Curvature Theory on Contact and Transfer Characteristics of Enveloping Curves

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Transfer Rate ◽  
Contact Point ◽  
Kinematic Model ◽  
Rigid Bodies ◽  
Transfer Velocity ◽  
The Third ◽  
Transfer Characteristics ◽  
Curvature Theory ◽  
Transfer Properties

Abstract In differential geometry, a curve is characterized by the curvature properties and so is a point trajectory in curvature theory. However, due to the rolling and sliding between contact curves, the characterization of enveloping curves embedded on rigid bodies in relative motion is not complete without the transfer rate of the contact point. This paper presents the new perspectives on not only the curvature characteristics but also the transfer characteristics between enveloping curves embedded on rigid bodies. The paper contains three parts. First, a pair of enveloping curves can be described by a point trajectory which traces two curves simultaneously. Second, the paper treated instant center as a tracing point, which traces the moving centrode and the fixed centrode on each of the bodies. This characterizes the rolling between centrodes and the transfer rate of the instant center on each of centrodes. The treatment can extend the instant center transfer velocity to any higher order. The third part is about the rolling and sliding between enveloping curves embedded on rigid bodies motion. A kinematic model to describe the transfer rate of contact point based on the motion of the instant center is proposed. The detailed curvature and transfer properties of line- and circle-envelopes are presented. Due to the simple treatment, this might be the first paper that successfully achieved the curvature properties of circle-envelopes. The method offers the vital kinematic aspect of enveloping curves distinctly different from the conventional curvature theory and enveloping theory.

Curvature Theory on Contact and Transfer Characteristics of Enveloping Curves

2018 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Cody Leeheng Chan
Keyword(s):  
Relative Motion ◽  
Contact Point ◽  
Rigid Bodies ◽  
Body Motion ◽  
Transfer Characteristics ◽  
Moving Body ◽  
Curvature Theory ◽  
The Veil ◽  
Motion Characteristics ◽  
Definition Of

In differential geometry, a curve is characterized by the curvature properties and so is a point trajectory in curvature theory. However, due to the rolling and sliding between contact curves, the characterization of enveloping curves embedded on rigid bodies in relative motion is not complete without the transfer (or shifting) characteristics of the contact point. This paper presents the new perspectives and the first comprehensive theory on not only the curvature characteristics but also the transfer characteristics between enveloping curves embedded on rigid bodies. The paper contains three parts. In the first part, a point traces a curve on the moving body and consequently traces a curve on the fixed body. Both generated curves form a pair of enveloping curves. This part establishes the foundation of the paper. Because each enveloping curve is treated as a point trajectory. One may examine all aspects of the enveloping process. Essentially this unmasks the veil that has hindered further understanding and observation of the enveloping behavior beyond the fundamental curvature. It represents a significant advancement on envelope theory. In the second part, the moving point is the instant center, which traces the moving centrode on the moving body and the fixed centrode on the fixed body. It characterizes the rolling between centrodes and the transfer characteristics of the instant center on each centrode. It not only offers a simple way to treat the instant center transfer (shifting) velocity but also successfully extends it to any order of motion. The third part is about the rolling and sliding of between enveloping curves embedded on rigid bodies in relative motion. It addresses the transfer characteristics of the contact on each of the contact curves for the first time. The transfer characteristics are functions of the rigid body motion characteristics. This part offers the vital kinematic aspect of enveloping curves distinctly different from the conventional curvature theory that addresses an individual curve. The proposed enveloping curvature theory offers an important model to account for all aspects of the contact and removes the veil that blurs the contact behavior caused by the traditional envelope definition of Fλxy=∂F∂λλxy=0. This is a kinematic solution for envelopes. The proposed theory is illustrated with an example of two rolling cylinders.

Gaunilo Parodies Anselm

2014 ◽  
Vol 17 (1) ◽  
pp. 45-71
Author(s):  
Geo Siegwart
Keyword(s):  
Detailed Comparison ◽  
The Third ◽  
Common Structure ◽  
Logical Reconstruction ◽  
Points Of View ◽  
And Function

The main objective is an interpretation of the island parody, in particular a logical reconstruction of the parodying argument that stays close to the text. The parodied reasoning is identified as the proof in the second chapter of the Proslogion, more specifically, this proof as it is represented by Gaunilo in the first chapter of his Liber pro insipiente. The second task is a detailed comparison between parodied and parodying argument as well as an account of their common structure. The third objective is a tentative characterization of the nature and function of parodies of arguments. It seems that parodying does not add new pertinent points of view to the usual criticism of an argument.

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

Optical Characterization of Silica Aerogel

1988 ◽  
Vol 121 ◽  
Author(s):  
Lawrence W. Hrubesh ◽  
Cynthia T. Alviso
Keyword(s):  
Silica Aerogel ◽  
Porous Silica ◽  
Optical Characterization ◽  
Optical Methods ◽  
Gradient Index ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
The Third ◽  
Third Dimension

ABSTRACTTwo optical methods are described for mapping the local variations of refractive index within monoliths of porous silica aerogel. One is an interferometrie measurement that produces “iso-index” fringes in a two dimensional image; an orthogonal view gives the third dimension information. The other method uses the deflection of a He-Ne laser beam to map the gradient index within a sample. The quantification of the measurements is described and the accuracy of the results is discussed.

Warfare, oracles and iron: a case study of production among the pre-colonial Klowe, in the light of some recent Marxist analyses

Africa ◽  
1984 ◽  
Vol 54 (2) ◽  
pp. 29-48 ◽  
Author(s):  
David Brown
Keyword(s):  
Third World ◽  
Theoretical Work ◽  
Central Place ◽  
Marxist Theory ◽  
The Third ◽  
Definition Of ◽  
Opening Paragraph ◽  
The Third World

Opening ParagraphIt is perhaps surprising that the recent resurgence of interest in the application of Marxist theory to the study of the historically non-capitalist societies of the Third World should have focused, at least in part, upon the stateless societies of Africa. To some extent, this interest in some of the least differentiated and least class-stratified of societies can be related to the fundamental problematic of Marxist sociology: the characterization of the stage of advanced communism, which remains so obscure in Marx's own theoretical work. An understanding of the dynamics of ‘primitive’ communism might be seen, therefore, as an essential precursor to this underlying concern. Certainly, the often highly tendentious views of Marxist writers on such issues as the definition of the state and the extent of exploitation in the primitive communist mode can be related to this need. However, the rise of Marxist anthropology has not only been presented as a problem of general evolutionary theory. Other influences have been offered to account for the new concern, the most widely cited being the supposed crisis of functionalism, and the resulting necessity for a complete reorientation of the whole discipline of anthropology. Stateless societies, having long occupied a central place in the field of anthropological enquiry, and yet outwardly presenting such simplicity of form, offer a particular challenge to the radical, and in several recent works have been interpreted in what is claimed to be a novel and distinctive way.

scholarly journals Expression, Purification, and Characterization of (R)-Sulfolactate Dehydrogenase (ComC) from the Rumen MethanogenMethanobrevibacter milleraeSM9

Archaea ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yanli Zhang ◽  
Linley R. Schofield ◽  
Carrie Sang ◽  
Debjit Dey ◽  
Ron S. Ronimus
Keyword(s):  
Biosynthetic Pathway ◽  
Critical Role ◽  
Reduction Reaction ◽  
Coenzyme M ◽  
Purification And Characterization ◽  
The Third ◽  
Optimal Activity ◽  
Methyl Coenzyme M Reductase

(R)-Sulfolactate dehydrogenase (EC 1.1.1.337), termed ComC, is a member of an NADH/NADPH-dependent oxidoreductase family of enzymes that catalyze the interconversion of 2-hydroxyacids into their corresponding 2-oxoacids. The ComC reaction is reversible and in the biosynthetic direction causes the conversion of (R)-sulfolactate to sulfopyruvate in the production of coenzyme M (2-mercaptoethanesulfonic acid). Coenzyme M is an essential cofactor required for the production of methane by the methyl-coenzyme M reductase complex. ComC catalyzes the third step in the first established biosynthetic pathway of coenzyme M and is also involved in methanopterin biosynthesis. In this study, ComC fromMethanobrevibacter milleraeSM9 was cloned and expressed inEscherichia coliand biochemically characterized. Sulfopyruvate was the preferred substrate using the reduction reaction, with 31% activity seen for oxaloacetate and 0.2% seen forα-ketoglutarate. Optimal activity was observed at pH 6.5. The apparentKMfor coenzyme (NADH) was 55.1 μM, and for sulfopyruvate, it was 196 μM (for sulfopyruvate theVmaxwas 93.9 μmol min−1 mg−1andkcatwas 62.8 s−1). The critical role of ComC in two separate cofactor pathways makes this enzyme a potential means of developing methanogen-specific inhibitors for controlling ruminant methane emissions which are increasingly being recognized as contributing to climate change.

Unraveling Paradoxical Theories for Rigid Body Collisions

1991 ◽  
Vol 58 (4) ◽  
pp. 1049-1055 ◽  
Author(s):  
W. J. Stronge
Keyword(s):  
Frictional Force ◽  
Contact Point ◽  
Tangential Velocity ◽  
Velocity Slip ◽  
Rigid Bodies ◽  
Contact Points ◽  
Before And After ◽  
Limited Applicability ◽  
Work Done ◽  
Impulsive Reaction

A collision between two rigid bodies has a normal impulsive reaction at the contact point (CP). If the bodies are slightly rough and the contact points have a relative tangential velocity (slip), there is also a frictional force that opposes slip. Small initial slip can halt before contact terminates; when slip halts the frictional force changes and the collision process is separated into periods before and after halting. An energetically consistent theory for collisions with slip that halts is based on the work done by normal (nonfrictional) forces during restitution and compression phases. This theory clearly separates dissipation due to frictional forces from that due to internal irreversible deformation. With this theory, both normal and tangential components of the impulsive reaction always dissipate energy during collisions. In contrast, Newton’s impact law results in calculations of paradoxical increases in energy for collisions where slip reverses. This law relates normal components of relative velocity for the CP at separation and incidence by a constant (the coefficient of restitution e). Newton’s impact law is a kinematic definition for e that generally depends on the slip process and friction; consequently it has limited applicability.

scholarly journals H. Walpole’s “Historic Doubts” in his Characterization of Richard III

2020 ◽  
Vol 20 (3) ◽  
pp. 337-343
Author(s):  
Natalia S. Krelenko ◽  
Keyword(s):  
Richard Iii ◽  
The Third

The article deals with the analysis of H. Walpole’s “Historic Doubts on the Life and Reign of King Richard the Third”. The focus of the article is on the attempt of reconsideration and rehabilitation of English king Richard III. An amateur historian and expert on the subtleties of politics, H. Walpole tried to establish a link between the development of the image of Richard III and political atmosphere prevailing in England after his death. Walpole’s work contains an interesting analysis of the views of the authors whose writings formed the basis of historical portrait of the last king of the House of York. It also contains a few remarks on the role and importance of history in society.

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