Alternative partner curves in the Euclidean 3-space

Yılmaz, Beyhan; Has, Aykut

doi:10.31801/cfsuasmas.538177

Cited by 3 publications

(4 citation statements)

References 8 publications

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“…Proof. By using the equations in (2) and the relation (11) with the fact that τ = 0 the proof is completed. □ Theorem 3.…”

Section: Tangent Associated Curvesmentioning

confidence: 97%

“…When substituted the given ODE, (11) into (8) we complete the first part of the proof for T * . Similarly, another deductions can be drawn as < T, N * > = < O * , N * >, and < T, B * > = < O * , B * >= 0, and using these we write…”

Section: Tangent Associated Curvesmentioning

confidence: 99%

“…For such curves, the association is based upon the Frenet elements of the curves. There have been other studies using different frames such as Darboux and Bishop to associate curves, as well ( [6][7][8][9][10][11]). From a distinct point of view, Choi and Kim (2012), introduced new associated curves of a given Frenet curve as the integral curves of vector fields [12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Associated curves from a different point of view in $E^3$

Şenyurt

Canlı

Ayvacı

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper, tangent, principal normal and binormal wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal and rectifying plane of its partner, respectively. For each associated curve, a new moving frame and the corresponding curvatures are formulated in terms of Frenet frame vectors. In addition to this, the possible solutions for distance functions between the curve and its associated mate are discussed. In particular, it is seen that the involute curves belong to the family of tangent associated curves in general and the Bertrand and the Mannheim curves belong to the principal normal associated curves. Finally, as an application, we present some examples and map a given curve together with its partner and its corresponding moving frame.

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“…Proof. By using the equations in (2) and the relation (11) with the fact that τ = 0 the proof is completed. □ Theorem 3.…”

Section: Tangent Associated Curvesmentioning

confidence: 97%

Section: Tangent Associated Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Associated curves from a different point of view in $E^3$

Şenyurt

Canlı

Ayvacı

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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show abstract

“…For such curves, the association is based upon the Frenet elements of the curves. There have been other studies using different frames such as Darboux and Bishop to associate curves, as well ( [3], [4], [6], [9], [15]). From a distinct point of view, Choi and Kim (2012), introduced new associated curves of a given Frenet curve as the integral curves of vector fields.…”

Section: Introductionmentioning

confidence: 99%

Associated curves in $E^3$ from a different point of view

ŞENYURT,

CANLI,

AYVACI

2024

Preprint

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In this paper, tangent, principal normal and binormal wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal and rectifying plane of its mate, respectively. For each associated curves a new moving frame and the corresponding curvatures are found, and in addition to this the possible solutions for distance functions between the curve and its associated mate are discussed. In particular, it is seen that the involute curves belong to the family of tangent associated curves, the Bertrand and the Mannheim curves belong to the principal normal associated curves. Finally, as an application, we present some examples and map a given curve together with its mate and their frames.

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Curves of stationary acceleration according to alternative frame

Güven,

Es,

Yaylı

2023

Filomat

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This paper investigates curves of stationary acceleration by using alternative frame which includes the principal normal vector, the derivative of principal normal vector and the Darboux vector. Mentioned curves are studied by the way of rigid body motions, that is to say a point in the moving body follows the curve and the alternative frame in the moving body stays aligned with the members of frame. It is determined that in which condition this special motion becomes to stationary acceleration motion. The matrix representations of a constant vector related to velocity vector of the motion which is used to characterize stationary acceleration is obtained by means of alternative frame curvatures. Some examinations are developed with some solutions of differential equations. The main result is attained as: general helix curves with linear curvature and torsion functions are curves of stationary acceleration which are curves in the rigid body motions group SE(3) correlated with robotics. The paths designed as stationary acceleration curves can lead the way to control the end-effectors of robots. Finally, some explanatory examples are imputed.

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Alternative partner curves in the Euclidean 3-space

Cited by 3 publications

References 8 publications

Associated curves from a different point of view in $E^3$

Associated curves from a different point of view in $E^3$

Associated curves in $E^3$ from a different point of view

Curves of stationary acceleration according to alternative frame

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