Dual Lorentzian spherical motions and dual Euler–Savary formula

Güngör, Mehmet Ali̇; Ersoy, Soley; Tosun, Murat

doi:10.1016/j.euromechsol.2009.03.007

Cited by 15 publications

(13 citation statements)

References 16 publications

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“…In this section, we give a short synopsis of the dual numbers theory, and dual Lorentzian vectors [11][12][13][14][15]. If a and a * are real numbers, the term a = a + εa * is named a dual number.…”

Section: Basic Conceptsmentioning

confidence: 99%

“…The center and radius of this circle can be specified by the Euler-Savary formula, if the place of the point is specified in the movable plane. In different types of geometry, the Euler-Savary formula had been generalized for a line trajectory, i.e., the construction of the Disteli formulae [4][5][6][7][11][12][13] . Therefore, we now shall look to the Euler-Savary and Disteli formulae for the timelike axodes by utilizing the equipment just acquired above.…”

Section: Euler-savary Formula For the Timelike Axodesmentioning

confidence: 99%

“…In the Minkowski 3-space E 3 1 , Lorentzian metric can have one of three Lorentzian causal characters; it can be positive, negative, or zero, while the metric in the Euclidean 3-space E 3 can only be positive definite. Therefore, the kinematic and geometric clarifications can be further meaningful in E 3 1 [11][12][13]. This study is as follows.…”

Section: Introductionmentioning

confidence: 99%

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One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

Almoneef,

Abdel-Baky

2023

Mathematics

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In this paper, based on the E. Study map, direct appearances were sophisticated for one-parameter hyperbolic dual spherical locomotions and invariants of the axodes. With the suggested technique, the Disteli formulae for the axodes were acquired and the correlations through kinematic geometry of a timelike line trajectory were provided. Then, a ruled analogy of the curvature circle of a curve in planar locomotions was expanded into generic spatial locomotions. Lastly, we present new hyperbolic proofs for the Euler–Savary and Disteli formulae.

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Section: Basic Conceptsmentioning

confidence: 99%

Section: Euler-savary Formula For the Timelike Axodesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

Almoneef,

Abdel-Baky

2023

Mathematics

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“…The first on by M.A. Gungor, S. Ersoy, M. Tosun [29] containing more information on the history, too. The second one written by Brunnthaler, Husty and Schröcker on four-bar mechanism ( [11]).…”

Section: Roulettesmentioning

confidence: 99%

Constructive curves in non-Euclidean planes

Horváth

2016

Preprint

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“…Abdel-Baky and Al-Solamy [10] proposed a novel geometrickinematic approach to one-parameter locomotion based on facts describing the locomotion of the axodes. A significant amount of research exists concerning the ISA and the axode invariants [11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

Almoneef,

Abdel-Baky

2023

Symmetry

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In this study, we establish a novel Lorentzian interpretation of the Euler–Savary (E−S) and Disteli (Dis) formulae. Subsequently, we proceed to establish a theoretical structure for a Lorentzian torsion line congruence which is the spatial symmetry of the Lorentzian circling-point dual curve, in accordance with the principles of the kinematic theory of spherical locomotions. Further, a timelike (Tlike) torsion line congruence is defined and its spatial equivalence is examined. The findings contribute to an enhanced comprehension of the interplay between axodes and Lorentzian spatial movements, which has possible significance in various disciplines, such as the fields of robotics and mechanical engineering.

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Dual Lorentzian spherical motions and dual Euler–Savary formula

Cited by 15 publications

References 16 publications

One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

Constructive curves in non-Euclidean planes

A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

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