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Journal articles on the topic 'Euler-Savary formula'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Sá Pereira, Nuno T., and Soley Ersoy. "Elliptical Harmonic Motion and Euler–Savary Formula." Advances in Applied Clifford Algebras 26, no. 2 (2015): 731–55. http://dx.doi.org/10.1007/s00006-015-0609-y.

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2

Alluhaibi, Nadia, and R. A. Abdel-Baky. "Kinematic geometry of hyperbolic dual spherical motions and Euler–Savary’s equation." International Journal of Geometric Methods in Modern Physics 17, no. 05 (2020): 2050079. http://dx.doi.org/10.1142/s0219887820500796.

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In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space [Formula: see text]. Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velo

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3

Dooner, D., R. García García, and J. M. Rico Martínez. "On spatial relations to the Euler-Savary formula." Mechanism and Machine Theory 189 (November 2023): 105427. http://dx.doi.org/10.1016/j.mechmachtheory.2023.105427.

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4

Gungor, M. A., S. Ersoy, and M. Tosun. "Dual Lorentzian spherical motions and dual Euler–Savary formula." European Journal of Mechanics - A/Solids 28, no. 4 (2009): 820–26. http://dx.doi.org/10.1016/j.euromechsol.2009.03.007.

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5

Tosun, M., M. A. Gungor, and I. Okur. "On the One-Parameter Lorentzian Spherical Motions and Euler-Savary Formula." Journal of Applied Mechanics 74, no. 5 (2007): 972–77. http://dx.doi.org/10.1115/1.2722775.

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In this paper, we have introduced one-parameter Lorentzian spherical motion. In addition to that, we have given the relations between the absolute, relative, and sliding velocities of these motions. Furthermore, the relations between fixed and moving pole curves in the Lorentzian spherical motions have also been obtained. At the end of this study, we have expressed the Euler-Savary formula for the one-parameter Lorentzian spherical motions.

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6

Dundar, Furkan Semih, Soley Ersoy, and Nuno T. Sá Pereira. "Bobillier Formula for the Elliptical Harmonic Motion." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 1 (2018): 103–10. http://dx.doi.org/10.2478/auom-2018-0006.

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AbstractIn this study, we have considered the elliptical harmonic motion which is the superposition of two simple harmonic motions in perpendicular directions with the same angular frequency and phase difference of π/2 . It is commonly recognized that a convenient formulation for problems in planar kinematics is obtained by using number systems. Here the elliptical numbers are used to derive the Bobillier formula with two different methods for aforesaid motion; the first method depends on the Euler-Savary formula and the second one uses the usual relations of the velocities and accelerations.

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7

Masal, Melek, Soley Ersoy, and Mehmet Ali Güngör. "Euler–Savary formula for the homothetic motion in the complex plane C." Ain Shams Engineering Journal 5, no. 1 (2014): 305–8. http://dx.doi.org/10.1016/j.asej.2013.09.006.

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8

Ersoy, Soley, and Mahmut Akyigit. "One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula." Advances in Applied Clifford Algebras 21, no. 2 (2010): 297–313. http://dx.doi.org/10.1007/s00006-010-0255-3.

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9

Huang, Zhi Dong, Yun Pu Du, and Yu Wang. "Design and Motion Analysis of Double-Rocker Mechanism with Horizontal Uniform Rectilinear Motion." Advanced Materials Research 442 (January 2012): 240–45. http://dx.doi.org/10.4028/www.scientific.net/amr.442.240.

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The geometry relationship of parameters in double-rocker mechanism is deduced. Utilizing Euler-Savary Formula, the double-rocker mechanism with horizontal uniform rectilinear motion is designed. The horizontal uniform rectilinear properties of the mechanism are analyzed. The mapping principle between parameters and the mechanism output motion is clarified. And the design method and principle for double-rocker mechanism with horizontal uniform rectilinear motion is proposed. The results in this paper facilitate the innovation design of double-rocker mechanism with horizontal uniform rectilinear

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10

Gürses, Nurten, and Salim Yüce. "On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes." Deu Muhendislik Fakultesi Fen ve Muhendislik 21, no. 61 (2019): 137–48. http://dx.doi.org/10.21205/deufmd.2019216114.

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11

Gürses, Nurten, Mücahit Akbiyik, and Salim Yüce. "One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$ C J." Advances in Applied Clifford Algebras 26, no. 1 (2015): 115–36. http://dx.doi.org/10.1007/s00006-015-0598-x.

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12

Almoneef, Areej A., and Rashad A. Abdel-Baky. "Kinematic Differential Geometry of a Line Trajectory in Spatial Movement." Axioms 12, no. 5 (2023): 472. http://dx.doi.org/10.3390/axioms12050472.

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This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide a theoretical expression of inflection line congruence, which is the spatial equivalent of the inflection circle of planar kinematics. Additionally, we introduce new proofs for the Euler–Savary and Disteli formulae and thoroughly analyze their spatial equivalence.

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13

Almoneef, Areej A., and Rashad A. Abdel-Baky. "One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode." Mathematics 11, no. 17 (2023): 3749. http://dx.doi.org/10.3390/math11173749.

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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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14

Li, Yanlin, Nadia Alluhaibi, and Rashad A. Abdel-Baky. "One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes." Symmetry 14, no. 9 (2022): 1930. http://dx.doi.org/10.3390/sym14091930.

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E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived.

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15

Almoneef, Areej A., and Rashad A. Abdel-Baky. "Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions." Axioms 12, no. 10 (2023): 915. http://dx.doi.org/10.3390/axioms12100915.

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This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence.

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16

Almoneef, Areej A., and Rashad A. Abdel-Baky. "Spacelike Lines with Special Trajectories and Invariant Axodes." Symmetry 15, no. 5 (2023): 1087. http://dx.doi.org/10.3390/sym15051087.

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The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fiel

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17

Almoneef, Areej A., and Rashad A. Abdel-Baky. "A Study on a Spacelike Line Trajectory in Lorentzian Locomotions." Symmetry 15, no. 10 (2023): 1816. http://dx.doi.org/10.3390/sym15101816.

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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,

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18

Nurten, (BAYRAK) GURSES, AKBIYIK Mucahit, and YUCE Salim. "Galilean Bobillier Formula for One-Parameter Planar Motions." November 30, 2015. https://doi.org/10.5281/zenodo.826739.

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In this present paper, Galilean Euler-Savary formula for the radius of curvature of the trajectory of a point in the moving Galilean plane (or called Isotropic plane) during one-parameter planar motion is taken into consideration. Galilean Bobillier formula is obtained by using the geometrical interpretation of the Galilean Euler-Savary formula.Moreover, a direct way is chosen to obtain Bobillier formula without using the Euler-Savary formula in the Galilean plane. As a consequence, the Galilean Euler-Savary will appear as aspecific case of Bobillier formula given in the Galilean plane.

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19

Ersoy, Soley, and Nurten Bayrak. "Bobillier Formula for One Parameter Motions in the Complex Plane." Journal of Mechanisms and Robotics 4, no. 2 (2012). http://dx.doi.org/10.1115/1.4006195.

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This is a brief note expanding on the aspect of Fayet (2002, “Bobillier Formula as a Fundamental Law in Planar Motion,” Z. Angew. Math. Mech., 82(3), pp. 207–210), which investigates the Bobillier formula by considering the properties up to the second order planar motion. In this note, the complex number forms of the Euler Savary formula for the radius of curvature of the trajectory of a point in the moving complex plane during one parameter planar motion are taken into consideration and using the geometrical interpretation of the Euler Savary formula, Bobillier formula is established for one

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20

Gungor, M.A., A.Z. Pirdal, and M. Tosun. "Euler-Savary Formula for the Lorentzian Planar Homothetic Motions." July 27, 2001. https://doi.org/10.5281/zenodo.9471.

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One-parameter planar homothetic motion of 3-lorentzian planes, two are moving and one is fixed, have been considered in ref. [19]. In this paper we have given the canonical relative systems of a plane with respect to other planes so that the plane has a curve on it, which is spacelike or timelike under homothetic motion.

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21

BALGETIR, ÄOZTEKIN Handan, and Mahmut ERGÄUT. "Euler-Savary's Formula for the Planar Curves in Two Dimensional Lightlike Cone." September 27, 2010. https://doi.org/10.5281/zenodo.9267.

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In this paper, we study the Euler-Savary's formula for the planar curves in the lightlike cone. We first define the associated curve of a curve in the two dimensional lightlike cone Q2:Then we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional lightlike cone Q2.

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22

Dooner, David, Ricardo Garcia Garcia, and José M. Rico. "THE BRESSESQUE SURFACE: DISTRIBUTION OF SCREW PITCH." Journal of Mechanisms and Robotics, October 14, 2024, 1–8. http://dx.doi.org/10.1115/1.4066848.

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Abstract Presented is an overview on the T-N interpretation of the famous planar Euler-Savary formula. The T-N spatial analog interpretation consists of two components: the established axial component along with a new transverse component. The axial component entails the spatial Euler-Savary relation involving the Disteli axis and motion parallel to the ISA (Instantaneous Screw Axis). The transverse component emulates the classical planar Euler-Savary relation involving motion perpendicular to the ISA. Within the T-N interpretation is an inflection surface together with a family of Bressesque

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23

Mucahit, AKBIYIK, and YUCE Salim. "The Moving Coordinate System and Euler-Savary's Formula for the One Parameter Motions On Galilean (Isotropic) Plane." July 3, 2017. https://doi.org/10.5281/zenodo.822219.

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In this article, one Galilean (or called Isotropic) plane moving relative to two other Galilean planes (or Isotropic Planes), one moving and the other fixed, was taken into consideration and the relation between the absolute, relative and sliding velocities of this movement and pole points were obtained. Also a canonical relative system for one-parameter Galilean planar motion was defined. In addition, Euler-Savary formula, which gives the relationship between the curvature of trajectory curves, was obtained with the help of this relative system.

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24

Li, Yanlin, Fatemah Mofarreh, and Rashad A. Abdel-Baky. "Kinematic-geometry of a line trajectory and the invariants of the axodes." Demonstratio Mathematica 56, no. 1 (2023). http://dx.doi.org/10.1515/dema-2022-0252.

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Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mec

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