Novel Periodic and Turning Motions in the Simplest Passive Walking Model

2014 ◽  
Author(s):  
M. R. Sabaapour ◽  
M. R. Hairi Yazdi ◽  
B. Beigzadeh
Keyword(s):  
Periodic Motion ◽  
Essential Feature ◽  
Basin Of Attraction ◽  
Three Dimensional ◽  
Surface Profile ◽  
Passive Walking ◽  
The Stability ◽  
Special Case ◽  
Stable Passive ◽  
Passive Turning

The ability to move along curved paths is an essential feature for biped walkers to move around obstacles. This study is aimed at extending passive walking concept for curved walking and turning to generate more natural and effective motion. Hence three-dimensional (3D) motion of a rimless spoked-wheel, as the simplest walking model, about a general vertical fixed coordinate system has been derived. Then, two kinds of a stable passive turning, i.e. limited and circular continuous have been considered and discussed. The first kind is actually transferring from a 2D periodic motion to another, and can be implemented on a straight slope surface. While, it was shown that the second kind is just related to novel 3D periodic motions and can be recognized on a special surface profile namely “helical slope” introduced here. The latter are interpreted as 3D fixed points of a Poincare return map again. So, their stability was evaluated numerically by a Jacobian analysis and demonstrated through several simulations. Results show asymptotical stability of such motions and their considerable basin of attraction with respect to initial states. In addition, the characteristic of passive turning is shown to be strictly connected with the value of the initial perturbed condition, for instance, to the initial inclination of the wheel. It is then surprising to note that the stability of a 3D passive periodic motion (turning) is higher than 2D one (straight walking) which is actually a special case just with an infinite radius of turn.

The development of three-dimensional wave-packets in unbounded parallel flows

1968 ◽  
Vol 32 (4) ◽  
pp. 801-808 ◽  
Author(s):  
M. Gaster ◽  
A. Davey
Keyword(s):  
Wave Packet ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Physical Plane ◽  
Parallel Flows ◽  
Flow Velocity Profile ◽  
The Stability ◽  
Special Case ◽  
Dimensional Wave

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

Stability Control of a Three-Dimensional Passive Walker by Periodic Input Based on the Frequency Entrainment

2011 ◽  
Vol 23 (6) ◽  
pp. 1100-1107 ◽  
Author(s):  
Soichiro Suzuki ◽  
◽  
Masamichi Takada ◽  
Yuta Iwakura ◽  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Stability Control ◽  
Human Gait ◽  
Mechanical Oscillator ◽  
Frequency Entrainment ◽  
Passive Walking ◽  
Periodic Input ◽  
The Stability ◽  
Human Gait Analysis

This study proposes a new control that stabilizes a three-dimensional (3D) passive walker without torque input at knees and ankles joints by using entrainment and a mechanical oscillator. It is difficult to stabilize a 3D biped passive walker in different environments because the range of initial conditions for stable walking is limited, so we designed a 3D biped passive walker as a passive walking platform by considering the results of human gait analysis to make the success of passive walking high. The stability of this platform was analytically determined by analyzing the frontal movement limit cycle. In the new control, the frontalmovement period is synchronized with the swing-leg period by a mechanical oscillator on the top of the walker. The mechanical oscillator controller generates a target path to synchronize oscillatormovement with swing-leg movement using frequency entrainment. The walker is stabilized when the frontal movement period was synchronized with the swing-leg period by periodic input generated by the mechanical oscillator. It was experimentally found consequently that the walker was stabilized on different slopes and flat floors.

scholarly journals Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160028 ◽  
Author(s):  
Ippei Obayashi ◽  
Shinya Aoi ◽  
Kazuo Tsuchiya ◽  
Hiroshi Kokubu
Keyword(s):  
Basin Of Attraction ◽  
Underlying Mechanism ◽  
The Body ◽  
Bipedal Walking ◽  
Dynamic Walking ◽  
Passive Dynamic Walking ◽  
Saddle Type ◽  
The Stability ◽  
Stable Passive ◽  
The Basin Of Attraction

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

Handheld Laser Scanner Research

2019 ◽  
Vol 952 (10) ◽  
pp. 47-54
Author(s):  
A.V. Komissarov ◽  
A.V. Remizov ◽  
M.M. Shlyakhova ◽  
K.K. Yambaev
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Test Site ◽  
Optical Systems ◽  
Advantages And Disadvantages ◽  
Site Survey ◽  
Laser Scanners ◽  
Three Dimensional Models ◽  
The Stability

The authors consider hand-held laser scanners, as a new photogrammetric tool for obtaining three-dimensional models of objects. The principle of their work and the newest optical systems based on various sensors measuring the depth of space are described in detail. The method of simultaneous navigation and mapping (SLAM) used for combining single scans into point cloud is outlined. The formulated tasks and methods for performing studies of the DotProduct (USA) hand-held laser scanner DPI?8X based on a test site survey are presented. The accuracy requirements for determining the coordinates of polygon points are given. The essence of the performed experimental research of the DPI?8X scanner is described, including scanning of a test object at various scanner distances, shooting a test polygon from various scanner positions and building point cloud, repeatedly shooting the same area of the polygon to check the stability of the scanner. The data on the assessment of accuracy and analysis of research results are given. Fields of applying hand-held laser scanners, their advantages and disadvantages are identified.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

scholarly journals Gum Tragacanth (GT): A Versatile Biocompatible Material beyond Borders

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1510 ◽  
Author(s):  
Mohammad Ehsan Taghavizadeh Yazdi ◽  
Simin Nazarnezhad ◽  
Seyed Hadi Mousavi ◽  
Mohammad Sadegh Amiri ◽  
Majid Darroudi ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Food Packaging ◽  
Three Dimensional ◽  
Great Promise ◽  
Anionic Polymer ◽  
Gum Tragacanth ◽  
New Horizons ◽  
Tissue Healing ◽  
The Stability ◽  
Therapeutic Substance

The use of naturally occurring materials in biomedicine has been increasingly attracting the researchers’ interest and, in this regard, gum tragacanth (GT) is recently showing great promise as a therapeutic substance in tissue engineering and regenerative medicine. As a polysaccharide, GT can be easily extracted from the stems and branches of various species of Astragalus. This anionic polymer is known to be a biodegradable, non-allergenic, non-toxic, and non-carcinogenic material. The stability against microbial, heat and acid degradation has made GT an attractive material not only in industrial settings (e.g., food packaging) but also in biomedical approaches (e.g., drug delivery). Over time, GT has been shown to be a useful reagent in the formation and stabilization of metal nanoparticles in the context of green chemistry. With the advent of tissue engineering, GT has also been utilized for the fabrication of three-dimensional (3D) scaffolds applied for both hard and soft tissue healing strategies. However, more research is needed for defining GT applicability in the future of biomedical engineering. On this object, the present review aims to provide a state-of-the-art overview of GT in biomedicine and tries to open new horizons in the field based on its inherent characteristics.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

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