Dynamic analysis of elementary differential gear with rigid links

Abstract

At present the machine dynamics investigations are conducted in the next directions: dynamic processes research in special machines; research of the machines which links are solids; research of mechanisms representing a combinations of a solids and elastic systems. In this paper the elementary differential gear with rigid links dynamics is investigated. A number of dynamic problems can be solved accurately enough without taking into account the loaded element elasticity. Research of dynamic processes of one degree of freedom mechanisms are quite fully published in scientific literature, which cannot be said about mechanisms that have two degrees of freedom. In this paper are compiled and solved the movement equations for differential mechanism with two degrees of freedom. Mechanism has two degrees of mobility, therefore, the position of all its links is determined by two generalized coordinates. The mechanism movement is described by two Lagrange equations of II kind. Rotation angles of the drive and driven shafts are taken as generalized coordinates. System of differential equations of the second order relativ generalized coordinates is compiled. All coefficients of this system can be calculated in advance. Joint solution of equations of the system makes it possible to determine the angular accelerations of the two main links. Equations for determining angular velocities and angular accelerations of drive and driven shafts are recieved.