The Steiner formula and the Holditch theorem for the homothetic motions on the planar kinematics

Tutar, Ayhan; Kuruoğlu, N.

doi:10.1016/s0094-114x(98)00028-7

Cited by 18 publications

(14 citation statements)

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“…Special case 2 : If k A = k B , ν 2 = 1 and λ 1 = 0 then Eq. (14) yields the Holditch theorem for the closed planar homothetic motion which was given by Tutar and Kuruoglu [3].…”

Section: A Generalization Of Holditch Theorem To Two Different Closedmentioning

confidence: 90%

A generalization of the Holditch Theorem for the planar homothetic motions

Yüce

Kuruoğlu

2005

Appl Math

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“…Special case 2 : If k A = k B , ν 2 = 1 and λ 1 = 0 then Eq. (14) yields the Holditch theorem for the closed planar homothetic motion which was given by Tutar and Kuruoglu [3].…”

Section: A Generalization Of Holditch Theorem To Two Different Closedmentioning

confidence: 90%

A generalization of the Holditch Theorem for the planar homothetic motions

Yüce

Kuruoğlu

2005

Appl Math

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“…The Steiner area formula and the Holditch theorem during one-parameter closed planar homothetic motions were expressed by Tutar [2]. We want to explain the relation between the Steiner formula and the polar moment of inertia for the closed planar homothetic inverse motions in complex plane and find experimental data equivalents of the theoretical results in this study.…”

Section: Introductionmentioning

confidence: 88%

On the Kinematics for the Closed Planar Homothetic Inverse Motions in Complex Plane

Sener¹,

Tutar²

2017

JAMP

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In this paper, the Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic inverse motions in complex plane. The Steiner point was defined when the rotation number was different zero and it was called the Steiner normal when the rotation number was equal to zero. The fixed pole point was given with its components and its relation between Steiner point or Steiner normal was explained. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and the moving arm of the telescopic crane. The theoretical concepts and results were applied for this motion.

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“…The Steiner area formula and the Holditch theorem during one parameter closed planar homothetic motions were expressed by [8]. We calculated the expression of the Steiner formula relative to the moving coordinate system under one parameter closed planar motions.…”

Section: Introductionmentioning

confidence: 99%

Characteristic Directions of Closed Planar Homothetic Motions

Tutar¹,

Sener²,

Inan³

2018

Int. J. of Appl. Math.

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In this paper, during one-parameter closed planar homothetic motions, the Steiner area formula and the polar moment of inertia were expressed. The Steiner point or Steiner normal concepts were described according to whether rotation number is different zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results obtained in the first section of this study were applied for this motion.

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The Steiner formula and the Holditch theorem for the homothetic motions on the planar kinematics

Cited by 18 publications

References 0 publications

A generalization of the Holditch Theorem for the planar homothetic motions

A generalization of the Holditch Theorem for the planar homothetic motions

On the Kinematics for the Closed Planar Homothetic Inverse Motions in Complex Plane

Characteristic Directions of Closed Planar Homothetic Motions

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