Oval Curves Research Articles

Continuum robots: Developing dexterity evaluation algorithms using efficient inverse kinematics

Performance evaluation and inverse kinematics (IK) for continuum robots are always hard and time-consuming. In this paper, an efficient dexterity evaluation algorithm based on IK (DEAIK) for continuum robots is proposed. The IK model is established using an oval curve equation to improve computational efficiency. The relationship between length distributions and dexterity distribution is obtained by the simulation in this paper. Length distribution of the two-segment continuum robot is optimized under the guidance of the dexterity indices using the fruit fly algorithm. Theoretical analysis and numerical simulations demonstrate that the dexterity of the structure-optimized continuum robot is better than that of the traditional continuum robot. The simulation shows that the DEAIK algorithm is 3.68 times faster than the algorithm based on forward kinematics. The IK algorithm in this paper is 3 203 times faster than the IK algorithm based on the Levenberg-Marquardt algorithm in the same accuracy. This work is significant for designing a high-performance continuum robot.

一类参数式李氏卵形曲线

一类参数式李氏卵形曲线

S-Shaped Transition Curves as an Element of Reverse Curves in Road Design

A road designing involves horizontal and vertical alignment. The horizontal geometry is formed by straight and curvilinear sections that are traditionally formed using circular and transition curves (mainly the clothoid). Different geometric systems that are designed using circular and transition curves are between others circular curves with symmetrical or unsymmetrical clothoids, combined curves, oval curves and reverse curves. Designing these systems is quite complex. Therefore, so-called S-shaped transition curves are an alternative to traditional approaches. These curves are known from literature and are modern geometric tools for the shaping of reverse curves. The paper analyses the basic geometric properties of these curves as well as compare to the geometry of the appropriate geometric systems, which are formed with clothoid or using S-shaped transition curves. In addition, a procedure for designing reverse curves using S-shaped transition curves was proposed. Another research topic was the comparison of the analysed reverse curves (created using polynomial transition curves) with traditional curves (created using the clothoid). The results of the studies, despite the noticeable differences in the geometry of the compared components, confirm the practical usefulness of the S-shaped transition curves for designing the geometry of the route.

Modelling levitated 2-lobed droplets in rotation using Cassinian oval curves

A simple model of rotating 2-lobed droplets is proposed by setting the outline shape of the droplet to the Cassinian oval, a mathematical curve that closely resembles in shape. By deriving the governing equation of the proposed model and obtaining its stationary solutions, the relationship between the angular velocity of rotation and the maximum deformation length is explicitly and precisely calculated. The linear stability analysis is performed for the stationary solutions, and it is demonstrated that the stability of the solutions depends only on the ratio of the deformation length to the radius of the central cross-section of the droplet, which is independent of the physical properties of the droplet. Via comparison with an experimental study, it is observed that the calculated result is consistent with the deformation behaviour of actual 2-lobed droplets in the range where the stationary solution of the proposed model is linearly stable. Therefore, the proposed model is a suitable model for reproducing the steady deformation behaviour of 2-lobed droplets in a wide range of viscosities, surface tensions, densities and initial radii of the droplet, and especially if the viscosity of the droplet is low, the entire process of deformation of the 2-lobed droplet, including the unsteady breakup process, can be very well reproduced by the proposed model.

James Clerk Maxwell (1831-1879)

JAMES Clerk MAXWELL, the celebrated Natural Philosopher and the father of electromagnetism, who laid the foundations for modern telecommunications theory, systems and applications, was born in 1831 in 14 India Street Edinburgh, Scotland. He was brought up at his father's country estate, Glenlair House in Dumfriesshire, Scotland, and he attended school at the Edinburgh Academy. Maxwell was a precocious child; he wrote his first paper on Oval Curves, when he was only 14 years old. The paper was presented to the Royal Society of Edinburgh-Scotland's national academy-on his behalf by James Forbes, Professor of Natural Philosophy at the University of Edinburgh, in 1846.

Towards an alternative gravitational theory

In 1680, Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadowed by the Kepler's first law (1609), namely the planets move around the sun describing conic orbits. Here, we describe the possibility that the Cassini's idea works at larger or smaller scales. Indeed, we consider the Spiric curves (which are a generalization of the Cassini oval) and present the first steps towards a Spiric gravitational theory. We show that from our formalism an ellipse associated with a planet can be obtained as a particular case.

Microlensed image centroid motions by an exotic lens object with negative convergence or negative mass

Gravitational lens models with negative convergence inspired by modified gravity theories, exotic matter and energy have been recently examined, in such a way that a static and spherically symmetric modified spacetime metric depends on the inverse distance to the $n$-th power ($n=1$ for Schwarzschild metric, $n=2$ for Ellis wormhole, and $n \neq 1$ for an extended spherical distribution of matter such as an isothermal sphere) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013), Izumi et al. PRD 88 024049 (2013)]. Some of the models act as if a convex lens, whereas the others are repulsive on light rays like a concave lens. The present paper considers microlensed image centroid motions by the exotic lens models. Numerical calculations show that, for large $n$ cases in the convex-type models, the centroid shift from the source position might move on a multiply-connected curve like a bow tie, while it is known to move on an ellipse for $n=1$ case and to move on an oval curve for $n=2$. The distinctive feature of the microlensed image centroid may be used for searching (or constraining) localized exotic matter or energy with astrometric observations. It is shown also that the centroid shift trajectory for concave-type repulsive models might be elongated vertically to the source motion direction like a prolate spheroid, whereas that for convex-type models such as the Schwarzschild one is tangentially elongated like an oblate spheroid.

The great Martian catastrophe and how Kepler fixed it

For a few weeks every 32 years, both the Ptolemaic and Copernican predictions for the position of Mars are off by close to 5 degrees—a problem first noticed by Tycho Brahe.

Measurement of pulmonary function with body plethysmograph in infants

To observe the alterations of pulmonary function in infants with respiratory diseases. A total of 900 infants with respiratory diseases were recruited and pulmonary function measured in 30 healthy infants. The tests were performed in the sleeping infants with sedation. Tidal breathing flow-volume (TBFV) loops were recorded when infants were breathing quietly. Passive flow-volume technique was used to obtain static respiratory system compliance and resistance. Functional residual capacity was measured by body plethysmograph. The TBFV loop showed proximate round or oval curve in healthy infants. The shape and parameters of TBFV loop had significant differences in infants with respiratory diseases as compared with healthy controls. The TBFV loop displayed a concave expiratory curve and ratio of time to reach tidal peak flow to total expiratory time, the expiratory volume till peak flow divided by the total expiratory volume significantly decreased in infants with small airway obstruction. The expiratory or inspiratory curve showed a plateau and the ratio of mid-expiratory to mid-inspiratory flow was less than 60% or over 150% in infants with upper airway obstruction. The TBFV loop turned narrow and lung volume decreased in infants with restrictive diseases. The TBFV loop show proximate round or oval curve in healthy infants. Pulmonary function has significant differences between healthy controls and infants with respiratory diseases. Pulmonary function test is useful in the assessment of respiratory diseases.

Spinning eggs—which end will rise?

We examine the spinning behavior of egg-shaped axisymmetric bodies whose cross sections are described by several oval curves similar to real eggs with thin and fat ends. We use the gyroscopic balance condition of Moffatt and Shimomura and analyze the slip velocity of the bodies at the point of contact as a function of θ, the angle between the axis of symmetry and the vertical axis, and find the existence of the critical angle θc. When the bodies are spun with an initial angle θinitial>θc, θ will increase to π, implying that the body will spin at the thin end. Alternatively, if θinitial<θc, then θ will decrease. For some oval curves, θ will reduce to 0 and the corresponding bodies will spin at the fat end. For other oval curves, a fixed point at θf is predicted, where 0<θf<θc. Then the bodies will spin not at the fat end, but at a new stable point with θf. The empirical fact that eggs more often spin at the fat than at the thin end is explained.

Theory of Sn Function Wave Guides

we study the conformal transformation z = sn ω to see how the constant u and constant v lines are transformed into the Z-plane curves to be utilized as boundaries of EM Waveguides, We give two sample curves for the lines v = K'/2 and u = K/2, The latter is believed to be new: a Cassinian oval curve of a = 1/k and β = 1/k √k'. Many curves can be drawn as boundaries of EM ware guides. We give formulas for drawing these curves and show that we can also use a good table of 4 significant figures to draw these curves, (11) and (17c) are new.

Parametrization of the Kobayashi-Maskawa matrix and CP violation.

The Kobayashi-Maskawa matrix with four-generation quarks is found by introducing two small parameters ${\ensuremath{\lambda}}_{k}$ (${\ensuremath{\lambda}}_{1}$\ensuremath{\equiv}${U}_{12}$,${\ensuremath{\lambda}}_{2}$\ensuremath{\equiv}${U}_{34}$) and taking into account experimental and unitarity constraints. Based on this, we analyze the possible difficulties the first three generations may face in accounting for CP violation in the ${K}^{0}$-K\ifmmode\bar\else\textasciimacron\fi{} $^{0}$ system. The additional contribution of the fourth generation and some constraints on ${\ensuremath{\lambda}}_{2}$, ${m}_{t\mathcal{'}}$, and the four-generation CP-violating phases ${\ensuremath{\varphi}}_{\mathrm{ij}}$ are discussed. From the measured value of the CP-violation parameter \ensuremath{\epsilon}, the relation between ${\ensuremath{\varphi}}_{14}$ and ${\ensuremath{\varphi}}_{24}$ is depicted by the oval curve(s). Furthermore, the relations of the curve(s) to ${\ensuremath{\lambda}}_{2}$, ${m}_{t\mathcal{'}}$, and other parameters are investigated.

Maxwell's Ovals and the Refraction of Light

This paper describes a family of oval curves first studied by Maxwell and which may be called generalized ellipses. Their equation may be written as follows: aS + bS′ = K, where a and b are certain integral values, K any value constant, and S and S′ the distances of a current point from the two foci. The simplest oval results from a = 1, b = 2. Other values of a and b generate similar ovals which are described. If in certain of these ovals the inside and outside regions are filled with material of a definite refractive index, then light proceeding from one focus to the other, will refract stigmatically at the oval surface.

The polar electrojet

It is shown that the polar electrojet which causes intense ‘negative bays’ or polar magnetic substorms in the high latitudes, flows usually westward in all longitudes along a closed oval curve. This substorm oval is also the site along which at the instant the active aurora is situated. Further, it appears to be the line of intersection of the outer boundary of the outer radiation belt with the ionosphere. The center of the oval is appreciably displaced from the earth's magnetic axis pole, along the midnight meridian. The oval coincides approximately with the statistically determined auroral zone only in the midnight sector. The strength of the polar electrojet is not uniform along the substorm oval; some of the excess current in the most intense part of the electrojet (near the midnight meridian) returns across the polar cap, encircling a focus in this cap; the remainder departs from the afternoon sector and crosses the midnight meridian to complete its circuit by rejoining the main westward flow in the morning sector, with its focus in the midnight sector not far outside the oval. This latter flow produces positive bays everywhere south of the focus; these bays can be particularly intense in the afternoon sector along the auroral zone, and were formerly interpreted as indicating the existence of an eastward polar electrojet. The changing geometry of the polar eleetrojet is brought into relation with the dynamical morphology of the simultaneous auroral substorm, which has lately been determined by study of simultaneous all-sky camera records from the entire polar region.

Spirals in Nature and Art

THAT spiral curves, or, more strictly, helices, and screw motions should play an important part both in the natural world and in structures constructed by human hands is a fact for which a mathematician can easily suggest an explanation on general grounds. Without professing to bring any extensive scientific or technical knowledge to bear on the subject, Mr. Cook has made a most interesting study of the resem-blances between the spiral forms occurring in nature and in art, and has produced a book the study of which will be a delightful recreation to any class of reader. Apart from the mere spiral form, Mr. Cook finds remarkable resemblances between the structure and sculpturing of certain staircases in France and those of the shells of certain mollusca. It is certain that Leonardo da Vinci studied shells, and that he was in France about the time when these staircases were built, and an obvious connection suggests itself. While the author's study of the works of Leonardo da Vinci—illustrated by copies of his drawings—is interesting, the connection of Leonardo's studies of the flight of birds with spiral curves strikes a reader as somewhat doubtful. Even Pettigrew's figure-of-eight-shaped curve, and the oval curve familiar to readers of Marey's “Vol des Oiseaux,” which represent, according to modern views, the relative paths of points on the wtings of a wasp and a bird, can hardly be said to produce a spiral curve when compounded with the forward motion of the animal.

1. On the Description of Oval Curves, and those having a plurality of Foci.

Mr Clerk Maxwell ingeniously suggests the extension of the common theory of the foci of the conic sections to curves of a higher degree of complication in the following manner:—(1.) As in the ellipse and hyperbola, any point in the curve has thesum or differenceof two lines drawn from two points orfoci= a constant quantity, so the author infers, that curves to a certain degree analogous, may be described and determined by the condition that the simple distance from one focusplusa multiple distance from the other, may be = a constant quantity; or more generally,mtimes the one distance+ ntimes the other = constant.