Synthesis of Rectilinear Motion by Mechanical Harmonic Function Generators

1962 ◽  
Vol 84 (1) ◽  
pp. 135-143
Author(s):  
Bernard W. Shaffer ◽  
Irvin Krause
Keyword(s):  
Fourier Series ◽  
Harmonic Function ◽  
Rectilinear Motion ◽  
Function Generators ◽  
General Method

A general method is presented for generating controlled rectilinear motion to any desired accuracy. The required motion is expressed in terms of a Fourier series whose coefficients are shown to be related to the governing dimensions of a plane mechanism. The mechanism may be designed to generate enough terms of the Fourier series to satisfy any desired accuracy. The technique is then used for a particular problem to illustrate its application and the method by which the error of approximation may be evaluated.

Modes of Explanation in the Aristotelian Mechanical Problems

2009 ◽  
Vol 14 (1-3) ◽  
pp. 22-42 ◽  
Author(s):  
Jean De Groot
Keyword(s):  
Basic Principle ◽  
Explanatory Power ◽  
Circular Motion ◽  
Rectilinear Motion ◽  
Posterior Analytics ◽  
Central Argument ◽  
Euclid’S Elements ◽  
General Method

AbstractScholars have been puzzled by the central argument of MP 1 where the author addresses the basic principle behind the balance and lever. It is not clear what is intended to provide the explanation—the dynamic concepts of force and constraint or the geometrical demonstration. Nor is it clear whether the geometrical part of the argument carries any logical force or has value as a proof. This paper makes a case for the cogency of the argument as a kinematic, not dynamic, account. MP 1 proceeds systematically as it extends the explanatory power of the parallelogram of movements from rectilinear motion to circular motion. Euclid's Elements I.43 provides insight on the author's procedure. His general method is demonstrative, as described in Posterior Analytics I.1.

scholarly journals XVIII. On a general method of producing exact rectilinear motion by linkwork

1875 ◽  
Vol 23 (156-163) ◽  
pp. 565-577 ◽  
Keyword(s):  
Accurate Result ◽  
British Association ◽  
Rectilinear Motion ◽  
Parallel Motion ◽  
The Subject ◽  
General Method

Since the invention by James W att, in 1784, of the 3-bar linkwork known as “Watt’s Parallel Motion,” which gives an approximate rectilinear motion, many attempts have been made to obtain a more perfect solution of the problem how to obtain accurate rectilinear motion by means of linkwork. Professor Tchebicheff succeeded in obtaining a 3-bar link-work giving a much closer approximation to a true result; but in his case, as in that of others, the solution is only approximate, and it may be, in fact, shown that with 3 bars an accurate result cannot be obtained. It was not until 1864 that the problem was solved; in that year M. Peaucellier made his memorable discovery of an accurate 7-bar solution; and in 1874, when the subject was brought prominently forward in England by Professor Sylvester, Mr. Hart, in a paper read before the British Association, gave a solution by means of 5 bars. Both these linkworks, as is now well known, depended upon the inversion of a circle with respect to a point on its circumference.

On the Extension of a Fourier Descriptor Based Method for Planar Four-Bar Linkage Synthesis for Generation of Open and Closed Paths

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Feng Gao ◽  
W. Z. Guo
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Efficient Method ◽  
Curve Fitting ◽  
Entire Period ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Closed Curves ◽  
Four Bar Linkage ◽  
General Method

In an earlier work, we have presented an efficient method for synthesizing crank-rocker mechanisms that are capable of generating perceptually simple and smooth low harmonic closed curves. In this paper, we seek to extend this approach to the synthesis of planar four-bar linkages for the generation of open curves. Instead of using Fourier transform that requires a function to be defined over the entire period, we combine finite Fourier series in a curve fitting scheme for the approximation of periodic as well as nonperiodic paths. This yields a general method for planar four-bar path generation that is applicable to both closed and open paths.

Studies of the anisotropy of electron-impurity scattering in metals by the use of the de Haas—van Alphen effect: application to gold

1973 ◽  
Vol 331 (1587) ◽  
pp. 497-523 ◽  
Keyword(s):  
Fourier Series ◽  
Fermi Surface ◽  
Series Representation ◽  
Impurity Scattering ◽  
General Representation ◽  
Fermi Surfaces ◽  
Dilute Alloys ◽  
Inversion Procedure ◽  
Shift Calculation ◽  
General Method

A general method is described for obtaining a map of the variation of the electronic lifetime over the Fermi surface using Dingle temperatures measured in the de Haas—van Alphen effect. The method requires a knowledge of the topography of the Fermi surface, and of the varia­tion of quasiparticle velocities over it. The local electronic lifetimes, Ƭ 8 ( k ), are deduced from the experimentally determined orbitally averaged values by means of an inversion procedure in which a general representation for Ƭ 8 ( k ) is used based, for example, on a Fourier series, harmonic expansion, or phase shift calculation, etc. In applying these ideas to gold we have employed a symmetrized Fourier series representation as used by Roaf (1962) and Halse (1969) in connexion with noble metal Fermi surfaces. Based upon studies of the dH—vA effect in dilute alloys of gold, results are presented in the form of topographic maps, showing the variation of Ƭ 8 ( k ) over the Fermi surface arising out of the presence of dilute concentrations of either Ag, Cu, Zn or Fe as impurity. The results reveal appreciable anisotropy in the electronic lifetime, which differs for different impurities, being most striking in Au(Ag) for which an extreme variation of 4.5:1 is observed, and least for Au(Fe) (at 1.2 K) in which the variation is only ca . 30% over the Fermi surface.

On the Extension of a Fourier Descriptor Based Method for Four-Bar Linkage Synthesis for Generation of Open and Closed Paths

2010 ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Feng Gao ◽  
W. Z. Guo
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Efficient Method ◽  
Curve Fitting ◽  
Entire Period ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Closed Curves ◽  
Four Bar Linkage ◽  
General Method

In an earlier work, we have presented an efficient method for synthesizing crank-rocker mechanisms that are capable of generating perceptually simple and smooth low-harmonic closed curves. In this paper, we seek to extend this approach to the synthesis of four-bar linkages for the generation of open curves. Instead of using Fourier transform that requires a function to be defined over the entire period, we combine finite Fourier series in a curve-fitting scheme for the approximation of periodic as well as non-periodic paths. This yields a general method for four-bar path generation that is applicable to both closed and open paths.

Torsion of beams of ⊥- and ∟- cross-sections

1934 ◽  
Vol 30 (4) ◽  
pp. 392-403 ◽  
Author(s):  
B. R. Seth
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Harmonic Function ◽  
Cross Section ◽  
Cross Sections ◽  
Fundamental Theorem ◽  
Conformal Transformation ◽  
Mathematical Solution ◽  
Rectilinear Polygon ◽  
General Method

The problem of the torsion of beams of ⊥- and L-cross-sections has received attention from very few authors despite its important technical applications. The first mathematical solution in this connection was obtained by F. Kötter in 1908 for an L-section both of whose arms are infinite. He attacked the problem by the use of the known solution of the rectangle and by application of the scheme of conformal transformation. Kötter's method, however, does not lend itself readily to the solution of the problem involving more than one re-entrant angle. The first solution for the torsion of a beam whose cross-section is a rectilinear polygon of n sides was published in 1921 by E. Trefftz who also applied his method to an infinite L-section. Recently I. S. Sokolnikoff has suggested a more general method depending upon the fundamental theorem of potential theory that a harmonic function is uniquely determined by the values assigned along the boundary of the region within which the harmonic function is sought, the boundary condition and the region being subject to certain well-known assumptions of continuity, connectivity, etc. As an illustration of his method he has given an approximate solution for a ⊥-section whose flange and web are both infinite.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

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