Mathematical Model of Worm-like Motion Systems with Finite and Infinite Degree of Freedom

Zimmermann, Klaus; Zeidis, Igor; Steigenberger, Joachim

doi:10.1007/978-3-7091-2552-6_53

Cited by 12 publications

(10 citation statements)

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“…Comparing the inequalities (22) with the conditions of stability and instability (19) and (20), it follows that the stationary amplitude corresponding to the lesser root of f (a) = 0, a 1 , is stable, and that the amplitude a 2 , corresponding to the greater root, is unstable. Now consider the case…”

Section: The Expression For the First Derivative Has The Form Of Eq mentioning

confidence: 94%

“…Some asymptotic methods for the solution of equations of nonlinear oscillations are presented in well-known monographs [1,2,4,5]. Nonlinear systems including discontinuous functions such as dry friction are especially considered in a series of publications [3,6,7,9,16,17,19,20]. In [19,20] the motion of two mass points connected by a linear spring is discussed.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear systems including discontinuous functions such as dry friction are especially considered in a series of publications [3,6,7,9,16,17,19,20]. In [19,20] the motion of two mass points connected by a linear spring is discussed. It is supposed that this linear oscillator is under the action of a small non-symmetric Coulomb dry friction force, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forced nonlinear oscillator with nonsymmetric dry friction

et al. 2006

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In this paper we discuss an approximately steady motion of an oscillator as a single whole with a constant "on the average" velocity. For that purpose we analyze the position and stability of some special points of the phase portrait. In the presence of internal excitation and nonsymmetric Coulomb dry friction, a motion of the oscillator with a constant "on the average" velocity is possible. The algebraic equation for this constant velocity is found. For different parameters of the model there exist at most three regimes of motion with a constant velocity, but only one or two of them are stable. The theoretical results obtained can be used for the design of worm-like moving robots.

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Section: The Expression For the First Derivative Has The Form Of Eq mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forced nonlinear oscillator with nonsymmetric dry friction

et al. 2006

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“…Animals like earthworms and snakes are good representatives that employing the vibration-driven system to locomote in various media. Learning from the earthworms and the snakes to develop bio-inspired locomotion robots is currently an attractive research field [1,2]. Compared to the conventional legged and wheeled robots, due to the relatively simpler structure, stronger controllability and higher miniaturization potential, these earthworm-like or snake like robots are promisingly to be used in disaster rescue, pipeline inspection and minimally invasive surgery.…”

Section: Introductionmentioning

confidence: 99%

Planar locomotion of a vibration-driven system with two internal masses

Zhan

Fang

2016

Applied Mathematical Modelling

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a b s t r a c tA vibration-driven system is modelled to achieve the expected planar locomotion in the present paper. The system is composed of a main rigid body and two internal and movable masses. Coulomb dry friction and nonholonomic constraint of the body are considered to model stick-slip effect and to ensure the motion without sideslip. It is seen that driving periodically the two masses in two orthogonal directions leads to the expected planar locomotion. Correspondingly, the translational and rotary velocities of the system are analytically obtained. As a result, the system can move not only along oblique line in any given slope but also along folding lines derived from the oblique lines in the different slopes.

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“…We determine the strength of the magnetic field producing a sinusoidal travelling small-amplitude wave on the surface of a magnetic fluid. In [2] we describe the motion of a chain of equal masses placed on a rough straight line and connected consecutively by linear viscoelastic elements (with the same parameters) under the action of a non-symmetric Coulomb dry frictional force. We also investigate the possibility of using the magneto-elastic element under the influence of a magnetic field for creating periodic internal motions and using this effect in designing autonomous mobile robots.…”

Section: Introductionmentioning

confidence: 99%

Modelling of worm‐like motion systems with magneto‐elastic elements

Zimmermann

Zeidis

Налетова

et al. 2004

phys. stat. sol. (c)

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Observing the locomotion of worms, one recognizes a conversion of (mostly periodic) internally driven motions into change of external position (undulatory locomotion). In this paper we consider the motion of a system of two material points, connected by a spring made of magnetisable elastic material. By the influence of a magnetic field the spring extends in the direction orthogonal to the field. Through an harmonic change of the field a small lengthening internal force appears. We investigate the system in vicinity of the main resonance. It is shown that through the presence of a non-symmetric Coulomb dry friction a motion of the system with a constant "on the average" velocity is possible and stable. We obtain the expression for velocity.

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Mathematical Model of Worm-like Motion Systems with Finite and Infinite Degree of Freedom

Cited by 12 publications

References 1 publication

Forced nonlinear oscillator with nonsymmetric dry friction

Forced nonlinear oscillator with nonsymmetric dry friction

Planar locomotion of a vibration-driven system with two internal masses

Modelling of worm‐like motion systems with magneto‐elastic elements

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