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Relevant bibliographies by topics / Dual spherical curve

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Academic literature on the topic 'Dual spherical curve'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Dual spherical curve"

1

Abdel-Baky, Rashad A., and Fatemah Mofarreh. "On an Explicit Characterization of Spherical Curves in Dual Lorentzian 3-Space D 1 3." Mathematical Problems in Engineering 2022 (June 25, 2022): 1–9. http://dx.doi.org/10.1155/2022/3044305.

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In this study, we developed a mathematical framework for studying spherical and null curves in dual Lorentzian 3-space D 1 3 . Considering the causal character of the dual curve, sufficient and necessary conditions for spacelike curves to be dual Lorentzian spherical were given. Also, new sufficient and necessary conditions for non-null curves to be hyperbolic dual spherical were presented. Then, an insight on curves with null-principal normal is reported.

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2

Taş, Ferhat, and Kazım İlarslan. "A new approach to design the ruled surface." International Journal of Geometric Methods in Modern Physics 16, no. 06 (2019): 1950093. http://dx.doi.org/10.1142/s0219887819500932.

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This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples

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3

Li, Yanlin, Yushu Zhu, and Qing-You Sun. "Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space." International Journal of Geometric Methods in Modern Physics 18, no. 01 (2020): 2150008. http://dx.doi.org/10.1142/s0219887821500080.

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For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space [Formula: see text] and a given point P, we can define naturally the pedal curve of [Formula: see text] relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities and locations of pedal points when the pseudo-sphere dual curve germs are nonsingular. Furthermore, we obtain the extension results in dualities, which has wid

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4

Liu, Haiming, and Donghe Pei. "Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/512020.

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The relatively parallel adapted frame or Bishop frame is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of biology, engineering, and computer graphics. The main result of this paper is using the relatively parallel adapted frame for classification of singularity type of Bishop spherical Darboux image and Bishop dual which are deeply related with a space curve and making them visualized by computer.

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McCarthy, J. M. "The Opposite Pole Quadrilateral as a Compatibility Linkage for Parameterizing the Center Point Curve." Journal of Mechanical Design 115, no. 2 (1993): 332–36. http://dx.doi.org/10.1115/1.2919196.

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In planar four-position kinematics, the centers of circles containing four positions of a point in a moving rigid body form the center point curve. This curve can be parameterized by analyzing a “compatibility linkage” obtained from a complex number formulation of the four-position problem. In this paper, we present another derivation of the center point curve using a special form of dual quaternions and the fact that it is identical to the pole curve. The defining properties of the pole curve lead to a parameterization by kinematic analysis of the opposite pole quadrilateral as a four-bar lin

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6

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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Jamal and Morgan. "Characterization of Material Properties Based on Inverse Finite Element Modelling." Inventions 4, no. 3 (2019): 40. http://dx.doi.org/10.3390/inventions4030040.

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This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker–Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element softwar

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8

Sahiner, Burak, Mustafa Kazaz, and Hasan Ugurlu. "A study on motion of a robot end-effector using the curvature theory of dual unit hyperbolic spherical curves." Filomat 30, no. 3 (2016): 791–802. http://dx.doi.org/10.2298/fil1603791s.

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In this paper we study the motion of a robot end-effector by using the curvature theory of a dual unit hyperbolic spherical curve which corresponds to a timelike ruled surface with timelike ruling generated by a line fixed in the end-effector. In this way, the linear and angular differential properties of the motion of a robot end-effector such as velocities and accelerations which are important information in robot trajectory planning are determined. Moreover, the motion of a robot end-effector which moves on the surface of a right circular hyperboloid of one sheet is examined as a practical

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Song, Yong Hui, Yong Yang, Wen Wen Gao, and Xin Zhe Lan. "Preparation of Silver Nanoplates in SDBS System." Materials Science Forum 620-622 (April 2009): 533–36. http://dx.doi.org/10.4028/www.scientific.net/msf.620-622.533.

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Silver nanoplates were prepared in the solution of sodium dodecyl benzene sulfonate (SDBS) and polyvinyl pyrrolidone (PVP) via reducing silver nitrate with hydrazine hydrate. X-ray diffraction (XRD) and Scanning electron microscope (SEM) were applied to identify phase and observe microstructure. The surface tension analysis showed that in SDBS + PVP system, the γ-C curve acted as dual-platform and the corresponding concentration turning points were C1 (0.8g/L) and C2 (6.0g/L) respectively. XRD analysis confirmed that the reduction product was element silver. SEM observation revealed that nano-

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10

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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Book chapters on the topic "Dual spherical curve"

1

Ericson, Thomas. "Spherical Codes Generated from Self-Dual Association Schemes." In Codes, Curves, and Signals. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5121-8_8.

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Conference papers on the topic "Dual spherical curve"

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Ge, Q. J., and Donglai Kang. "Geometric Design of Smooth Composite Ruled Surface Strips Using Dual Spherical Geometry." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0086.

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Abstract This paper deals with geometric construction of smooth composite ruled surface strips. Oriented lines that constitute the rulings of the ruled surfaces are represented by unit vectors with three components over the ring of dual numbers. The problem of designing a smooth ruled surface is studied as that of designing a one-real-parametric curve on the unit dual sphere. Geometric conditions for piecing two ruled surfaces smoothly are developed using differential geometry of curves on the dual sphere. A coordinate-frame invariant method for line segmentation is also presented. Finally, a

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2

Huran, Liu. "The Machining of the Spherical Gear With Concave Cone Teeth and Its Cutting Tool." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10074.

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The spherical gear, or globular gear is a ball, on the ball there are a series of holes. The spherical gear is the key component of the robot’s wrist. As shown in fig.1, by using the spherical crowns of two different spherical centers as a joint curve surface, and their spherical center as a rotational center, the spherical gearing can be formed on two spherical surfaces with convex teeth and concave teeth engaging each other. The robot’s wrist differs from the wrist of human kind in that, it can transmit rotational movement from the upper arm to the lower arm continuously, while the angle bet

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3

Purwar, Anurag, Zhe Jin, and Q. J. Ge. "Computer Aided Synthesis of Rational Motion Under Kinematic Constraints of Spatial SS Open Chains." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49954.

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In this paper, we study the problem of rational motion interpolation under kinematic constraints of spatial SS open chains. The objective is to synthesize a smooth rational motion that interpolates a given set of end effector positions and satisfies the kinematic constraints imposed by spatial SS open chains. The kinematic constraints under consideration define a constraint manifold representing all the positions available to the end effector. By choosing dual quaternion representation for the displacement of the end effector, the problem is reduced to designing a smooth curve in the space of

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4

Choi, Junghun. "The Elastic Limits of Colon Tissues for Different Radii of a Tool Tip End Using a Simple Modeling." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38672.

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Mechanical properties of colon tissues are very important to prevent trauma and perforation during colonoscopy procedure. Most of forces are generated by the shaft of a colonoscope and a distal tip. A shaft of a colonoscope causes mechanical trauma at various locations. A distal tip of a colonoscope can cause not only for mechanical trauma but also serious perforation. In this study, elastic limits of forces were predicted for different sizes of a simplified shape of a tool tip end with a simple characteristic modeling. Published data on the various parts of a colon were used for the reference

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