Plane Motions of Rigid Body Controlled by Means of Movable Mass
- PDF / 475,701 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 20 Downloads / 179 Views
ANICS
Plane Motions of Rigid Body Controlled by Means of Movable Mass Academician F. L. Chernousko* Received June 29, 2020; revised June 29, 2020; accepted July 1, 2020
Abstract—The plane motions of a rigid body controlled by means of an auxiliary movable point mass are considered. Dry friction forces act between the body and the horizontal plane. It is shown that, under certain conditions, the body can be transferred to an arbitrary state in the plane so that the system is completely controllable. Keywords: rigid-body dynamics, dry friction, control, mobile robots DOI: 10.1134/S1028335820090025
The problems of the dynamics of a rigid body that carries movable masses are relevant in connection with the creation of mobile robots, which have no external movable elements [1–3]. These robots, called capsule robots, can be sealed and able to move in aggressive and vulnerable environments, in pipes, inside living organisms, and to perform the operations of inspection, monitoring, diagnostics, etc. A number of studies have been devoted to the one-dimensional translational motion of these systems in the presence of external resistance forces, and the optimal driving modes are constructed [4, 5]. The two-dimensional plane motions, which are important for constructing rotations of mobile robots, were studied in [6, 7] in the presence of dry friction forces between the body and the horizontal plane. In these studies, it is assumed that the internal moving masses have two degrees of freedom with respect to the carrying body and consist of a rotor and a material point.
MECHANICAL SYSTEM The system consists of a rigid body P of mass M and a material point Q of mass m (Fig. 1). Let us denote by C the center of mass of the body P and assume that one of the principal central axes of inertia of the body is vertical. The body slides along the fixed horizontal plane OXY in the gravity field leaning on three points Ai. In the case of three supporting points, the rigid body is a statically definable system; therefore, the normal reactions Ni at the points Ai are unambiguously determined. The dry friction forces Fi acting on the body P at the points Ai obey the Coulomb law with the friction coefficient f. If vi is the velocity of the supporting point Ai, the friction forces are determined by the relations
f N i vi , vi Fi ≤ fN i , if Fi = −
if
vi = vi > 0,
vi = 0,
(1)
i = 1,2,3.
The material point Q is equipped with an actuator and moves relative to the body P along a horizontal
In this study, as in [8], we consider the case of one movable point, which controls the plane motion of a body in the presence of dry friction forces between it and the plane. It is shown that the system is completely controllable under fairly general assumptions. It can be transferred to an arbitrary state on the plane even if the point has only one degree of freedom and moves relative to the body along a certain curve.
A2
Q
C
[
A3
A1
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 117526 Russian * e-mail: chern@ipmnet.
Data Loading...
