Paradoxical Mechanics for Creation of Adaptive Gear Mechanism – Devoted to International Day of Science

Abstract

Paradox of the mechanism theory has been detected in connection with attempts of practical use mechanism with two degree of freedom and one entry for achievement of power adaptation. According to the mechanism theory and machines such mechanism is statically indefinable. However recently there were patents and publications with the description of efficient two mobile adaptive mechanisms with one entry. Paradox of the mechanism theory consists in the following: the kinematic chain with two degree of freedom and one entry containing the closed contour is statically and kinematically definable. In Ivanov's works the proof of definability of two mobile kinematic chain motion is resulted on the basis of additional analytical constraint by a virtual works principle. A certain geometrical image comparable to design there should match to analytical additional constraint. The present work is devoted to disclosing of a geometric constraint of parameters of kinematic chain with two degree of freedom and to statement of the mechanism theory paradox in geometrical and an analytic form. Work is executed on the basis of regularities of mechanics and mechanism theory.