• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.861-873
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• 2005

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic Bezier curves. Each approximation method is $G^1$ end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.

• Design & Manufacturing
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• v.17 no.1
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• pp.33-39
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• 2023

The ball end mill is a type of cutting tool that is widely used to process complex mold shapes including aspheric surfaces. Unlike the flat end mill in which the cutting edge is formed on the cylindrical handle, the cutting edge is formed from the cylindrical handle to the hemispherical shape, which is advantageous for processing curved shapes. However, since the cutting speed continuously changes during machining due to the helix angle of the cutting edge or the machining inclination angle, it is difficult to obtain a precise machined surface. Therefore, in this paper, machining was performed while changing the helix angle of the ball end mill and the angle of the machining slope under the same cutting conditions for STD 11 material, which is widely used as a mold material. Through this, the effect of the two variables on the roughness of the machined surface was analyzed. As a result, if the helix angle was 0 degrees, it showed the best surface roughness of Ra. 0.16 ㎛. When the helix angle was 20 degrees, the best surface roughness of Ra. 0.18 ㎛ was occurred.

• Molecules and Cells
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• v.42 no.10
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• pp.729-738
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• 2019

Autophagy is an important process for protein recycling. Oligomerization of p62/SQSTM1 is an essential step in this process and is achieved in two steps. Phox and Bem1p (PB1) domains can oligomerize through both basic and acidic surfaces in each molecule. The ZZ-type zinc finger (ZZ) domain binds to target proteins and promotes higher-oligomerization of p62. This mechanism is an important step in routing target proteins to the autophagosome. Here, we determined the crystal structure of the PB1 homo-dimer and modeled the p62 PB1 oligomers. These oligomer models were represented by a cylindrical helix and were compared with the previously determined electron microscopic map of a PB1 oligomer. To accurately compare, we mathematically calculated the lead length and radius of the helical oligomers. Our PB1 oligomer model fits the electron microscopy map and is both bendable and stretchable as a flexible helical filament.

• Journal of the Korean Geosynthetics Society
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• v.13 no.2
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• pp.41-47
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• 2014

Various prediction methods for the bearing capacity of helical piles have been introduced with consideration of both the steel shaft and the helix plates attached to the shaft. In this paper, three representative methods, that is, individual bearing method, cylindrical shear method, and torque correlation method are discussed and compared to each other. The prediction methods were verified by comparing with a series of loading test results performed on moderate-size helical piles from the companion paper. As a result, the measured bearing capacity is greater than the bearing capacity predicted by the cylindrical shear method, but smaller than that of the individual bearing method. In addition, the bearing capacity predicted by the torque correlation method is in good agreement with the measured bearing capacity.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.221-238
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• 2016

One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non-cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.

• Wind and Structures
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• v.30 no.1
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• pp.15-27
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• 2020

This paper reports the study on development and verification of numerical models and analyzes of flow at high speed around structural elements in the shape of a curved pipe (e.g., a fragment of a water slide). Possibility of engineering estimation of wind forces acting on an object in the shape of a helix is presented, using relationships concerning toroidal and cylindrical elements. Determination of useful engineering parameters (such as aerodynamic forces, pressure distribution, and air velocity field) is presented, impossible to obtain from the existing standard EN 1991-1-4 (the so-called wind standard). For this purpose, flow at high speed around a torus and helix, arranged both near planar surface and high above it, was analyzed. Analyzes begin with the flow around a cylinder. This is the simplest object with a circular cross-section and at the same time the most studied in the literature. Based on this model, more complex models are analyzed: first in the shape of half of a torus, next in the shape of a helix.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.714-719
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• 2004

This paper presents two numerical algorithms for registration of cross-sectional medical images such as CT (Computerized Tomography) or MRI (Magnetic Resonance Imaging) by using geometrical information from helix or line fiducials. The registration algorithms are designed to be used for a surgical robot working inside cavities of human body. A cylindrical device with a combination of line and helix fiducials were also devised and is supposed to be attached to the end-effector of surgical robot. The algorithms and the fiducial pattern were tested in various computer-simulated situations, and the results indicate excellent overall registration accuracy.

• Proceedings of the Polymer Society of Korea Conference
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• 2006.10a
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• pp.173-173
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• 2006

We have explored a strategy to control the supramolecular nano-structures self-assembled from rigid segments through attachment of flexible chains through microphase separation and anisotropic arrangement. Supramolecular structures formed by self-assembly of rigid building blocks can be precisely controlled from 1-D layered, 3-D bicontinuous cubic to 2-D cylindrical structures by systematic variation of the type and relative length of the respective blocks. Furthermore, depending on the individual molecular architectures, rigid building blocks self-assemble into a wide range of supramolecular structures such as honeycomb, disk, cylinder, helix, tube, barrel stave, and nano-cage.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.144-149
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• 1996

In this paper, the clamping type forging of helical gears has been investigated. Clamping type forging is an operation in which the product is constrained to extrude sideways through an orifice in the container wall. Punch is cylindrical shaped. The punch compresses a cylindrical billet placed in a die insert. As a consequence the material flows in a direction perpendicular to that of punch movement. The forging has been analysed by using the upper-bound method. A kinematically admissible velocity field has been developed, wherein, an involute curve has been introduced to represent tooth profile of the gear. Numerical calculations have been carried out to investigate the effects of various parameters, such as module, number of teeth, helix angle, friction factor and initial height of billet on the forging of helical gears.

• Steel and Composite Structures
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• v.21 no.3
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• pp.605-628
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• 2016

The energy absorption characteristics of diamond core sandwich cylindrical columns under axial crushing process depend greatly on the amount of material which participates in the plastic deformation. Both the single-objective and multi-objective optimizations are performed for columns under axial crushing load with core thickness and helix pitch of the honeycomb core as design variables. Models are optimized by multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). Results show that optimization improves the energy absorption characteristics with constrained and unconstrained peak crashing load. Also, it is concluded that the aluminum tube has a better energy absorption capability rather than steel tube at a certain peak crushing force. The results justify that the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. A ranking technique for order preference (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a multi-criteria decision which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. Furthermore, local and global sensitivity analyses are performed to assess the effect of design variable values on the SEA and PCF functions in design domain. Based on the sensitivity analysis results, it is concluded that for both models, the helix pitch of the honeycomb core has greater effect on the sensitivity of SEA, while, the core thickness has greater effect on the sensitivity of PCF.