N. N. Bolotnik

Russian Academy of Sciences, Moskva, Moscow, Russia

Are you N. N. Bolotnik?

Claim your profile

Publications (41)14.1 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: The motion of a chain of three identical bodies along a straight line in a dry-friction medium is studied. The motion is excited and controlled by changing the distances between the bodies of the chain. An undulatory excitation mode is proposed, in which the distances between the adjacent bodies of the chain change periodically and the time histories of the distances in the pairs of adjacent bodies consecutively repeat each other with a constant time shift. It looks like a wave is running along the chain. The necessary and sufficient conditions for the system to be able to move from rest are established. For a specific excitation mode, in which the time histories of the distances between the bodies of the chain are defined as piecewise quadratic functions, a steady-state motion of the system is studied for the case where the friction force is small in comparison with the force necessary for a body of the chain to be moved from a state of rest through a distance characterizing the amplitude of oscillations of adjacent bodies during the excitation period.
    ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik 12/2013; 93(12). · 0.95 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A mechanical system consisting of a movable base and an object (rigid body) connected to the base by means of a two-degree-of-freedom gimbal with mutually perpendicular axes is considered. The possibility to eliminate the projection of the apparent acceleration of a given object point on the plane perpendicular to an object-fixed axis by controlling the rotation of the gimbal frames is investigated. The apparent acceleration of a given object point is the difference between the absolute acceleration vector and the gravitational acceleration vector at this point. Sufficient conditions under which this goal is attainable in principle are formulated. Equations governing the rotation of the gimbal frames are derived. This problem is related to the development of control systems for gravity-sensitive technologies in spacecraft.
    Journal of Computer and Systems Sciences International 05/2012; 51(3). · 0.25 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: tu-ilmenau.de Abstract. The paper deals with non-traditional vibration- driven locomotion systems. In the first part, the motion of a chain of interconnected bodies (mass points) along a straight line on a rough surface is considered. The system is subjected to kinematic constraints modeling the excitation mode. It is assumed that there is dry (Coulomb's) friction acting between the plane and each body. The magnitude of the friction force depends on the direction of the motion. The expression for the average velocity of the steady-state motion of the system as a whole is found. In the second part, the motion of two bodies (mass points) connected by a linear spring is studied for the case, where the coefficient of friction is independent of the direction of the motion. The system is driven by two unbalanced rotors attached to the bodies. It is shown, that the direction of motion can be reversed without changing the direction of rotation of the rotors.
    01/2011;
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The motion of a finite chain of identical bodies along a straight line in a resistive medium is studied. The major aim of this study is to investigate the fundamental properties of such systems, in particular, their ability to move from a state of rest and sustain the motion at constant average velocity in media with different resistance properties and the influence of the control strategy on the motion. The motion is excited and controlled by changing the distances between the bodies of the chain. For a given friction law, the necessary and sufficient conditions for the system to be able to move from rest are established.
    ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik 12/2010; 91(4):259 - 275. · 0.95 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Design of mobile robots that can move without wheels or legs is an important engineering and technological problem. Self-propelling mechanisms that consist of a body that has contact with a rough surface and internal masses are considered. Asymmetry in friction that is necessary for the robot to move can be provided in several ways. First, the robot can be equipped with specific contact devises that provide anisotropy for the coefficient of friction, i.e., the coefficient of friction depends on the direction of motion. For example, the contact surface of the robot can be covered with needles. Second, this asymmetry can be provided for isotropic friction by changing the normal pressure of the robot on supporting surface. A number of mathematical models of such systems are presented in the paper. KeywordsDesign-In-pipe robots-Modelling-Vibration-driven robots
    03/2010: pages 465-477;
  • D. V. Balandin, N. N. Bolotnik
    [Show abstract] [Hide abstract]
    ABSTRACT: A limiting performance of shock isolation is studied for an object modeled by two rigid bodies connected by a viscoelastic element with a linear characteristic. The object is attached to a movable base by means of a shock isolator, which is regarded as a device that produces a control force between the base and the object. The base and the object move along the same straight line. The base is subject to an external shock excitation that is characterized by the time history of the acceleration of the base. A control law is defined for the shock isolator to minimize the maximum magnitude of the displacement of the object relative to the base, provided that the force of interaction between the components of the object does not exceed a prescribed value. An algorithm for constructing the exact solution of the problem under certain assumptions is presented. A technique for constructing an approximate solution for an object having high stiffness is described. The optimal control is shown to have impulse components. Examples are given. The two-component model considered in the paper is known to have been utilized to describe the mechanical response of a human body to a shock load along the spine or from thorax to back. Therefore, the problem under consideration can be regarded as a benchmark optimal control problem for a system that protects from injuries cased by shock loads. Solution of such problems is highly topical for development of safety systems for vehicles.
    Journal of Computer and Systems Sciences International 01/2009; 48(2):206-219. · 0.25 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The motion of the system is excited by two identical unbalanced rotors based on the respective bodies. Major attention is given to the steady-state motion. A nearly-resonant excitation mode, when the angular velocities of the rotor are close to the natural frequency of the system, is considered. A set of algebraic equations for determining an approximate value of the average steady-state velocity of the entire system is obtained for the case of small friction. It is shown that control of the steady-state motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity, and varying the detuning enables one to change the direction of the motion.
    Multibody System Dynamics 01/2009; 22(2):199-219. · 2.02 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The motion of a body controlled by movable internal masses in a resistive environment along a horizontal straight line is considered. Optimal periodic modes of motion are constructed for the internal masses to maximize the average speed of the velocity-periodic motion of the body. The maximum displacement allowed for the internal masses inside the body, as well as the relative velocities or accelerations of these masses are subjected to constraints. Three types of the resistance laws — piece-wise linear friction, quadratic friction, and Coulomb's dry friction — are considered.
    12/2008: pages 31-40;
  • [Show abstract] [Hide abstract]
    ABSTRACT: To improve the protection of a wheelchair-seated person with disabilities traveling in a vehicle from injuries in a crash, it is proposed to attach the wheelchair to a movable platform separated from the vehicle body by means of a shock isolator. The control of the platform is designed to reduce the occupant's injury risk, as compared with the case of the attachment of the wheelchair directly to the vehicle. The isolator design is based on the minimization of the force transmitted to the wheelchair occupant, provided that the space allowed for the platform to move relative to the vehicle is constrained. The possibility of pre-acting control, when the isolator is engaged for a time prior to the crash, is discussed. Passive tiedown and restraint systems are studied, although it is recognized that active systems could provide even lower injury risks. A multibody model of the platform-based occupied wheelchair is utilized for full-scale simulation of the response of the system to a crash pulse. The simulation shows a noticeable reduction in the injury risk due to the platform and an even greater reduction of injury with pre-acting control.
    Medical Engineering & Physics 04/2008; 30(2):258-67. · 1.78 Impact Factor
  • D. V. Balandin, A. S. Belozerov, N. N. Bolotnik
    [Show abstract] [Hide abstract]
    ABSTRACT: The limiting possibilities of the protection of the human head from impacts by means of helmets are analyzed. The shell (base) of the helmet is assumed to decelerate after an impact against an obstacle with constant acceleration during a given time interval. The minimum of the peak magnitude of the displacement of the head (the object to be protected) relative to the helmet shell is determined, provided that the injury risk index does not exceed a prescribed tolerable value, as well as the corresponding time history of the absolute acceleration of the head. The injury risk index is defined by the HIC functional. This functional is adopted as a standard measure for the head injury risk in crash tests of vehicles, as well as in the tests of shock protection equipment for industries and sports. The time history of the motion of the head and the peak magnitude of the displacement of the head relative to the helmet shell are studied as functions of the shock pulse duration (the deceleration time of the helmet shell). The case of the instantaneous shock, when the shell comes to an instantaneous stop after hitting the obstacle, was considered in [1].
    Journal of Computer and Systems Sciences International 01/2008; 47(1):93-102. · 0.25 Impact Factor
  • N. N. Bolotnik, T. Yu. Figurina
    [Show abstract] [Hide abstract]
    ABSTRACT: The problem of the optimal control of a rigid body moving along a rough horizontal plane due to motion of two internal masses is solved. One of the masses moves horizontally parallel to the line of motion of the main body, while the other mass moves in the vertical direction. Such a mechanical system models a vibration-driven robot–a mobile device able to move in a resistive medium without special propellers (e.g., wheels, legs or caterpillars). Periodic motions are constructed for the internal masses to ensure velocity-periodic motion of the main body with maximum average velocity, provided that the period is fixed and the magnitudes of the accelerations of the internal masses relative to the main body do not exceed prescribed limits. Based on the optimal solution obtained for a fixed period without any constraints imposed on the amplitudes of vibration of the internal masses, a suboptimal solution that takes such constraints into account is constructed.
    Pmm Journal of Applied Mathematics and Mechanics - PMM J APPL MATH MECH-ENGL TR. 01/2008; 72(2):126-135.
  • Nikolai N. Bolotnik, Tatiana Yu. Figurina
    [Show abstract] [Hide abstract]
    ABSTRACT: An optimal control problem is solved for a rigid body that moves along a straight line on a rough horizontal plane due to the motion of two internal masses. One of the masses moves horizontally parallel to the line of motion of the system's main body and the other mass moves vertically. Such a mechanical system models a vibration-driven robot able to move in a resistive medium without special propelling devices (wheels, legs or caterpillars). A periodic motion of the internal masses is constructed to ensure a velocity-periodic motion of the main body with a maximum average velocity, provided that the period is flxed and the accelerations of the internal masses relative to the main body lie within prescribed limits. This statement does not constrain the amplitude of vibrations of the internal masses. Based on the solution of the problem, a suboptimal control that takes this constraint into account is constructed.
    01/2007;
  • Journal of Dynamic Systems Measurement and Control-transactions of The Asme - J DYN SYST MEAS CONTR. 01/2007; 129(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The rectilinear motion on a horizontal rough plane of a vibration-driven system consisting of a carrying body, which interacts with the plane directly, and of internal masses that perform harmonic oscillations relative to the carrying body is considered. The vertical and horizontal oscillations of the internal masses have the same frequency, but are shifted in phase. It is shown that by controlling the phase shift of the horizontal and vertical oscillations and their frequencies, it is possible to change the direction and magnitude of the average velocity of the steady motion of the carrying body. A similar system may provide a model of a vibration-driven robot that does not require special limbs (wheels, legs, or chain tracks)
    Journal of Computer and Systems Sciences International 09/2006; 45(5):831-840. · 0.25 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The controlled motion of a rigid inhomogeneous cylinder over a rough horizontal plane is considered. The control is provided by controlled motion of internal masses. Mathematical models are constructed that correspond to rolling without loss of contact or slippage. The conditions for the physical implementability of such a motion are derived. The case where the internal moving masses from a rigid flywheel the centre of inertia of which lies on the axis of the cylinder is investigated in detail. A near-time-optimal feedback control that enables the total energy to be changed in a required way is constructed on the basis of an asymptotic approach. The main operating modes are simulated, namely, swinging up of the cylinder to a large angular amplitude, rotation with a prescribed energy, deceleration of rolling to a complete stop, and oscillations and rotations in the neighbourhood of the separatrix.
    Journal of Applied Mathematics and Mechanics 01/2006; · 0.26 Impact Factor
  • Journal of The Brazilian Society of Mechanical Sciences and Engineering - J BRAZ SOC MECH SCI ENG. 01/2006; 28(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The optimal control of the deceleration of a particle moving along a straight line after an impact against a surface covered with an impact isolation coating is considered. The force applied to the particle by the surface is treated as the control variable, that is, the control force replaces the coating. The deceleration distance is minimized under the constrained value of the HIC functional - an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impact-induced head injury of a human being. The solution indicates the limiting capabilities of the prevention from the head injuries in the case of traffic accidents, falling, or other occurrences by means of an appropriate coating of the surface against which impacts can occur.
    Physics and Control, 2005. Proceedings. 2005 International Conference; 09/2005
  • Journal of Dynamic Systems Measurement and Control-transactions of The Asme - J DYN SYST MEAS CONTR. 01/2005; 127(3).
  • D.V. Balandin, N.N. Bolotnik, W.D. Pilkey
    [Show abstract] [Hide abstract]
    ABSTRACT: A review of recent research on the limiting performance analysis of impact isolation systems for injury prevention is presented. A limiting performance analysis establishes the absolute optimum for a performance index measuring the quality of an isolation system by solving an optimal control problem. Problems related to the optimal design of a crashworthy helicopter seat, automobile seatbelts, and sporting helmets are discussed.
    Physics and Control, 2003. Proceedings. 2003 International Conference; 09/2003
  • [Show abstract] [Hide abstract]
    ABSTRACT: The motion of an eight-legged tube-crawling robot through a curved (toroidal) tube is investigated in terms of kinematics. A class of regular gaits implementing such a motion is defined. In these gaits, the center of mass of the robot body moves by the same distance during each step, and, at the beginning and the end of each step, the center of mass of the robot body lies on the axis of the tube and, moreover, the axis of the robot is tangential to that of the tube. Each step consists of two half-steps. During each half-step the robot body performs a plane-parallel motion in the plane where the feet of the supporting legs lie. The parameters of the gait are calculated, and some qualitative features of the motion of the robot are analyzed. Computer simulation results are presented. The analysis of the motion of the robot in a toroidal tube is important for planning and control of the passage of the robot through turns of a pipeline.*Communicated by W. Book.
    Mechanics Based Design of Structures and Machines - MECH BASED DES STRUCT MECH. 01/2002; 30(4):431-462.