Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Torkil Kollsker ◽  
Thomas J. R. Stidsen
Keyword(s):  
Three Dimensional ◽  
Static Equilibrium

Instability of isolated three-dimensional magnetic null points

1998 ◽  
Vol 59 (3) ◽  
pp. 537-541 ◽  
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Null Point ◽  
Static Equilibrium ◽  
Flux Surface ◽  
Form Part ◽  
Magnetic Null ◽  
Transverse Oscillations

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

Visualization of the Contact Force Solution Space for Multi-Limbed Robots

2005 ◽  
Vol 128 (1) ◽  
pp. 295-302 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Solution Space ◽  
Entire Solution ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them, and then the static equilibrium equations are applied. Using the friction cone equation at each foot contact point, the problem is then transformed into a geometrical one. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the entire solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Jamming analyses for dual peg-in-hole insertions in three dimensions

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 83-91 ◽  
Author(s):  
Yanqiong Fei ◽  
Xifang Zhao
Keyword(s):  
Screw Theory ◽  
Three Dimensional ◽  
Equilibrium States ◽  
Contact Forces ◽  
Three Dimensions ◽  
Static Equilibrium ◽  
Moment Equations ◽  
Force Moment

In this paper, jamming analyses of the three dimensional dual peg-in-hole are presented. First, for a three dimensional dual peg-in-hole, possible contact states are enumerated and geometric analyses are presented. Second, the contact forces are described by the screw theory in three dimensions. The force/moment equations for static equilibrium states of three dimensional dual-peg insertions are derived. Third, jamming diagrams are obtained. Eleven kinds of possible jamming diagrams are analyzed. Finally, an experiment of a dual peg-in-hole assembly is presented to show the effectiveness of the above analyses.

On Stability of SDOF Systems with Asymmetric Bi-Linear Hysteresis Subjected to Seismic Excitations

2021 ◽  
pp. 2171002
Author(s):  
Patricio Quintana Gallo ◽  
Rodrigo Meneses
Keyword(s):  
Equilibrium Position ◽  
Numerical Study ◽  
Three Dimensional ◽  
Initial Position ◽  
Technical Note ◽  
Static Equilibrium ◽  
Hysteresis Curve ◽  
Restoring Force ◽  
Seismic Engineering ◽  
Sequence Of Events

This technical note presents a numerical study on the stability of single degree of freedom (SDOF) systems with asymmetric bi-linear hysteretic restoring force, subjected to earthquake excitations. The aim is to report: (a) the existence of an unstable behavior in the response of such systems, under a specific ground motion, given small modifications of the yielding conditions of the hysteresis model, and (b) the introduction of a novel three-dimensional graphic visualization of the problem. The modifications of the yielding conditions were introduced via the symmetry-breaking produced by very small variations of the static equilibrium position of the system, equivalent to having an initial position and restoring force different from zero and symmetric yielding. The concise study comprises of nonlinear dynamic analyses of three system cases, one of them with symmetric (reference) and two with asymmetric yielding conditions. The results show that the system presented a stable response and severe ratcheting toward the weakest yielding direction for the symmetric and asymmetric cases, respectively. Differences as large as [Formula: see text]% between the asymmetric and reference cases were obtained for the residual displacement of the systems, due to variations as small as [Formula: see text]% in the static-equilibrium position, and consequent [Formula: see text]% variations of the positive/negative yielding displacements and forces. In turn, negligible variations of the velocity between the three cases were predicted. To conclude, the paper introduces novel three-dimensional representations of the solution-curve and of the hysteresis cycles of the systems, deepening the discussion on the identified bifurcation. The 3D hysteresis curve, in particular, can be of much use for seismic engineering and mechanical studies, either numerical or experimental, as it allows visualizing the sequence of events in the hysteresis plots in a much clearer fashion compared to the traditional two-dimensional counterparts.

The static equilibrium of drag anchors in sand

1996 ◽  
Vol 33 (4) ◽  
pp. 574-583 ◽  
Author(s):  
S R Neubecker ◽  
M F Randolph
Keyword(s):  
Equilibrium Solution ◽  
Limit Equilibrium ◽  
Three Dimensional ◽  
Limit Equilibrium Method ◽  
Solution Procedure ◽  
Static Equilibrium ◽  
Static Limit ◽  
Centrifuge Model ◽  
Calcareous Sands ◽  
Good Agreement

This paper examines the static equilibrium of drag anchors during embedment in sand. A limit equilibrium method is developed to allow the anchor holding capacity to be predicted given a specific anchor geometry and position relative to the free surface of the sand. The method is based on the earlier approach of Le Lievre and Tabatabaee, but is extended to include a three-dimensional soil wedge, which is consistent with experimental observation. The solution procedure is also extended to be more applicable for anchors at a preultimate stage by incorporating a force behind the anchor fluke. To calibrate the method, a series of centrifuge model anchor tests has been performed in silica and calcareous sands. The static capacity of the anchor during embedment is compared with the static limit equilibrium solution and good agreement is demonstrated. Key words: drag anchor, statics, sand, limit equilibrium, ultimate holding capacity.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

Ultrastructural Investigations of the Contractile Filaments of Amoebae

1974 ◽  
Vol 32 ◽  
pp. 188-189
Author(s):  
P.L. Moore
Keyword(s):  
Cytoplasmic Streaming ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Amoeboid Movement ◽  
Different Types ◽  
Chemical Conditions ◽  
Complete Interpretation

Previous freeze fracture results on the intact giant, amoeba Chaos carolinensis indicated the presence of a fibrillar arrangement of filaments within the cytoplasm. A complete interpretation of the three dimensional ultrastructure of these structures, and their possible role in amoeboid movement was not possible, since comparable results could not be obtained with conventional fixation of intact amoebae. Progress in interpreting the freeze fracture images of amoebae required a more thorough understanding of the different types of filaments present in amoebae, and of the ways in which they could be organized while remaining functional.The recent development of a calcium sensitive, demembranated, amoeboid model of Chaos carolinensis has made it possible to achieve a better understanding of such functional arrangements of amoeboid filaments. In these models the motility of demembranated cytoplasm can be controlled in vitro, and the chemical conditions necessary for contractility, and cytoplasmic streaming can be investigated. It is clear from these studies that “fibrils” exist in amoeboid models, and that they are capable of contracting along their length under conditions similar to those which cause contraction in vertebrate muscles.

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