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.

On the kinematic interpretation of timelike ruled surfaces

2015 ◽  
Vol 12 (10) ◽  
pp. 1550127 ◽  
Author(s):  
Mehmet Önder ◽  
Zehra Ekinci
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Reference Surface ◽  
Screw Axis ◽  
Lorentzian Space ◽  
Timelike Ruled Surface ◽  
Instantaneous Screw Axis ◽  
Associated Surfaces ◽  
Instantaneous Screw ◽  
Mannheim Offset

Timelike ruled surfaces are studied in dual Lorentzian space [Formula: see text] by considering E. Study Mapping and Blaschke frame. A reference timelike ruled surface is considered and associated surfaces are defined. First, it is shown that the surface generated by the instantaneous screw axis (ISA) is a Mannheim offset of reference surface. Later, the kinematic interpretations between these surfaces are introduced by means of Blaschke 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 Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces

2016 ◽  
Vol 34 (1) ◽  
pp. 85-98 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surfaces ◽  
Developable Surface ◽  
Integral Invariants ◽  
Offset Surfaces ◽  
Spherical Images ◽  
Mannheim Offset

In this study, we give the dual characterizations of Mannheim offsets of ruled surfaces in terms of their integral invariants and obtain a new characterization of the Mannheim offsets of developable surface, i.e., we show that the striction lines of developable Mannheim offset surfaces are Mannheim partner curves. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of ruled surfaces and their integral invariants.

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

Non-lightlike ruled surfaces with constant curvatures in Minkowski 3-space

2018 ◽  
Vol 15 (04) ◽  
pp. 1850068 ◽  
Author(s):  
Ahmad Tawfik Ali
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Ruled Surface ◽  
Timelike Curve ◽  
Ruled Surfaces ◽  
Base Curve ◽  
Timelike Ruled Surface ◽  
Interesting Theorem

We study the non-lightlike ruled surfaces in Minkowski 3-space with non-lightlike base curve [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] are the tangent, principal normal and binormal vectors of an arbitrary timelike curve [Formula: see text]. Some important results of flat, minimal, II-minimal and II-flat non-lightlike ruled surfaces are studied. Finally, the following interesting theorem is proved: the only non-zero constant mean curvature (CMC) non-lightlike ruled surface is developable timelike ruled surface generated by binormal vector.

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 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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