Recent zbMATH articles in MSC 70Ehttps://zbmath.org/atom/cc/70E2024-03-13T18:33:02.981707ZWerkzeugTopological analysis of pseudo-Euclidean Euler top for special values of the parametershttps://zbmath.org/1528.370492024-03-13T18:33:02.981707Z"Altuev, Murat K."https://zbmath.org/authors/?q=ai:altuev.murat-k"Kibkalo, Vladislav A."https://zbmath.org/authors/?q=ai:kibkalo.vladislav-aleksandrovichSummary: An analogue of the Euler top is considered for a pseudo-Euclidean space is under consideration. In the cases when the geometric integral or area integral vanishes the bifurcation diagrams of the moment map are constructed and the homeomorphism class of each leaf of the Liouville foliation is determined. For each arc of the bifurcation diagram, for one of the two possible cases of the mutual arrangement of the moments of inertia, the types of singularities in the preimage of a small neighbourhood of this arc (analogues of Fomenko 3-atoms) are determined, and for nonsingular isoenergy and isointegral surfaces an invariant of rough Liouville equivalence (an analogue of a rough molecule) is constructed. The pseudo-Euclidean Euler system turns out to have noncompact noncritical bifurcations.A nonholonomic model and complete controllability of a three-link wheeled snake robothttps://zbmath.org/1528.370552024-03-13T18:33:02.981707Z"Artemova, Elizaveta M."https://zbmath.org/authors/?q=ai:artemova.elizaveta-markovna"Kilin, Alexander A."https://zbmath.org/authors/?q=ai:kilin.aleksandr-aleksandrovichSummary: This paper is concerned with the controlled motion of a three-link wheeled snake robot propelled by changing the angles between the central and lateral links. The limits on the applicability of the nonholonomic model for the problem of interest are revealed. It is shown that the system under consideration is completely controllable according to the Rashevsky-Chow theorem. Possible types of motion of the system under periodic snake-like controls are presented using Fourier expansions. The relation of the form of the trajectory in the space of controls to the type of motion involved is found. It is shown that, if the trajectory in the space of controls is centrally symmetric, the robot moves with nonzero constant average velocity in some direction.On the relative rotation of rigid parts and the visco-elastic torsion bushing elementhttps://zbmath.org/1528.700022024-03-13T18:33:02.981707Z"Lidström, Per"https://zbmath.org/authors/?q=ai:lidstrom.perSummary: In this paper the interaction between two rigid parts of a multibody, connected by an ideal spherical joint equipped with a visco-elastic torsion bushing element, is derived. The model allows for arbitrary relative rotations of the parts and involves a non-linear torsion stiffness of the bushing. An expression for the interaction between the parts is derived and a specialization to the isotropic bushing element is presented.Gyrostatic Suslov problemhttps://zbmath.org/1528.700042024-03-13T18:33:02.981707Z"Maciejewski, Andrzej J."https://zbmath.org/authors/?q=ai:maciejewski.andrzej-j"Przybylska, Maria"https://zbmath.org/authors/?q=ai:przybylska.mariaSummary: In this paper, we investigate the gyrostat under influence of an external potential force with the Suslov nonholonomic constraint: the projection of the total angular velocity onto a vector fixed in the body vanishes. We investigate cases of free gyrostat, the heavy gyrostat in the constant gravity field, and we discuss certain properties for general potential forces. In all these cases, the system has two first integrals: the energy and the geometric first integral. For its integrability, either two additional first integrals or one additional first integral and an invariant \(n\)-form are necessary. For the free gyrostat we identify three cases integrable in the Jacobi sense. In the case of heavy gyrostat three cases with one additional first integral are identified. Among them, one case is integrable and the non-integrability of the remaining cases is proved by means of the differential Galois methods. Moreover, for a distinguished case of the heavy gyrostat a co-dimension one invariant subspace is identified. It was shown that the system restricted to this subspace is super-integrable, and solvable in elliptic functions. For the gyrostat in general potential force field conditions of the existence of an invariant \(n\)-form defined by a special form of the Jacobi last multiplier are derived. The class of potentials satisfying them is identified, and then the system restricted to the corresponding invariant subspace of co-dimension one appears to be integrable in the Jacobi sense.Signatures of physical constraints in rotating rigid bodieshttps://zbmath.org/1528.700052024-03-13T18:33:02.981707Z"Gutierrez Guillen, G. J."https://zbmath.org/authors/?q=ai:gutierrez-guillen.g-j"Arroyo, E. Aldo"https://zbmath.org/authors/?q=ai:arroyo.e-aldo"Mardešić, P."https://zbmath.org/authors/?q=ai:mardesic.pavao"Sugny, D."https://zbmath.org/authors/?q=ai:sugny.dominiqueSummary: We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery phase and in the tennis racket effect.On the descent of a skier down a straight trackhttps://zbmath.org/1528.700062024-03-13T18:33:02.981707Z"Lokshin, B. Ya."https://zbmath.org/authors/?q=ai:lokshin.boris-yakovlevich"Samsonov, V. A."https://zbmath.org/authors/?q=ai:samsonov.vitaly-a(no abstract)Stability of stationary motions of mechanical systems with a particular Goryachev-Chaplygin integralhttps://zbmath.org/1528.700072024-03-13T18:33:02.981707Z"Novikov, M. A."https://zbmath.org/authors/?q=ai:novikov.m-a(no abstract)Dynamic modeling and analysis of hybrid driven multi-link press mechanism considering non-uniform wear clearance of revolute jointshttps://zbmath.org/1528.700082024-03-13T18:33:02.981707Z"Chen, Xiulong"https://zbmath.org/authors/?q=ai:chen.xiulong"Tang, Yuefei"https://zbmath.org/authors/?q=ai:tang.yuefei"Gao, Shun"https://zbmath.org/authors/?q=ai:gao.shunSummary: The multi-link press mechanism is developing in the direction of high speed and high precision. However, the non-uniform wear of joint clearance seriously affects the output motion accuracy of mechanism. In order to accurately predict the impact of wear clearance on precision press mechanism, this paper takes the hybrid drive seven-bar press mechanism as an example, a method of dynamic modeling and analysis for the press mechanism with non-uniform wear clearance is developed. First, the contact force and friction force at the clearance are solved based on the L-N model and modified Coulomb friction model respectively, and the dynamic model of press mechanism with clearances is developed by Lagrangian multiplier method. Then, the wear characteristics of joint clearance are predicted by Archard model. Finally, the influences of factors such as wear times, friction coefficient and driving velocities on wear characteristics of kinematic pair and the dynamic response of press mechanism are discussed respectively. This study offers a theoretical basis for dynamic behavior prediction of press mechanism with multiple non-uniform wear clearances, and lays a foundation for the design and manufacture of high-precision press.Dynamic characteristics of helical gears incorporating the effects of coupled sliding frictionhttps://zbmath.org/1528.700092024-03-13T18:33:02.981707Z"Jiang, Hanjun"https://zbmath.org/authors/?q=ai:jiang.hanjun"Liu, Fuhao"https://zbmath.org/authors/?q=ai:liu.fuhaoSummary: Sliding friction is an important source of excitation for gear vibration and noise. However, the axial friction caused by the axial mesh force of the helical gear may excite the gear vibration, which is often ignored by researchers. In this study, firstly, an analytical model of mesh stiffness for helical gears incorporating the friction force and mesh force is proposed. And then, a dynamic model of helical gears with coupled sliding friction is established. The dynamic model includes the transverse friction, the axial friction and the effect of friction on mesh stiffness. Finally, the effect of coupled sliding friction on the dynamic characteristics of helical gears incorporating the proposed analytical mesh stiffness model is investigated. The results show that friction leads to the increase or reduction of mesh stiffness before or after the mesh position where the direction of the friction force is reversed. The oscillations of the dynamic responses become more significant incorporating the effects of coupled sliding friction, especially with the increase of friction coefficient. The developed dynamic model of helical gears incorporating the effects of coupled sliding friction may lead to a more realistic dynamic response.Calculation method of mesh stiffness for helical gear pair with manufacturing errors, assembly errors and tooth modificationshttps://zbmath.org/1528.700102024-03-13T18:33:02.981707Z"Liu, Chang"https://zbmath.org/authors/?q=ai:liu.chang.1|liu.chuang|liu.chang"Shi, Wankai"https://zbmath.org/authors/?q=ai:shi.wankai"Liu, Kun"https://zbmath.org/authors/?q=ai:liu.kunSummary: For the accurate calculation of the time-varying mesh stiffness (TVMS) of helical gear pairs, a novel method is proposed in this paper. This proposed method can predict the TVMS based on the gear accuracy grade or the measurement coordinates of the tooth surface. The abnormal meshing phenomena caused by manufacturing errors (MEs), assembly errors (AEs), and tooth modifications (TMs), such as the loss of contact of tooth pairs, out-of-line meshing, and eccentric loads, are considered in the calculation process. The proposed method was verified to be effective for both spur and helical gear pairs. The effects of MEs, AEs, and TMs on the TVMS of helical gear pairs were also investigated. The results showed that the pitch, helix, and misalignment deviations were the main influencing factors of the TVMS in MEs and AEs. Both profile modification and lead crowning reduced the mean of the TVMS. The proposed method is expected to provide accurate TVMS excitation data of gear transmission systems for dynamic analysis.A dynamic model as a tool for design and optimization of propulsion systems of transport meanshttps://zbmath.org/1528.700112024-03-13T18:33:02.981707Z"Peruń, Grzegorz"https://zbmath.org/authors/?q=ai:perun.grzegorzSummary: Designing power transmission systems is a complex and often time-consuming problem. In this task, various computational tools make it possible to speed up the process and verify a great many different solutions before the final one is developed. It is widely possible today to conduct computer simulations of the operation of various devices before the first physical prototype is built. The article presents an example of a dynamic model of power transmission systems, which has been developed to support work aimed at designing new and optimizing existing systems of that type, as well as to help diagnose them by designing diagnostic algorithms sensitive to early stages of damage development. The paper also presents sample results of tests conducted with the model, used at the gear design stage. In the presented model, the main goal is to reproduce the phenomena occurring in gears as well as possible, using numerous experiments in this direction featured in the literature. Many already historical models present different ways of modeling, but they often made significant simplifications, required by the limitations of the nature of computational capabilities. Differences also result from the purpose of the models being developed, and the analysis of these different ways of doing things makes it possible to choose the most appropriate approach.Changing the spatial orientation of a rigid body using one moving mass in the presence of external forceshttps://zbmath.org/1528.700122024-03-13T18:33:02.981707Z"Shmatkov, Anton M."https://zbmath.org/authors/?q=ai:shmatkov.anton-mSummary: The problem of changing the spatial orientation of a rigid body according to a given program using a movable mass interacting with it in the presence of external forces is considered. An equation is obtained that describes the motion of this mass. The properties that the statement of the problem must satisfy in order for it to have a solution are revealed. Equations for calculating the reorientation program are obtained. They are based on the properties of the vector, which is the difference between the vector of the derivative of the angular momentum of a rigid body, determined by a given reorientation program, and the vector of the moment of external forces acting on the solid during the implementation of this program. It is shown that this difference determines three main variants of the algorithm. For the most complicated case, an example of the spatial reorientation of a mechanical system is considered. The resulting relationships can be used to control spacecraft and robotic systems.Robot workspace approximation with modified bicentered Krawczyk methodhttps://zbmath.org/1528.700132024-03-13T18:33:02.981707Z"Maminov, Artem"https://zbmath.org/authors/?q=ai:maminov.artem"Posypkin, Mikhail"https://zbmath.org/authors/?q=ai:posypkin.mikhail-aSummary: The article considers the application of numerical method based on bicentered Krawczyk operator for solving the problem of the robot workspace approximation with box constraints. We applied several modifications for approximation of the solution sets of the indeterminate system of nonlinear equations and compare it with basic method. All methods were tested on a passive orthosis robot, which is part of the lower limb rehabilitation system. A mathematical model of the mechanism kinematics is presented. We evaluate the efficiency of the considered approaches, compute and visualize the robot workspace for different parameters sets.
For the entire collection see [Zbl 1516.90004].Estimation of robot states with Poisson process based on EKF approximate of Kushner filter: a completely coordinate free Lie group approachhttps://zbmath.org/1528.700142024-03-13T18:33:02.981707Z"Rana, Rohit"https://zbmath.org/authors/?q=ai:rana.rohit"Gaur, Prerna"https://zbmath.org/authors/?q=ai:gaur.prerna"Agarwal, Vijyant"https://zbmath.org/authors/?q=ai:agarwal.vijyant"Parthasarathy, Harish"https://zbmath.org/authors/?q=ai:parthasarathy.harishSummary: In this paper, a Lie coordinate-free torque based Euler-Lagrange equations of motion are developed for a 3-D link (3-DOF) robot. Intentional torque and jerky torque (non-intentional torque) are considered as the inputs to the dynamic profile of the robot. The jerky torque is modelled as a superposition of compound Poisson processes, which is a unique feature. The state vector of the robot, i.e., angular position and angular velocity vector, is thus a Markov process whose transition probability generator can be expressed in terms of the rate of the compound Poisson process that defines the jerky torque. Proof of frame invariance is provided to support the coordinate-free robot dynamics profile. Noise-free measurement is investigated as an ideal case. Angular position measurement is considered with white Gaussian noise. Further, an implementable finite-dimensional EKF approximate to Kushner-Kallianpur filter is obtained to estimate the robot state vector. Finally, the simulations are implemented on commercially available Omni bundle robot.On the combination of multiple harmonics in direct and parametric forcing of an oscillator: new results on parametric amplificationhttps://zbmath.org/1528.700232024-03-13T18:33:02.981707Z"Abboud, Eddy"https://zbmath.org/authors/?q=ai:abboud.eddy"Grolet, Aurélien"https://zbmath.org/authors/?q=ai:grolet.aurelien"Mahe, Hervé"https://zbmath.org/authors/?q=ai:mahe.herve"Thomas, Olivier"https://zbmath.org/authors/?q=ai:thomas.olivierSummary: In this article, we focus on the study of a forced single degree of freedom Hill-type differential equation, which can be found in particular in the modeling of gear interactions. We consider that the variable part of the stiffness is composed of several harmonics, and that the forcing term contains a constant part and a single harmonic component. The response of the equation is estimated using methods such as the multiple scale method and the harmonic balance method, and the results are compared to the ones obtained using numerical time integration. The phenomenon of parametric amplification, classically observed when the second harmonic of the parametric driving interacts with the first harmonic of the direct driving, is here observed and quantitatively investigated in the case of more complex direct and parametric interactions. The simplest case is the one with a constant direct forcing, seldom described in the literature. Then, more complex situations with both harmonic and constant forcing leads to parametric amplification with more complex behavior.On the dynamics of vibro-impact systems with ideal and non-ideal excitationhttps://zbmath.org/1528.700302024-03-13T18:33:02.981707Z"Zukovic, Miodrag"https://zbmath.org/authors/?q=ai:zukovic.miodrag"Hajradinovic, Dzanko"https://zbmath.org/authors/?q=ai:hajradinovic.dzanko"Kovacic, Ivana"https://zbmath.org/authors/?q=ai:kovacic.ivanaSummary: This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system is exposed to a non-ideal excitation. The impact occurs during the motion of the oscillator when it fits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibrating and vibro-impact systems with an ideal and non-ideal excitation are analysed. Analytical and numerical solutions are obtained for the vibrating system with the ideal excitation. Numerical analyses of the vibrating system with the non-ideal excitation is then conducted, where the characteristic curves for this system are found analytically. Numerical simulations are also carried out for other two systems and the results obtained are shown in terms of frequency-response diagrams, time-displacement diagrams and basins of attraction. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For the vibro-impact system with the non-ideal excitation, the average value of its frequency is used.Integration of variable stiffness actuators in a five-bar device to assist in active rehabilitation of the armhttps://zbmath.org/1528.740772024-03-13T18:33:02.981707Z"Contreras-Calderón, M. G."https://zbmath.org/authors/?q=ai:contreras-calderon.m-g"Castillo-Castañeda, E."https://zbmath.org/authors/?q=ai:castillo-castaneda.eduardo"Laribi, M. A."https://zbmath.org/authors/?q=ai:laribi.m-aSummary: Active arm rehabilitation involves restoring muscle tone by applying force to the arm to produce traction and compression on the muscles. Devices for rehabilitation assistance can be exoskeleton or end-effector type. This paper uses an end-effector type device, which provides an opposing force to the patient's arm's movement to tone their muscles during active rehabilitation. To provide that force, large and expensive motors with high torque are required. In order to avoid the use of motors, it is proposing a variable stiffness actuator integrated into a five-bar mechanism for active arm rehabilitation assistance in this work. The five-bar mechanism has a pantograph attached to amplify the workspace and emulates the arm rehabilitation trajectories, the patient holding onto the end-effector to trace the trajectories. The end-effector provides a constant opposing force to the patient's arm's movement, which activates the muscles. Thus, our proposal is the integration of an actuator with variable stiffness to replace the motors. The mechanism synthesis is presented to determine the parameters to vary the stiffness that provides a constant force in the five-bar mechanism end-effector.Geodesic structure of a rotating regular black holehttps://zbmath.org/1528.830682024-03-13T18:33:02.981707Z"Bautista-Olvera, Brandon"https://zbmath.org/authors/?q=ai:bautista-olvera.brandon"Degollado, Juan Carlos"https://zbmath.org/authors/?q=ai:degollado.juan-carlos"German, Gabriel"https://zbmath.org/authors/?q=ai:german.gabrielSummary: We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of orbital motion. We have found that there is a fourth constant of motion that determines the dynamics of orbits out the equatorial plane similar as in the Kerr black hole. Through detailed analyses of the corresponding effective potentials for massive particles the possible orbits are numerically simulated. A comparison with the trajectories in a Kerr spacetime shows that the differences appear when the black holes rotate slowly for large values of the characteristic length parameter.Gyroscopic precession in the vicinity of a static blackhole's event horizonhttps://zbmath.org/1528.830802024-03-13T18:33:02.981707Z"Majumder, Paulami"https://zbmath.org/authors/?q=ai:majumder.paulami"Nayak, K. Rajesh"https://zbmath.org/authors/?q=ai:nayak.k-rajeshSummary: In this article, we investigate gyroscopic precession in the vicinity of a spherically symmetric static event horizon. Our goal is to address whether the gyroscopic precession frequency diverges when approaching an event horizon. To do so, we employ the Frenet-Serret formalism of gyroscopic precession, which provides a complete covariant formalism, and extend it to include arbitrary timelike curves. We analyze the precession frequency near the Schwarzschild and Schwarzschild-anti-de-Sitter black holes, using horizon-penetrating Kerr-Schild coordinates to eliminate coordinate singularities near the horizon. Our study shows that a diverging gyroscopic precession frequency is not a universal feature for a trajectory crossing an event horizon. As a counter-example, we construct a timelike curve passing through the event horizon along which the gyroscopic precession frequency remains finite at the horizon.Impact of multiple modes on the evolution of self-interacting axion condensate around rotating black holeshttps://zbmath.org/1528.830812024-03-13T18:33:02.981707Z"Omiya, Hidetoshi"https://zbmath.org/authors/?q=ai:omiya.hidetoshi"Takahashi, Takuya"https://zbmath.org/authors/?q=ai:takahashi.takuya"Tanaka, Takahiro"https://zbmath.org/authors/?q=ai:tanaka.takahiro"Yoshino, Hirotaka"https://zbmath.org/authors/?q=ai:yoshino.hirotaka(no abstract)Energy formula, surface geometry and energy extraction for Kerr-Sen black holehttps://zbmath.org/1528.830822024-03-13T18:33:02.981707Z"Pradhan, Parthapratim"https://zbmath.org/authors/?q=ai:pradhan.parthapratimSummary: We evaluate the \textit{surface energy \((\mathcal{E}_s^\pm)\), rotational energy} \((\mathcal{E}_r^\pm)\) \textit{and electromagnetic energy} \((\mathcal{E}_{em}^\pm)\) for a \textit{Kerr-Sen black hole (BH)} having the event horizon \((\mathcal{H}^+)\) and the Cauchy horizon \((\mathcal{H}^-)\). Interestingly, we find that the \textit{sum of these three energies is equal to the mass parameter i.e.}\(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M}\) . Moreover in terms of the \textit{ scale parameter} \((\zeta_\pm)\), \textit{the distortion parameter} \((\xi_\pm)\) \textit{and a new parameter} \((\sigma_\pm)\) which corresponds to the area \((\mathcal{A}_\pm)\), the angular momentum \((J)\) and the charge parameter \((Q)\), we find that the \textit{mass parameter in a compact form} \(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M} =\frac{\zeta_\pm}{2} \sqrt{\frac{1+2 \sigma_\pm^2}{1-\xi_\pm^2}}\) which is valid through all the horizons \(( \mathcal{H}^\pm)\). We also compute the \textit{equatorial circumference and polar circumference} which is a gross measure of the BH surface deformation. It is shown that when the spinning rate of the BH increases, the \textit{equatorial circumference increases} while the \textit{polar circumference decreases}. We show that there exist two classes of geometry separated by \(\xi_\pm =\frac{1}{2}\) in Kerr-Sen BH. In the regime \(\frac{1}{2}<\xi_\pm \leq \frac{1}{\sqrt{2}}\), the Gaussian curvature is negative and there exist \textit{two polar caps} on the surface. While for \(\xi_\pm <\frac{1}{2}\), the Gaussian curvature is positive and the surface will be an oblate deformed sphere. Furthermore, we compute the exact expression of \textit{rotational energy that should be extracted from the BH via Penrose process}. The maximum value of rotational energy which is extractable should occur for \textit{extremal Kerr-Sen BH} i.e. \(\mathcal{ E}_r^+ =\left( \sqrt{2}-1\right) \sqrt{\frac{J}{2}}\).Spins of primordial black holes formed with a soft equation of statehttps://zbmath.org/1528.830842024-03-13T18:33:02.981707Z"Saito, Daiki"https://zbmath.org/authors/?q=ai:saito.daiki"Harada, Tomohiro"https://zbmath.org/authors/?q=ai:harada.tomohiro"Koga, Yasutaka"https://zbmath.org/authors/?q=ai:koga.yasutaka"Yoo, Chul-Moon"https://zbmath.org/authors/?q=ai:yoo.chul-moon(no abstract)Dynamics of slender single-link flexible robotic manipulator based on Timoshenko beam theoryhttps://zbmath.org/1528.931632024-03-13T18:33:02.981707Z"Rao, Priya"https://zbmath.org/authors/?q=ai:rao.priya"Chakraverty, S."https://zbmath.org/authors/?q=ai:chakraverty.snehashish"Roy, Debanik"https://zbmath.org/authors/?q=ai:roy.debanikSummary: It is well known that irrespective of the joint signature, namely serial or articulated, a single-link manipulator has a great application in the field of robotics. For the study of dynamics of single-link manipulators, the conjugate problem is studied based on Timoshenko beam theory. Governing differential equations and the boundary conditions are usually considered as exact and the formulation leads to an eigenvalue problem where the elements of the matrices are in exact form. In view of the above, this chapter investigates the said problem in particular for a single-link semi-compliant flexible robotic manipulator. After the successful modelling of the single-link manipulator, with Timoshenko beam theory, the model has been compared with the existing calculation of an undamped Euler-Bernoulli cantilever beam as well, taking tip mass to be zero. The study extends further by taking tip mass to be non-zero and the results are compared with mass-loaded clamped-free Timoshenko beam. These comparisons are found to be in good agreement.
For the entire collection see [Zbl 1523.37002].