Synthesizing Mechanical Chains for Morphing Between Spatial Curves

2019 ◽  
Author(s):  
Yucheng Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Revolute Joints ◽  
Morphometric Analyses ◽  
Helical Segment ◽  
Varying Length ◽  
A Chain ◽  
Curvature And Torsion ◽  
Synthesis Methodology ◽  
Spatial Curves

Abstract This work investigates the kinematic synthesis methodology for designing a chain of three-dimensional bodies to match a set of arbitrary spatial curves. The bodies synthesized can be one of three types: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its geometry but may be scaled to become larger or smaller. To realize mechanical chains, only rigid and helical segments are used. After designing the segments, they may be aligned with the original spatial curves with their ends connected via an optimization. For two curves, these connections may be made with revolute joints to obtain high accuracy. For three or more curves, spherical joint connections allow for the best accuracy. To compare curves as is useful in morphometry, all three segment types may be employed. In this case, an accurate description of the changes between curves is important, and optimizing to connect the segments is not needed. The procedure for redefining the curves in a way that the techniques in this paper may be applied, as well as the methodologies for synthesizing the three segment types are presented. Examples include a continuum robot problem and the morphometric analyses of chochlear curves and the lambdoidal suture. This work extends the established planar techniques for synthesizing mechanisms and addressing morphometric issues that are motivated with curves in two-dimensions.

Synthesizing Mechanical Chains for Morphing Between Spatial Curves

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Yucheng Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Shape Change ◽  
Two Dimensions ◽  
Revolute Joints ◽  
Spatial Features ◽  
Morphometric Analyses ◽  
Helical Segment ◽  
A Chain ◽  
Curvature And Torsion ◽  
Synthesis Methodology ◽  
Spatial Curves

Abstract This paper extends the kinematic synthesis methodology for designing a chain of bodies to match a set of arbitrary curves to the spatial case. The methodology initiates with an arbitrary set of spatial curves, and concludes with a set of bodies defined by their spatial features. The bodies synthesized can be one of three types: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its geometry but may be scaled to become larger or smaller. To realize mechanical chains for mechanisms that achieve spatial shape change, only rigid and helical segments are used. After designing the segments, they may be aligned with the original spatial curves with their ends connected via an optimization. For two curves, these connections may be made with revolute joints to obtain high accuracy. For three or more curves, spherical joint connections allow for best accuracy. To compare curves as is useful in morphometry, all three segment types may be employed. In this case, an accurate description of the changes between curves is important, and optimizing to connect the segments is not needed. The procedure for redefining the curves in a way that the techniques in this paper may be applied, as well as the methodologies for synthesizing the three segment types are presented. Examples include a continuum robot problem and the morphometric analyses of cochlear curves and the lambdoidal suture located on a human skull. This work extends the established planar techniques for synthesizing mechanisms and addressing morphometric issues that are motivated with curves in two-dimensions.

Design and Analysis of Reduced Degree of Freedom Modular Snake Robot

2017 ◽  
Author(s):  
Peter Racioppo ◽  
Wael Saab ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Three Dimensional ◽  
Cross Sectional ◽  
Design Synthesis ◽  
Snake Robot ◽  
Routing Schemes ◽  
Revolute Joints ◽  
Modular Units ◽  
A Chain ◽  
The Moment ◽  
And Control

This paper presents the design and analysis of an underactuated, cable driven mechanism for use in a modular robotic snake. The proposed mechanism is composed of a chain of rigid links that rotate on parallel revolute joints and are actuated by antagonistic cable pairs and a multi-radius pulley. This design aims to minimize the cross sectional area of cable actuated robotic snakes and eliminate undesirable nonlinearities in cable displacements. A distinctive feature of this underactuated mechanism is that it allows planar serpentine locomotion to be accomplished with only two modular units, improving the snake’s ability to conform to desired curvature profiles and minimizing the control complexity involved in snake locomotion. First, the detailed mechanism and cable routing scheme are presented, after which the kinematics and dynamics of the system are derived and a comparative analysis of cable routing schemes is performed, to assist with design synthesis and control. The moment of inertia of the mechanism is modeled, for future use in the implementation of three-dimensional modes of snake motion. Finally, a planar locomotion strategy for snake robots is devised, demonstrated in simulation, and compared with previous studies.

scholarly journals Comparison of 2D SEM imaging with 3D micro-tomographic imaging for phylogenetic inference in brittle stars (Echinodermata: Ophiuroidea)

Zoosymposia ◽  
2019 ◽  
Vol 15 (1) ◽  
pp. 146-158 ◽  
Author(s):  
SABINE STÖHR ◽  
ELIZABETH G. CLARK ◽  
BEN THUY ◽  
SIMON A. F. DARROCH
Keyword(s):  
Data Collection ◽  
Three Dimensional ◽  
Morphological Characters ◽  
Two Dimensions ◽  
Tomographic Imaging ◽  
Three Dimensions ◽  
Verbal Description ◽  
Brittle Stars ◽  
Advantages And Disadvantages ◽  
Morphometric Analyses

Recent efforts to reconstruct the phylogeny of brittle stars (ophiuroids) have shown the need for more objective and reproducible data collection methods than the traditional visual examination and verbal description of morphological characters. Complex skeletal structures may be better understood in three dimensions than in two dimensions obtained from techniques like scanning electron microscopy (SEM). We test this hypothesis using three types of three-dimensional tomographic imaging methods—lab-based micro-CT, X-ray microscopy and synchrotron-based tomography—to examine the morphology of ophiuroid arms, and compare them with two-dimensional data obtained from SEM. We describe the advantages and disadvantages of each instrument and set of parameters in terms of the ease and efficiency of data collection for morphometric analyses. We present new morphological observations obtained by digital sectioning of three-dimensional images that could not be achieved with SEM. Overall, our findings suggest that three-dimensional imaging has a high potential to address the gaps in knowledge of the internal ophiuroid skeleton, which will be pivotal to providing morphological characters that will aid in phylogenetic reconstructions.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals Three-dimensional quantification of twisting in the Arabidopsis petiole

2021 ◽  
Author(s):  
Yuta Otsuka ◽  
Hirokazu Tsukaya
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Light Sheet ◽  
Underlying Mechanism ◽  
Two Dimensions ◽  
Observation Angle ◽  
Differential Growth ◽  
Light Sheet Microscopy ◽  
Definition Of ◽  
Twisting Angle

AbstractOrganisms have a variety of three-dimensional (3D) structures that change over time. These changes include twisting, which is 3D deformation that cannot happen in two dimensions. Twisting is linked to important adaptive functions of organs, such as adjusting the orientation of leaves and flowers in plants to align with environmental stimuli (e.g. light, gravity). Despite its importance, the underlying mechanism for twisting remains to be determined, partly because there is no rigorous method for quantifying the twisting of plant organs. Conventional studies have relied on approximate measurements of the twisting angle in 2D, with arbitrary choices of observation angle. Here, we present the first rigorous quantification of the 3D twisting angles of Arabidopsis petioles based on light sheet microscopy. Mathematical separation of bending and twisting with strict definition of petiole cross-sections were implemented; differences in the spatial distribution of bending and twisting were detected via the quantification of angles along the petiole. Based on the measured values, we discuss that minute degrees of differential growth can result in pronounced twisting in petioles.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

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