GEOMETRICAL MODELING OF THE UNFOLDING OF SPATIAL ROD STRUCTURES, SIMILAR TO THE FOUR-LINK PENDULUM, IN WEIGHTLESSNESS

Abstract

We have continued studying geometrical models of unfolding, under conditions of weightlessness, the orbital rod structures whose elements are connected similar to a four-link pendulum [21‒24]. The links of the structure move due to the action of pulses from pyrotechnic jet engines at the endpoints of the links. The description of the motion of the derived inertial unfolding of a rod structure is based on the Lagrange equation of the second kind, and, given the conditions of weightlessness, constructed using solely the kinetic energy of the system. The relevance of the subject is defined by the need to improve and study the new technological schemes for unfolding the frames of space infrastructures. These include the frames of parabolic antennas, whose elements are a family of similar confocal parabolas obtained when one of them rotates, at a certain angular step, around a common axis. In addition, it is of interest to consider the new technologies for performing mounting operations in orbit using the structures of mechanical grippers (the type of a "robot's arm"), located outside spacecraft. Based on the inertial unfolding of four-link rod structures, we developed schemes of action of manipulators to grip cylindrical bodies whose axes are in parallel or perpendicular relative to the surface of a spacecraft. We have defined parameters and initial conditions for starting the motion of a four-link rod structure in order to obtain the required arrangement of links. It is shown that the implementation of variants of the inertial unfolding requires that the endpoints of links should be exposed to the action of a set of pyrotechnic devices whose pulses' magnitudes are determined by the coordinates of vector U¢={0.1, 1.9, 1.3, 2.5} in conventional units and the time it stops should be determined. We have constructed plots of change over time in the functions of the angles' values as the generalized coordinates, as well as the first and second derivatives from these functions. The result is the evaluation of strength characteristics of the system at the time of braking (stopping) the process of unfolding. The results are intended for the geometrical modeling of variants of unfolding four-link rod structures under conditions of weightlessness. For example, frames for orbital infrastructures, as well as mechanical manipulators to grip space objects