Discussion on Minimal Curvature Variation in Cubic Hermite Curve Construction

Abstract We simplify and extend prior work by Held and Spielberger [CAD 2009, CAD&A 2014] to obtain spiral-like paths inside of planar shapes bounded by straight-line segments and circular arcs: We use a linearization to derive a simple algorithm that computes a continuous spiral-like path which (1) consists of straight-line segments, (2) has no self-intersections, (3) respects a user-specified maximum step-over distance, and (4) starts in the interior and ends at the boundary of the shape. Then we extend this basic algorithm to double-spiral paths that start and end at the boundary, and show how these double spirals can be used to cover complicated planar shapes by composite spiral paths. We also discuss how to improve the smoothness and reduce the curvature variation of our paths, and how to boost them to higher levels of continuity. Highlights The algorithm computes a spiral path within planar shapes with and without islands. It respects a user-specified maximum step-over distance. Double spirals and composite spiral paths can be computed. Heuristics for smoothing the spirals are discussed. The algorithm is simple and easy to implement, and suitable for various applications.

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Cutter Path Optimization during High-Speed Machining of Numerical Control

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.341-342.318 ◽

2011 ◽

Vol 341-342 ◽

pp. 318-322

Author(s):

Yong Xiang Gao

Keyword(s):

High Speed ◽

Numerical Control ◽

Process Efficiency ◽

Feed Speed ◽

High Speed Machining ◽

Cutting Depth ◽

Curvature Variation ◽

Cutter Path ◽

Feed Mode ◽

Path Curvature

During the high-speed machining, cutter path of numerical control needs to satisfy the following requirements. There has no colliding among work pieces, fixtures and so on. The cutter path variation cannot too dramatically and the vibration should in the controlled area during the process. Feed speed can modify with path curvature variation and cutting depth need to be equality. This article will analyze and research in the mode of cutter advanced and retreats, cutter movement mode, cutter feed mode and cutter path of corner treatment during the high-speed process programming that could effective optimize cutter path, process efficiency and quality.

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Simulation Analysis of Springback for Lead Frame Copper Alloy

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.560-561.1048 ◽

2012 ◽

Vol 560-561 ◽

pp. 1048-1051 ◽

Cited By ~ 1

Author(s):

Juan Hua Su ◽

Feng Zhang Ren ◽

Ze Yang

Keyword(s):

Integrated Circuit ◽

Copper Alloy ◽

High Performance ◽

Simulation Analysis ◽

Copper Alloys ◽

Lead Frame ◽

Bending Performance ◽

Curvature Variation ◽

Modeling Software ◽

Bending Radius

The bending performance of lead frame materials is a very important in improving the quality of lead frame alloys and meeting the needs of high performance integrated circuit. The sringback amount of curvature variation of CuFeP , CuCrZrMg , CuNiSi and CuCrSnZn alloy are researched by numerical simulation. Bending model is built by 3D modeling software, and the necessary post-processing is carried out. The bending springback amount △K of the four kinds of copper alloy materials are calculated out. The results show that the sringback amount of curvature variation of four copper alloys at the same condition from large to small in turn is CuCrZrMg, CuNiSi, CuFeP, CuCrSnZn. Smaller the minimum relatively bending radius of copper alloy used in lead frame, less the springback amount and better the forming performance.

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Elliptic jets. Part 1. Characteristics of unexcited and excited jets

Journal of Fluid Mechanics ◽

10.1017/s0022112089002843 ◽

1989 ◽

Vol 208 ◽

pp. 257-320 ◽

Cited By ~ 356

Author(s):

Fazle Hussain ◽

Hyder S. Husain

Keyword(s):

Shear Layer ◽

Initial Conditions ◽

Experimental Studies ◽

Three Dimensional ◽

Vortical Structures ◽

Aspect Ratios ◽

Curvature Variation ◽

Section Shape ◽

Plane Jets ◽

Circular Jets

This paper summarizes experimental studies of incompressible elliptic jets of different aspect ratios and initial conditions, and effects of excitations at selected frequencies and amplitudes. Elliptic jets are quite different from the extensively studied plane and circular jets - owing mainly to the fact that the azimuthal curvature variation of a vortical structure causes its non-uniform self-induction and hence complex three-dimensional deformation. Such deformation, combined with properly selected excitation can substantially alter entrainment and other turbulence phenomena, thus suggesting preference for the elliptic shape in many jet applications. The dominance of coherent structures in the jet far field is evident from the finding that switching over of the cross-section shape continues at least up to 100 equivalent diameters De. The locations and the number of switchovers are strongly dependent on the initial condition, on the aspect ratio, and, when excited, on the Strouhal number and the excitation level. We studied jets with constant exit momentum thickness θe, all around the perimeter, thus separating the effects of azimuthal variations of θe, (typical of elliptic jets) and of the shear-layer curvature. Also investigated are the instability characteristics, and enhanced entrainment caused by bifurcation as well as pairing of vortical structures. We discuss shear-layer and jet- column domains, and find the latter to be characterized by two modes : the preferred mode and the stable pairing mode - similar to those found in circular jets -both modes scaling on the newly-defined lengthscale De. The paper documents some time- average measurements and their comparison with those in circular and plane jets.

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Modified theories of gravity with non-minimal curvature-matter coupling

10.1063/1.3462709 ◽

2010 ◽

Author(s):

Orfeu Bertolami ◽

Miguel Carvalho Sequeira ◽

Jean-Michel Alimi ◽

André Fuözfa

Keyword(s):

Modified Theories Of Gravity ◽

Matter Coupling ◽

Theories Of Gravity ◽

Minimal Curvature

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Gravitropic Movement in Wheat Coleoptile is Regulated by Ultradian Growth Oscillations

10.1101/093146 ◽

2017 ◽

Author(s):

Renaud Bastien ◽

Olivia Guayasamin ◽

Stéphane Douady ◽

Bruno Moulia

Keyword(s):

Postural Control ◽

Elongation Rate ◽

Recent Model ◽

Wheat Coleoptile ◽

Differential Growth ◽

Oscillatory Dynamics ◽

Curvature Variation ◽

Perturbation Experiment ◽

The Relationship

AbstractTo stand straight and upright along their growth, plants needs to regulate actively their posture. Gravitropic movement, which occurs when plants modify their growth and curvature to orient their aerial organ against the force of gravity, is a major feature of this postural control. A recent model has shown that graviception and proprioception are sufficient to account for the gravitropic movement and subsequent organ posture demonstrated by a range of species. However, some plants, including wheat coleoptiles, exhibit a stronger regulation of posture than predicted by the model. Here, we performed an extensive kinematics study on wheat coleoptiles during a gravitropic perturbation experiment in order to better understand this unexpectedly strong regulation. Close temporal observation of the data revealed that both perturbed and unperturbed coleoptiles showed oscillatory pulses of elongation and curvature variation that propagated from the apex to the base of their aerial organs. In perturbed (tilted) coleoptiles, we discovered a non-trivial coupling between the oscillatory dynamics of curvature and elongation. This relationship appears to be critical to the postural control of the organ, and indicates the presence of a mechanism that is capable of affecting the relationship between elongation rate, differential growth, and curvature.

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