MOTION EQUATIONS OF ROLLER-ANNULAR MECHANISMS WITH ONE VARIABLE COEFFICIENT

Abstract

The paper is devoted to the methodology for deduction of motion equations of roller-annular mechanisms representing a non-holonomic system with two degrees of freedom on the basis of general dynamics theorems about changes of momentum and kinetic moment. Establishing relations between dynamic values, characterizing system motion and acting forces as active ones so reaction relations  such approach admits clearly evident physical interpretation. As a result of such approach a mathematical model of the investigated object in the form of differential equations with several interrelated variable coefficients has been developed in the paper. Equations are transformed in the form which is convenient for solving problems of analysis and synthesis with one variable coefficient. Analysis of equation structure permits to make a conclusion that dynamics of transient processes of non-holonomic mechanisms is determined not only by acting forces, masses and their initial states but also by the law of changing first kinematic transfer functions and speed of their changes.