scholarly journals The dual spatial quaternionic expression of ruled surfaces

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 403-411
Author(s):  
Abdussamet Caliskan ◽  
Süleyman Şenyurt
Keyword(s):  
Unit Sphere ◽  
Dual Space ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Integral Invariants ◽  
Dual Expression

In this paper, the ruled surface which corresponds to a curve on dual unit sphere is rederived with the help of dual spatial quaternions. We extend the term of dual expression of ruled surface using dual spatial quaternionic method. The correspondences in dual space of closed ruled surfaces are quaternionically expressed. As a consequence, the integral invariants of these surfaces and the relationships between these invariants are shown

On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings

2015 ◽  
Vol 08 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Lorentzian Space ◽  
Integral Invariants ◽  
Timelike Ruled Surface ◽  
Spherical Images

In this paper, we give the characterizations for Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space [Formula: see text]. We obtain the relations between terms of their integral invariants and also we give new characterization for the Mannheim offsets of developable timelike ruled surface. Moreover, we find relations between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.

scholarly journals On the Blaschke approach of ruled surface

2003 ◽  
Vol 34 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Rashad A. Abdel Baky
Keyword(s):  
Unit Sphere ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Necessary Condition ◽  
Original Surface ◽  
Distribution Parameters ◽  
Local Properties

In this paper using E. Study map and the Blaschke approach we studied a ruled surface as a curve on the dual unit sphere. The Blaschke approach proceeds by defining a sequence of ruled surfaces associated with the ruled surface. The relative positions of these surfaces and their distribution parameters characterize the local properties of the original surface. A necessary condition for a ruled surface to be closed is derived. Moreover, an example of application is investigated in detail.

scholarly journals A new approach to design the ruled surface

2019 ◽  
Vol 16 (06) ◽  
pp. 1950093
Author(s):  
Ferhat Taş ◽  
Kazım İlarslan
Keyword(s):  
Unit Sphere ◽  
Ruled Surface ◽  
Geometric Design ◽  
Control Points ◽  
Computer Aided Geometric Design ◽  
New Approach ◽  
Transference Principle ◽  
Integral Invariants ◽  
Computer Aided ◽  
Novel Method

This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples and the motion interpolation was shown as an embodiment of this method.

Dual curves associated with the Bonnet ruled surfaces

2020 ◽  
Vol 17 (13) ◽  
pp. 2050204
Author(s):  
Muradı̇ye Çı̇mdı̇ker Aslan ◽  
Gülşah Aydın Şekerci̇
Keyword(s):  
Dual Space ◽  
Geodesic Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Principal Curvatures ◽  
Bonnet Surface ◽  
Euclidean Three Space ◽  
Dual Curve ◽  
Three Space

An interest problem arises to determine the surfaces in the Euclidean three space, which admit at least one nontrivial isometry that preserves the principal curvatures. This leads to a class of surface known as a Bonnet surface. The intention of this study is to examine a Bonnet ruled surface in dual space and to calculate the dual geodesic trihedron of the dual curve associated with the Bonnet ruled surface and derivative equations of this trihedron by the dual geodesic curvature. Also, we find that the dual curvature, the dual torsion for the dual curves associated with the Bonnet ruled surface which are different from any dual curves. Moreover, some examples are obtained about the Bonnet ruled surface.

scholarly journals RULED SURFACES AND TANGENT BUNDLE OF PSEUDO-SPHERE OF NATURAL LIFT CURVES

2020 ◽  
Vol 20 (3) ◽  
pp. 573-586
Author(s):  
EMEL KARACA ◽  
MUSTAFA CALISKAN
Keyword(s):  
Unit Sphere ◽  
Gaussian Curvature ◽  
Tangent Bundle ◽  
Mean Curvature ◽  
Shape Operator ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Curve Shape ◽  
Lift Curve

In this article, firstly, the isomorphism between the subset of the tangent bundle of Lorentzian unit sphere, TM, and Lorentzian unit sphere, S12 is represented. Secondly, the isomorphism between the subset of hyperbolic unit sphere, TM, and hyperbolic unit sphere, H2 is given. According to E. Study mapping, any curve on S12 or H2 corresponds to a ruled surface in R13. By constructing these isomorphisms, we correspond to any natural lift curve on TM or TM a unique ruled surface in R13. Then we calculate striction curve, shape operator, Gaussian curvature and mean curvature of these ruled surfaces. We give developability condition of these ruled surfaces. Finally, we give examples to support the main results.

scholarly journals The quaternionic expression of ruled surfaces

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5753-5766 ◽  
Author(s):  
Süleyman Şenyurt ◽  
Abdussamet Çalışkan
Keyword(s):  
Ruled Surface ◽  
Distribution Parameter ◽  
Ruled Surfaces ◽  
Integral Invariants

In this paper, firstly, the ruled surface is expressed as a spatial quaternionic. Also, the spatial quaternionic definitions of the Striction curve, the distribution parameter, angle of pitch and the pitch are given. Finally, integral invariants of the closed spatial quaternionic ruled surfaces drawn by the motion of the Frenet vectors {t,n1,n2} belonging to the spatial quaternionic curve ? are calculated.

scholarly journals Characteristics of the double-cycled motion-ruled surface of the Schatz linkage based on differential geometry

2014 ◽  
Vol 229 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Lei Cui ◽  
Jian S Dai ◽  
Chung-Ching Lee
Keyword(s):  
Differential Geometry ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Full Rotation ◽  
Kinematic Properties

This paper applies Euclidean invariants from differential geometry to kinematic properties of the ruled surfaces generated by the coupler link and the constraint-screw axes. Starting from investigating the assembly configuration, the work reveals two cycle phases of the coupler link when the input link finishes a full rotation. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link, where Euclidean invariants are obtained and singularities are identified. This work further presents the constraint ruled surface that is generated by the constraint screw axes and unveils its intrinsic characteristics.

On the integral invariants of a closed ruled surface

1990 ◽  
Vol 39 (1-2) ◽  
pp. 80-91 ◽  
Author(s):  
Osman G�rsoy
Keyword(s):  
Ruled Surface ◽  
Integral Invariants

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.

scholarly journals Kähler Yamabe minimizers on minimal ruled surfaces

2002 ◽  
Vol 90 (2) ◽  
pp. 180
Author(s):  
Christina W. Tønnesen-Friedman
Keyword(s):  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Ruled Surface ◽  
Ruled Surfaces

It is shown that if a minimal ruled surface $\mathrm{P}(E) \rightarrow \Sigma$ admits a Kähler Yamabe minimizer, then this metric is generalized Kähler-Einstein and the holomorphic vector bundle $E$ is quasi-stable.

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