scholarly journals A study of curvature theory for different symmetry classes of Hamiltonian

Pramana ◽  
2021 ◽  
Vol 95 (3) ◽  
Author(s):  
Y R Kartik ◽  
Ranjith R Kumar ◽  
S Rahul ◽  
Sujit Sarkar
Keyword(s):  
Symmetry Classes ◽  
Curvature Theory

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

scholarly journals Structure–function relationships of the plant cuticle and cuticular waxes — a smart material?

2006 ◽  
Vol 33 (10) ◽  
pp. 893 ◽  
Author(s):  
Hendrik Bargel ◽  
Kerstin Koch ◽  
Zdenek Cerman ◽  
Christoph Neinhuis
Keyword(s):  
Structure Function ◽  
Smart Materials ◽  
Self Assembly ◽  
Water Repellency ◽  
Cuticular Waxes ◽  
Form Complex ◽  
Symmetry Classes ◽  
Research Activities ◽  
Terrestrial Habitats ◽  
Surface Waxes

The cuticle is the main interface between plants and their environment. It covers the epidermis of all aerial primary parts of plant organs as a continuous extracellular matrix. This hydrophobic natural composite consists mainly of the biopolymer, cutin, and cuticular lipids collectively called waxes, with a high degree of variability in composition and structure. The cuticle and cuticular waxes exhibit a multitude of functions that enable plant life in many different terrestrial habitats and play important roles in interfacial interactions. This review highlights structure–function relationships that are the subjects of current research activities. The surface waxes often form complex crystalline microstructures that originate from self-assembly processes. The concepts and results of the analysis of model structures and the influence of template effects are critically discussed. Recent investigations of surface waxes by electron and X-ray diffraction revealed that these could be assigned to three crystal symmetry classes, while the background layer is not amorphous, but has an orthorhombic order. In addition, advantages of the characterisation of formation of model wax types on a molecular scale are presented. Epicuticular wax crystals may cause extreme water repellency and, in addition, a striking self-cleaning property. The principles of wetting and up-to-date concepts of the transfer of plant surface properties to biomimetic technical applications are reviewed. Finally, biomechanical studies have demonstrated that the cuticle is a mechanically important structure, whose properties are dynamically modified by the plant in response to internal and external stimuli. Thus, the cuticle combines many aspects attributed to smart materials.

Analysis of Approximate Four-Bar Straight-Line Mechanisms

1965 ◽  
Vol 87 (3) ◽  
pp. 291-296 ◽  
Author(s):  
D. Tesar ◽  
J. P. Vidosic
Keyword(s):  
Detailed Data ◽  
Design Data ◽  
Straight Line ◽  
Curvature Theory

Four-bar linkages possess many unique advantages as straight-line mechanisms. Formulations involving linkage geometry and curvature theory are developed to yield the lengths of the approximate straight line for specified accuracies. Design data such as link dimensions, transmission angles, and crank rotation angles are also obtained. Classical mechanisms including the Watt, Evans, Chebychev, and Roberts types are analyzed and compared. More detailed data, including a design data chart, are presented for linkages based on a Ball-double Burmester point.

scholarly journals A curvature theory for discrete surfaces based on mesh parallelity

2009 ◽  
Vol 348 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Alexander I. Bobenko ◽  
Helmut Pottmann ◽  
Johannes Wallner
Keyword(s):  
Discrete Surfaces ◽  
Curvature Theory

scholarly journals On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cumali Ekici ◽  
Yasin Ünlütürk ◽  
Mustafa Dede ◽  
B. S. Ryuh
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
End Effector ◽  
Timelike Ruled Surface ◽  
Curvature Theory ◽  
Differential Properties

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.

An approach for designing a developable and minimal ruled surfaces using the curvature theory

2020 ◽  
Vol 18 (01) ◽  
pp. 2150015
Author(s):  
Fatma Güler
Keyword(s):  
Computer Graphics ◽  
Computer Aided Design ◽  
Research Topic ◽  
Ruled Surfaces ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Curvature Theory ◽  
Active Research ◽  
Aided Design

Developable surfaces are defined to be locally isometric to a plane. These surfaces can be formed by bending thin flat sheets of material, which makes them an active research topic in computer graphics, computer aided design, computational origami and manufacturing architecture. We obtain condition for developable and minimal ruled surfaces using rotation frame. Also, the validity of the theorems is illustrated with examples.

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