scholarly journals Smarandache Ruled Surfaces according to Darboux Frame in E 3

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Soukaina Ouarab
Keyword(s):  
Architectural Design ◽  
Sufficient Conditions ◽  
Surface Modeling ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Regular Surface ◽  
New Approach ◽  
Darboux Frame ◽  
Necessary And Sufficient

This paper presents a new approach of constructing special ruled surfaces and aims to study their developability and minimalist conditions. Our concept opens opportunities for application in engineering, surface modeling, and architectural design. The principle of our study is to introduce the original definitions of Smarandache ruled surfaces according to Darboux frame of a curve lying on an arbitrary regular surface in E 3 . It concerns T g -Smarandache ruled surface, T n -smarandache ruled surface, and g n -Smarandache ruled surface. New theorems giving necessary and sufficient conditions for those surfaces to be developable and minimal are investigated. Finally, an example with illustrations is presented.

scholarly journals Sweeping surface of center curve on surface in Euclidean 3-space E³

2021 ◽  
Vol 20 ◽  
pp. 235-243
Author(s):  
Rashad A. Abdel-Baky ◽  
Fatemah Mofarreh
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Moving Frame ◽  
Regular Surface ◽  
Geometrical Properties ◽  
Darboux Frame ◽  
Curve On Surface ◽  
Necessary And Sufficient

For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.

scholarly journals Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E 3

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Soukaina Ouarab
Keyword(s):  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Regular Curve ◽  
Necessary And Sufficient

In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3 . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.

scholarly journals Direction Curves Associated with Darboux Vectors Fields and Their Characterizations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nidal Echabbi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Formula Unit ◽  
Regular Surface ◽  
Darboux Vector ◽  
Spherical Curve ◽  
Constant Torsion ◽  
Darboux Frame ◽  
Necessary And Sufficient ◽  
Unit Normal

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to this, we have seen the cases where the Darboux invariants δ o , δ r , and δ n are, respectively, zero. Finally, we enrich our study by giving some examples.

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

A New Approach to Type Synthesis of Spatial Robotic Mechanisms

1992 ◽  
Author(s):  
Akhtar N. Malik ◽  
D. R. Kerr
Keyword(s):  
Robot Manipulators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Type Synthesis ◽  
End Effector ◽  
New Approach ◽  
Parallel Platform ◽  
Necessary And Sufficient

Abstract This paper presents a new approach for carrying out the type synthesis of spatial parallel platform-type mechanisms, used as robot manipulators. It takes into account the total mobility of the system and the partial mobility of its sub-mechanisms. The paper also provides the necessary and sufficient conditions for the mechanisms to function with specified end-effector freedoms, which are described in two theorems. The total number of possible mechanisms with given mobility and structure are tabulated. The work is based on a modified Grübler mobility criterion and also on the consideration of kinematic restraints.

scholarly journals Characteristic Properties of Type-2 Smarandache Ruled Surfaces According to the Type-2 Bishop Frame in E 3

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ibrahim Al-Dayel ◽  
E. M. Solouma
Keyword(s):  
Sufficient Conditions ◽  
Special Kind ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Minimal Amount ◽  
Bishop Frame ◽  
Necessary And Sufficient

In this paper, we define and investigate a special kind of ruled surfaces called type-2 Smarandache ruled surfaces related to the type-2 Bishop frame in E 3 . From this point and depending on the type-2 Bishop curvature, we provide the necessary and sufficient conditions that allow these surfaces to be developable in a minimal amount of time. Furthermore, an example is given to clear the results.

scholarly journals A New Approach to Mannheim Curve in Euclidean 3-Space

2021 ◽  
Vol 54 ◽  
Author(s):  
Ali UÇUM ◽  
Çetin Camcı ◽  
Kazım İlarslan
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
New Approach ◽  
3 Dimensional ◽  
Mannheim Curve ◽  
Necessary And Sufficient

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.

scholarly journals K-type slant helices on spacelike and timelike surfaces

2021 ◽  
Vol 25 (2) ◽  
pp. 201-220
Author(s):  
Santosh Kumar ◽  
Buddhadev Pal
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Timelike Surface ◽  
Spacelike Curve ◽  
Slant Helix ◽  
Darboux Frame ◽  
Necessary And Sufficient

We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.

A new approach to canal surface with parallel transport frame

2017 ◽  
Vol 14 (02) ◽  
pp. 1750026 ◽  
Author(s):  
İlim Kiṣi ◽  
Günay Öztürk
Keyword(s):  
Parallel Transport ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Canal Surface ◽  
New Approach ◽  
Canal Surfaces ◽  
Necessary And Sufficient

In the present study, we attend to the canal surfaces with the spine curve [Formula: see text] according to the parallel transport frame in Euclidean [Formula: see text]-space [Formula: see text]. We give an example of these surfaces and obtain some results about curvature conditions in [Formula: see text]. Moreover, the visualizations of projections of canal surfaces are presented. Lastly, we give the necessary and sufficient conditions for canal surfaces to become weak superconformal.

scholarly journals Timelike Sweeping Surfaces According to Type-2 Bishop Frame in Minkowski 3–space

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Developable Surface ◽  
Bishop Frame ◽  
Tangential Surface ◽  
Necessary And Sufficient

In this paper, we express timelike sweeping surfaces using rotation minimizing frames in Minkowski 3–Space E3 1 . Necessary and sufficient conditions for timelike sweeping surfaces to be developable ruled surfaces are derived. Using these, we analyze the conditions when the resulting timelike developable surface is a cylinder, cone or tangential surface.

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