Design of Mechanisms to Trace Plane Curves

2016 ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Fourier Series ◽  
Algebraic Curve ◽  
Design Methodology ◽  
Plane Curve ◽  
Plane Curves ◽  
The Third ◽  
Universality Theorem ◽  
Serial Chain ◽  
Plane Algebraic Curve ◽  
Trace Curves

This paper describes a mechanism design methodology that assembles standard components to trace plane curves that have a Fourier series parameterization. This approach can be used to approximate complex plane curves to interpolate image boundaries constructed from points. We describe three ways to construct a mechanism that generates a curve from a Fourier series parameterization. One uses Scotch yoke linkages for each term of Fourier series which are added using a belt drive. The second approach uses a coupled serial chain for each coordinate Fourier parameterization. The third method uses one constrained coupled serial chain to trace a specified plane curve. This work can be viewed as a version of the Kempe Universality Theorem that states that a linkage exists that can trace any plane algebraic curve. In our case, we include belts and pulleys, and obtain linkages that trace curves that have Fourier parameterizations.

Design of Mechanisms to Draw Trigonometric Plane Curves

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Fourier Transform ◽  
Design Methodology ◽  
Plane Curve ◽  
Plane Curves ◽  
Trigonometric Functions ◽  
The Third ◽  
Universality Theorem ◽  
Serial Chain ◽  
Cable Drive ◽  
Serial Chains

This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coordinate trigonometric functions, which are then added using a belt or cable drive. The second approach uses two-coupled serial chains obtained from the coordinate trigonometric functions. The third approach combines the coordinate trigonometric functions to define a single-coupled serial chain that draws the plane curve. This work is a version of Kempe's universality theorem that demonstrates that every plane trigonometric curve has a linkage which draws the curve. Several examples illustrate the method including the use of boundary points and the discrete Fourier transform to define the trigonometric curve.

scholarly journals Design of a Linkage System to Write in Cursive

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Mechanical System ◽  
Complex Plane ◽  
Design Methodology ◽  
Plane Curves ◽  
Chinese Characters ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Cursive Handwriting ◽  
Serial Chain ◽  
Serial Chains

This paper presents a design methodology for a system of linkages that can trace planar Bezier curves that represent cursive handwriting of the alphabet and Chinese characters. This paper shows that the standard degree n Bezier curve can be reparameterized so that it takes the form of a trigonometric curve that can be drawn by a one degree-of-freedom coupled serial chain consisting of 2n links. A series of cubic Bezier curves that define a handwritten name yields a series of six-link coupled serial chains that trace these curves. We then show how to simplify this system using cubic trigonometric Bezier curves to obtain a series of four-link serial chains that approximate the system of Bezier curves. The result is a methodology for the design of a mechanical system that draws complex plane curves such as the cursive alphabet and Chinese characters.

Plane Curves With Nodes

1989 ◽  
Vol 41 (2) ◽  
pp. 193-212 ◽  
Author(s):  
Robert Treger
Keyword(s):  
General Position ◽  
Algebraic Curve ◽  
Plane Curve ◽  
Exceptional Case ◽  
Plane Curves ◽  
Nodal Plane ◽  
Nodal Curve

A smooth algebraic curve is birationally equivalent to a nodal plane curve. One of the main problems in the theory of plane curves is to describe the situation of nodes of an irreducible nodal plane curve (see [16, Art. 45], [10], [7, Book IV, Chapter I, §5], [12, p. 584], and [3]).Let n denote the degree of a nodal curve and d the number of nodes. The case (AZ, d) — (6,9) has been analyzed by Halphen [10]. It follows from Lemma 3.5 and Proposition 3.6 that this is an exceptional case. The case d ≦n(n + 3)/6, d ≦(n — 1)(n — 2)/2, and (n, d) ≠ (6,9) was investigated by Arbarello and Cornalba [3]. We present a simpler proof (Corollary 3.8).We consider the main case which is particularly important due to its applications to the moduli variety of curves, compare [19, Chapter VIII, Section 4]. Let Vn,d be the variety of irreducible curves of degree n with d nodes and no other singularities such that each curve of Vn,d can be degenerated into n lines in general position (see [17]).

scholarly journals A bound for the Milnor number of plane curve singularities

2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Arkadiusz Płoski
Keyword(s):  
Singular Point ◽  
Algebraic Curve ◽  
Plane Curve ◽  
Milnor Number ◽  
Plane Curve Singularities ◽  
Curve Singularities ◽  
Plane Algebraic Curve

AbstractLet f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

scholarly journals Plane Curves Which are Quantum Homogeneous Spaces

2021 ◽  
Author(s):  
Ken Brown ◽  
Angela Ankomaah Tabiri
Keyword(s):  
Hopf Algebras ◽  
Final Section ◽  
Homogeneous Spaces ◽  
Plane Curve ◽  
Plane Curves ◽  
Closed Field ◽  
Quantum Homogeneous Space ◽  
Central Elements ◽  
Pointed Hopf Algebras ◽  
Future Work

AbstractLet $\mathcal {C}$ C be a decomposable plane curve over an algebraically closed field k of characteristic 0. That is, $\mathcal {C}$ C is defined in k2 by an equation of the form g(x) = f(y), where g and f are polynomials of degree at least two. We use this data to construct three affine pointed Hopf algebras, A(x, a, g), A(y, b, f) and A(g, f), in the first two of which g [resp. f ] are skew primitive central elements, with the third being a factor of the tensor product of the first two. We conjecture that A(g, f) contains the coordinate ring $\mathcal {O}(\mathcal {C})$ O ( C ) of $\mathcal {C}$ C as a quantum homogeneous space, and prove this when each of g and f has degree at most five or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when g has degree three A(x, a, g) is a PBW deformation of the localisation at powers of a generator of the downup algebra A(− 1,− 1,0). The final section of the paper lists some questions for future work.

The prediction of the cyclic mechanical behavior of stainless steel 304L at room temperature

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hala Messai ◽  
Salim Meziani ◽  
Athmane Fouathia
Keyword(s):  
Stainless Steel ◽  
Design Methodology ◽  
Room Temperature ◽  
Type Model ◽  
Good Prediction ◽  
304L Stainless Steel ◽  
Content Type ◽  
The Third ◽  
Chaboche Model

Purpose The purpose of this paper is to highlight the performance of the Chaboche model in relation to the database identification, tests with imposed deformations were conducted at room temperature on 304L stainless steel specimens. Design/methodology/approach The first two tests were performed in tension-compression between ±0.005 and ±0.01; in the third test, each cycle is composed of the combination of a compression tensile cycle between ±0.01 followed by a torsion cycle between ±0.01723 (non-proportional path), and the last, uniaxial ratcheting test with a mean stress between 250 MPa and −150 MPa. Several identifications of a Chaboche-type model were then performed by considering databases composed of one or more of the cited tests. On the basis of these identifications, the simulations of a large number of ratchet tests in particular were carried out. Findings The results present the effect of the optimized parameters on the prediction of the behavior of materials which is reported in the graphs, Optimizations 1 and 2 of first and second tests and Optimization 4 of the third test giving a good prediction of the increasing/decreasing pre-deformation amplitude. Originality/value The quality of the model's predictions strongly depends on the richness of the database used for the identification of the parameters.

scholarly journals INDIAN SERIALS AND THE INDIAN NATIONAL CENTRE FOR ISSN

2020 ◽  
pp. 359-372
Author(s):  
Viswanath G. S G. S ◽  
Jaya Rawat ◽  
Vijendra Kumar ◽  
G. Mahesh
Keyword(s):  
Higher Education ◽  
Design Methodology ◽  
Regulatory Framework ◽  
Annual Reports ◽  
Information Discovery ◽  
Unique Identifier ◽  
Development Stages ◽  
The Third ◽  
National Centre ◽  
Vital Element

Purpose ISSN, the unique identifier is a vital element for information discovery. This paper chronicles the 35-year journey of the ISSN National Centre, India from its inception in 1986 to the year 2019. It also explores the different development stages of ISSN Indian Centre, and presents the challenges faced by the Centre, particularly in the ISSN assignment process, cataloguing and collaboration. Design/methodology/approach All the data for the article were collected from the in-house records of the ISSN National Centre’s annual reports and other registers for analysis. Findings During the first two decades, on an average of 177 ISSNs were assigned every year. However, during the third decade of 2007 to 2019, on an average of 1573 ISSNs were assigned every year. The spurt in the ISSNs during the last decade have been triggered by certain changes in the higher education regulatory framework in India. Originality/value This is a first-hand account of the ISSN activities of the Centre that also releases data on ISSNs assigned in India.

Optimal trade-in and third-party collection authorization strategies under trade-in subsidy policy

Kybernetes ◽  
2018 ◽  
Vol 47 (5) ◽  
pp. 854-872 ◽  
Author(s):  
Kaiying Cao ◽  
Qiushi Bo ◽  
Yi He
Keyword(s):  
Design Methodology ◽  
Profit Maximization ◽  
The Other ◽  
Third Party ◽  
Subsidy Policy ◽  
Content Type ◽  
The Third ◽  
Optimal Decisions ◽  
The Third Party ◽  
Practical Implications

Purpose This paper aims to study whether the recycling of a third party competes with the trade-in service of a manufacturer, and explores the optimal trade-in and third-party collection authorization strategies for the manufacturer. Design/methodology/approach According to whether to authorize a third party to collect its used products, the manufacturer has two choices: one is not authorization (NA); the other is authorization (A). This paper uses profit-maximization model to investigate the optimal decisions of the manufacturer and the third party under NA and A, respectively, and then explores which choice is better for the manufacturer. Findings It is observed that there is a competition between trade-in service and third-party recycling when the durability parameter of the used product is relatively small. Moreover, when the durability parameter of the used product is relatively large, A is always better choice for the manufacturer; otherwise, NA is a better choice except for the case that the unit trade-in subsidy is low and the salvage of the used product is high. Practical implications These results provide managerial insights for the manufacturer and the third party to make decisions in the field of recycling. Originality/value This paper is among the first papers to study the competition between trade-in program and third party’s collecting program under government’s trade-in subsidy policy. Moreover, this paper presents the conditions under which the manufacturer should authorize or not authorize the third party to collect its used products.

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