Abstract
KEYWORDS:
dynamic, nonholonomic automotive transmissions, variable speed drive.
ABSTRACT:
Many of the nonholonomic mechanical transmissions can be recognized as variable speed drives contained in many complex machine systems of modern technique. These mechanical systems are non-holonomic, because the connections are differential. Non-holonomic systems have connections which are functions of speed and acceleration. The non-holonomic constrain exists in the equation for changeable transmission ratio iv of variable speed drive in the working process. In variable speed drives, nonholonomic constraints are described by differential equations from which it is not possible directly to deduce geometric characteristics by their integration. We have to find first the differential equations of motion and after that by integration relation between input and output of the system got. This is the basis of non-holonomic mechanics and gives the difference from holonomic mechanics where are all connections having geometric characteristic and there are no limits for speed and acceleration in the system. Having in mind this large use of mechanical variable speed drives in technique, the aim of this paper is to describe and give an approach for evaluation the dynamically behavior as well as to estimate the stability one of the general practical example of nonholonomic automotive transmissions in the real conditions. For dynamical description of mechanical nonholonomic system Appell`s differential equations are used. By numerical solving of differential equations of motion, answer concerning the working stability as well as the dynamical and kinematical behavior of observed system is obtained.