Kinematical Aspects of Levi-Civita Transport of Vectors and Tensors Along a Surface Curve

2016 ◽  
pp. 213-249
Author(s):  
James Casey
Keyword(s):  
Surface Curve

A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Talat Körpınar ◽  
Yasin Ünlütürk
Keyword(s):  
Vector Fields ◽  
Elastic Surface ◽  
Geometrical Characterization ◽  
Lorentzian Space ◽  
New Approach ◽  
Darboux Vector ◽  
Moving Particle ◽  
The Relationship ◽  
Surface Curve

AbstractIn this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper by providing bienergy-curve graphics for different cases.

Designing and Mapping Trimming Curves on Surfaces Using Orthogonal Projection

1990 ◽  
Author(s):  
Joseph Pegna ◽  
Franz-Erich Wolter
Keyword(s):  
Differential Equation ◽  
Orthogonal Projection ◽  
Broad Class ◽  
Design Tool ◽  
Space Curve ◽  
Computationally Efficient ◽  
Curves On Surfaces ◽  
Surface Representations ◽  
Differential Properties ◽  
Surface Curve

Abstract In the design and manufacturing of shell structures it is frequently necessary to construct trimming curves on surfaces. The novel method introduced in this paper was formulated to be coordinate independent and computationally efficient for a very general class of surfaces. Generality of the formulation is attained by solving a tensorial differential equation that is formulated in terms of local differential properties of the surface. In the method proposed here, a space curve is mapped onto the surface by tracing a surface curve whose points are connected to the space curve via surface normals. This surface curve is called to be an orthogonal projection of the space curve onto the surface. Tracing of the orthogonal projection is achieved by solving the aforementionned tensorial differential equation. For an implicitely represented surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This method has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations. Orthogonal projection of a curve onto a surface was also developed in the context of surface blending. The orthogonal projection of a curve onto two surfaces to be blended provides not only a trimming curve design tool, but it was also used to construct smooth natural maps between trimming curves on different surfaces. This provides a coordinate and representation independent tool for constructing blend surfaces.

After Grinding NC Grinding of Large Curved Surface

2013 ◽  
Vol 819 ◽  
pp. 3-6
Author(s):  
Hong Yu Han ◽  
Lu Fu ◽  
Ying Liang Yu
Keyword(s):  
Grinding Wheel ◽  
Machining Accuracy ◽  
Wheel Wear ◽  
Large Circle ◽  
Cnc Grinding ◽  
Scope Of Application ◽  
Circular Surface ◽  
Half Axis ◽  
Nc Grinding ◽  
Surface Curve

Additional power head with common milling machine.Two and a half axis CNC system are used for CNC grinding circular surface curve trajectory. The advantages of this processing method are: We can avoid the influence on processing of lead screw clearance because of changing the parts clamping position,effectively ensure the integrity of the great circle arc curve trajectory. Because of using digital control technology in grinding process is instantaneous automatic compensation of grinding wheel wear, the machining accuracy of parts in outline is improved, the machining error is decreased. it will effectively ensure the consistency of the large circle curve precision.This method has the effect of infer other things from one fact for CNC grinding of large circular arc curve parts. Broaden the scope of application of CNC technology and practical.

Analysis on the Scattering Characteristics of Two Stray Light Removing Metal Surfaces

2012 ◽  
Vol 571 ◽  
pp. 115-119
Author(s):  
Jian Jun Chen ◽  
Zhen Ma ◽  
Xue Ting Duan ◽  
Qiong Liu ◽  
Juan Han ◽  
...  
Keyword(s):  
Specular Reflection ◽  
Measurement Data ◽  
Measuring Method ◽  
Stray Light ◽  
Aluminum Surface ◽  
Experiment Research ◽  
Anodized Aluminum ◽  
Optical System Design ◽  
Objective Reference ◽  
Surface Curve

For the purpose of stray light suppression, black anodized and sandblasted aluminum alloy is widespread used in spaceborne cameras. Base on the relative measuring method, in the white light irradiation, measure relative backscatter intensity and BRDF of two black anodized and sandblasted sample surfaces. Contrast these surfaces scattering characteristics. Finally BRDF curves have been drawn with measurement data. In the curves, the BRDF of sandblasted aluminum surface is nearly linear relation. Anodized surface curve, it’s pulse pattern that BRDF sharply increases among the region of critical angles. It is indicate that in critical angle range, anodized aluminum surface specularity is visible and can be treated as specular reflection which harm for stray light suppression. This experiment research can provide objective reference of these two material’s scattering characteristics in specific optical system design.

Surface-Curve Contact in 4-Axis NC Machining of Sculptured Surfaces Using Anural Cutter

2010 ◽  
Vol 37-38 ◽  
pp. 1372-1375
Author(s):  
Hu Ran Liu
Keyword(s):  
Differential Equation ◽  
Nc Machining ◽  
Sculptured Surfaces ◽  
End Mill ◽  
Ball End Mill ◽  
Axis Orientation ◽  
Milling Tool ◽  
Swept Surface ◽  
Complicated Surface ◽  
Surface Curve

This is the highly effective method. In this paper an innovative theory for machining complicated surface is presented. By using a anural milling tool instead of ball-end mill or the flat-ended tool, and by adjusting the axis of cutter relative to the surface, the two surfaces, the swept surface and the required surface, have the same curvatures, up to as high as 3rd order. Through the deduction of differential equation, some theory on partial touching between surfaces and surfaces when manufacturing has been explored. The problem of axis orientation under this condition has also been discussed clearly. The outside of the circular tool is a surface; the surface to be machined is a groove, which can be represented by its transverse line. In this case the problem is attributed to the contact between surface and curve.

The Diagnosis Research of Cover Sheet Spring Recover on the Compensate Fuzzy Nerve Net of Multi-Input Defer

2014 ◽  
Vol 599-601 ◽  
pp. 1883-1886
Author(s):  
Zhan Jun Liu
Keyword(s):  
Model Error ◽  
Building Model ◽  
Nerve Net ◽  
Cover Sheet ◽  
Number Curve ◽  
Surface Curve

The model of compensate fuzzy nerve net on multi-input defer is built. The net frame and studied algorithm of compensate fuzzy nerve net on multi-input defer is introduced .It is used that practical use on multi-input defer and higher containing mistake of compensate fuzzy nerve net, and it is given that the building model error tortuous surface, curve of net input and curve of all error number curve, which is combined with goal example. The result is showed in spring recover of cover sheet that the all error of compensate fuzzy nerve net on multi-input defer is reduced by 7.5 percent, and diagnostic precision is increased by 6.3 percent.

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