Rough Horizontal Plane Research Articles

Collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough horizontal surface.

Using the three-dimensional discrete element method, we numerically investigate the collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough-horizontal plane by systematically varying a broad range of values of the initial column aspect ratio, cohesive stress, and liquid viscosity. The results show that the kinetic energy, half runout time, and runout distance increase with increasing the initial column aspect ratio but decrease with increasing the cohesive and viscous effects of the binding liquid, while the toe angle and deposit height decrease with increasing the aspect ratio and increase with increasing cohesive stress and liquid viscosity. Remarkably, by defining a dimensionless scaling number that incorporates the Bond number and initial column aspect ratio, this allows us to nicely describe the kinetic energy, half runout time, deposition height, runout distance, and toe angle. These unified descriptions may provide insights into the physical properties of the collapse dynamics and deposition morphology of low-viscocohesive granular columns, leading to good explanations of the complex properties of natural disaster events.

Modified Three-Element Modeling and Robust Tracking Control for a Planar Pneumatic Soft Actuator

In pneumatic soft robotics systems, pneumatic soft actuators (PSAs) are the most important components, so it is necessary to study the precise modeling and control over PSAs for application. This paper focuses on a self-designed planar PSA, named pneumatic bellow actuator (PBA), and proposes a modified three-element model (MTEM) and a nonlinear disturbance observer-based sliding mode control (NDO-based SMC) method to achieve the robust tracking control objective of the PBA with multiple uncertainties. Firstly, the dynamic characteristics of the PBA are analyzed based on experimental data obtained from open-loop experiments of the PBA. Then, based on these dynamic characteristics, a semi-phenomenological MTEM is established considering coupling between the dynamics of the PBA and load as well as friction, which can describe the dynamics of the PBA with changing loads in the rough horizontal plane precisely. Model parameters are then identified by Levenberg-Marquardt (LM) algorithm. Next, identification errors, device disturbances and external disturbances are regarded as the multiple uncertainties of the PBA, and the NDO-based SMC method is proposed based on the MTEM to realize the robust tracking control objective of the PBA. The stability of the control system is proved. The effectiveness of the proposed method is verified by experiments.

Analytical research of the Hopf bifurcation in the problem of motion of the rattleback

We consider the classical problem of the nonholonomic system dynamics — the problem of motion of a heavy rigid body on an perfectly rough horizontal plane. The effect of loss of stability of permanent rotation of a body at a certain critical value of its angular velocity is discussed. It is proved that this effect is accompanied by the occurrence of periodic motions of the body with a frequency close to the critical value, that is, the Hopf bifurcation takes place. It is proved by direct calculation of the first Lyapunov coefficient that the corresponding periodic motions are unstable.

On periodic motions of a body with an internal moving mass on a rough horizontal plane in the case of anisotropic friction

We consider a mechanical system consisting of a body moving on a horizontal plane and a mobile internal mass, which moves in a circle with a constant velocity. Dry anis ot ropic friction force acts between the body and the plane. The body moves without jumping. Five periodic modes of motion are established and conditions of their existence are found. A qualitative analysis of each periodic modes has been performed. In the plane of parameters the domains corresponding to the above periodic modes are determined.

Vibroimpact Mobile Robot

A simple model of a capsule robot is studied. The device moves upon a rough horizontal plane and consists of a capsule with an embedded motor and an internal moving mass. The motor generates a harmonic force acting on the bodies. Capsule propulsion is achieved by collisions of the inner body with the right wall of the shell. There is Coulomb friction between the capsule and the support, it prevents a possibility of reversal motion. A periodic motion is constructed such that the robot gains the maximal average velocity.

Topological Types of Isoenergy Surfaces in the System of the Chaplygin Ball with a Rotor

The problem of rolling the balanced dynamically nonsymmetric ball with a rotor on a rough horizontal plane is considered. Topological types of isoenergy surfaces of this integrable Hamiltonian system are found. Curves are constructed on the plane of the parameters $$\mathbb{R}^{2}(h,c)$$ separating it into regions so that all points of the same region correspond to isoenergy surfaces with identical Fomenko–Zieschang invariants.

Investigation of the Motion of a Heavy Body of Revolution on a Perfectly Rough Plane by the Kovacic Algorithm

Investigation of various problems of mechanics and mathematical physics is reduced to the solution of second-order linear differential equations with variable coefficients. In 1986, the American mathematician J. Kovacic proposed an algorithm for solution of a second-order linear differential equation in the case where the solution can be expressed in terms of so-called Liouville functions. If a linear second-order differential equation has no Liouville solutions, the Kovacic algorithm also allows one to ascertain this fact. In this paper, we discuss the application of the Kovacic algorithm to the problem of the motion of a heavy body of revolution on a perfectly rough horizontal plane. The existence of Liouville solutions of the problem is examined for the cases where the rolling body is an infinitely thin disk, a disk of finite thickness, a dynamically symmetric torus, a paraboloid of revolution, and a spindle-shaped body.

Dynamics and motion control of a capsule robot with an opposing spring

Non-classical locomotion systems have the perspective for a wide application in the vast fields of bio-medical and maintenance technology. Capsule bots are small, simple, and reliable realizations with a great potential for practical application. In this paper, the motion of a capsule-type mobile robot along a straight line on a rough horizontal plane is studied applying analytical and experimental methods. The robot consists of a housing and an internal body attached to the housing by a spring. The motion of the system is generated by a force that acts between the housing and the internal body and changes periodically in a pulse-width mode. The average velocity of the motion of the robot is studied as a function of the excitation parameters. The results from the model-based and experimental investigations agree with each other. It can be concluded that the presented robot design can be a basis for the creation of mobile robotic systems with locomotion properties that can be controlled by the parameters of a periodic actuation force.

On the Motion of a Symmetrical Vehicle with Omniwheels with Massive Rollers

The dynamics of a symmetrical vehicle with omniwheels, moving along a fixed, absolutely rough horizontal plane, is considered, making the following assumptions: the mass of each roller is nonzero, there is a point contact between the rollers and the plane, and there is no slip. The equations of motion composed with the use of the Maxima symbolic computation system, contain additional terms, proportional to the axial moment of inertia of the roller and depending on angles of rotation of the wheels. The mass of the rollers is taken into account in those phases of motion when there is no change of rollers at the contact. The mass of rollers is considered to be negligible when wheels change from one roller to another. It is shown that a set of motions, existing in the inertialess model (i.e., the model that does not take into account mass of rollers), disappears, as well as its linear first integral. The main types of motion for a symmetrical three-wheeled vehicle, obtained by a numerical integration of equations of motion, are compared with results obtained on the basis of the inertialess model.

Dry friction distributed over a contact patch between a rigid body and a visco-elastic plane

We consider the dynamics of an absolutely rigid body moving along a rough horizontal plane. We assume that the plane deforms during the motion so that the contact patch is non-planar and has non-zero, but comparatively small area. In the contact patch, the vertical reactions are proportional to the vertical deformations and their rates, that is, we consider Kelvin–Voigt model. The tangent forces are assumed to be classic Coulomb dry friction in sliding regime (no stiction in contact patch). Due to the viscous part of Kelvin–Voigt law, the contact patch, the plane’s normal reaction, friction force and torque depend on the position, orientation, velocity of the center of mass and the angular velocity of the body. The model does not involve any additional dynamic parameter and gives the friction force and torque directly for any given state of the body. To show the advances of the model, we recall the analytical solution of Cauchy’s initial problem with general initial conditions of ODE governing the dynamics of the homogeneous sphere on a horizontal plane (results of Zobova and Treschev in Proc. Steklov Inst. Math. 281:91–118, 2013). Here we generalize the model for arbitrary convex bodies and study its main properties. The model is compared to the continuous velocity-base friction model for pure sliding (Brown and McPhee in ASME J. Comput. Nonlinear Dyn. 11(5):054502, 2016) and to the combined dry friction (Awrejcewicz and Kudra in Multibody Syst. Dyn., 2018, https://doi.org/10.1007/s11044-018-9624-9 ) in case of sliding with spinning. We illustrate the model considering the results of numerical integration of the Cauchy problem for a controlled differential-drive vehicle on a horizontal plane.

On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane

On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane

Comparison of the system “Chaplygin ball with a rotor” and the Zhukovskii system from the rough Liouville equivalence point of view

A problem of symplectic geometry is considered, namely, topological analysis of a rolling dynamically balanced non-symmetric ball with a rotor on a rough horizontal plane is considered. The Liouville equivalence between this system and the Zhukovskii system is studied.

Motion of a body sliding on a rough horizontal plane and supported at three points

The problem on the motion of a heavy solid body supported by a rough horizontal plane at three points (“tripod” [1]) is considered. The contacts at the support points are assumed unilateral and subject to the laws of dry friction. The dynamics of the possible motions of such a body under the action of forces of gravity and dry friction is studied.

Nonexistence of liouvillian solutions in the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough plane

Using the Kovacic algorithm, the nonexistence of liouvillian solutions in the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough horizontal plane for almost all values of parameters of the problem is proven.

On final motions of a Chaplygin ball on a rough plane

A heavy balanced nonhomogeneous ball moving on a rough horizontal plane is considered. The classical model of a “marble” body means a single point of contact, where sliding is impossible. We suggest that the contact forces be described by Coulomb’s law and show that in the final motion there is no sliding. Another, relatively new, contact model is the “rubber” ball: there is no sliding and no spinning. We treat this situation by applying a local Coulomb law within a small contact area. It is proved that the final motion of a ball with such friction is the motion of the “rubber” ball.

Capsule-type vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion

A model of a mobile capsule robot that consists of the housing and internal body is considered. The internal body can move relative to the housing along a straight line. The internal body is attached to the housing by a spring. The system motion is excited by a force that acts between the housing and the internal body. The force changes in a pulse-width periodic mode. The robot's motion along a straight line on a rough horizontal plane is investigated. It is assumed that the dry Coulomb friction acts between the housing and the plane. The dependence of the average steady state robot velocity on excitation parameters is analyzed. It is established that it is possible to control the magnitude and direction of the robot motion by changing the period and the duty cycle of the pulse-width excitation signal. The effect of the variation in the direction of the robot motion due to changing the excitation period is observed. This effect is associated with the phenomenon of resonance.

Analytic study of a rolling sphere on a rough surface

In this paper it is realized an analytic study of the rolling’s sphere on a rough horizontal plane under the action of its own gravity. The necessities of integration of the system of dynamical equations of motion lead us to find a reference system where the motion equations should be transformed into simpler expressions and which, in the presence of some significant hypothesis to permit the application of some original methods of analytical integration. In technical applications, the bodies may have a free rolling motion or a motion constrained by geometrical relations in assemblies of parts and machine parts. This study involves a lot of investigations in the field of tribology and of applied dynamics accompanied by experiments. Multiple recordings of several trajectories of the sphere, as well as their treatment of images, also followed by statistical processing experimental data allowed highlighting a very good agreement between the theoretical findings and experimental results.

Chaplygin’s ball with a rotor: Non-degeneracy of singular points

A problem of a dynamically balanced asymmetric ball with a rotor rolling over a rough horizontal plane is considered. Earlier, A. Y. Moskvin constructed bifurcation diagrams of the momentum map and bifurcation complexes in order to study the dynamics of the system and to obtain singular solutions. A natural development of this research is a fine Liouville analysis of the system. The first step in this direction is presented in the paper, namely, we verify the non-degeneracy of singularities and describe the Liouville foliation in a neighborhood of singular points of the momentum map.

Swadloon: Direction Finding and Indoor Localization Using Acoustic Signal by Shaking Smartphones

We propose an accurate acoustic direction finding scheme, Swadloon , according to the arbitrary pattern of phone shaking in a rough horizontal plane. Swadloon leverages sensors of the smartphone without the requirement of any specialized devices. Our Swadloon design exploits a key observation: the relative displacement and velocity of the phone-shaking movement corresponds to the subtle phase and frequency shift of the Doppler effects experienced in the received acoustic signal by the phone. Swadloon tracks the displacement of smartphone relative to the acoustic direction with the resolution less than 1 millimeter. The direction is then obtained by combining the velocity from the displacement with the one from the inertial sensors. Major challenges in implementing Swadloon are to measure the displacement precisely and to estimate the shaking velocity accurately when the speed of phone-shaking is low and changes arbitrarily. We propose rigorous methods to address these challenges, and apply Swadloon to several case studies: Phone-to-Phone direction finding, indoor localization and tracking. Our extensive experiments show that the mean error of direction finding is around 2.1 degree within the range of 32 m. For indoor localization, the 90-percentile errors are under 0.92 m. For real-time tracking, the errors are within 0.4 m for walks of 51 m.

Nonlinear dynamics of the rattleback: a nonholonomic model

For a solid convex body moving on a rough horizontal plane—known in mechanics as a rattleback—numerical simulations are used to discuss and illustrate dynamical phenomena that are characteristic of the motion due to the nonholonomic nature of the mechanical system; the relevant feature is the nonconservation of the phase volume in the course of the dynamics evolution. In such a system, a local compression of the phase volume can produce behavior features similar to those exhibited by dissipative systems, such as the presence of stable equilibrium points relevant to stationary rotations; limit cycles (rotations with oscillations), and strange chaotic attractors. A chart of dynamical regimes is plotted in a plane of parameters whose axes are the total mechanical energy and the angle of relative rotation of the geometric and dynamic principal axes of the body. The transition to chaos through a sequence of Feigenbaum period doubling bifurcations is demonstrated. A number of strange attractors are considered, for which phase portraits, Lyapunov exponents, and Fourier spectra are presented.