link is a fundamental concept in machines and mechanisms.