Vector Method for Determination of Kinematic Parameters of Ideal Inertial Module in Stop Mode

Abstract

The presence of a generalized scheme of the pulse mechanism created by A. I. Leonov does not have a universal mathematical description of parameters by continuous analytical functions, therefore each design is described, for the most part, by complex systems of differential equations, but the lack of clarity in presenting the results makes it difficult to intuitively understand dynamic processes. The objective of the research is the clarity in the study of the kinematic parameters of imbalance of the ideal inertia module during stop mode operation for predicting the dynamic indexes as continuous in time functions. The research method is based on a vector simulation of spherical motion parameters. To do this, a fixed Cartesian coordinate system is introduced so that the plane of the base circle of the initial cone of the jet conical wheel is aligned with the horizontal plane, and the axis of the satellite drive (geometric axis of the carrier) is aligned with the applicate axis. The central axis of the mechanism crossing the diameter of the jet wheel is aligned with the abscissa axis on the complementary branch of which at the initial moment there is the mass center of imbalance. In the stop mode the absolute motion of a point is determined by the result of its rotation around the satellite axis at the speed lying in the plane of the base of the initial cone of the satellite and around the drive axis at a speed which parallel to the plane of the initial cone of the jet wheel. Projections of the absolute velocity and the absolute acceleration of imbalance point on the coordinate axis, in turn, determine the projections of the components of the velocity vector and acceleration vector on the planes of the fixed Cartesian coordinate system, respectively. Determining the arms of these components in the planes of projections relative about the center of the axis makes it possible to further predict the dynamic parameters at certain points of the trajectory (at particular time or another). Analytical calculations of modular values of linear and angular velocities and accelerations, as well as drawing of the appropriate diagrams were performed using the operators of MathCAD software.