Analytical method for locating the secondary instant centres of indeterminate planar linkages

2008 ◽  
Vol 223 (2) ◽  
pp. 491-502 ◽  
Author(s):  
C-M Kung ◽  
L-C T Wang
Keyword(s):  
Fourth Order ◽  
Analytical Method ◽  
Polynomial Equation ◽  
Automated Analysis ◽  
Numerical Examples ◽  
Order Polynomial ◽  
Velocity Information ◽  
Planar Linkages ◽  
Fourth Order Polynomial ◽  
Order Polynomial Equation

This article presents a new analytical method for locating secondary instant centres (SICs) of indeterminate planar linkages. In this method the SICs are first discriminated into three classes according to their level of geometric dependencies. The concepts of instant-centre digraph, instant-centre walk, and instant-centre circuit are then introduced to establish the recursive relationships between the classified instant centres. It is shown that the location of the instant centres within an instant-centre circuit can be evaluated recursively by first solving a second-order polynomial equation. In addition, by combining the recurrence conditions of several related instant-centre walks, the locations of SICs that are not within an instant-centre circuit can be solved analytically from a fourth-order polynomial equation. The proposed method does not rely on any velocity information or graphical techniques; therefore, it can be applied systematically to all types of indeterminate linkages. It can also be implemented on digital computers for automated analysis. Three numerical examples are presented to demonstrate the usage of this method.

scholarly journals Improved Inherent Flaw Model for Tensile Fracture of Cracked Composite Laminates

1999 ◽  
Vol 8 (5) ◽  
pp. 096369359900800
Author(s):  
P.K. Govindan Potti ◽  
B. Nageswara Rao ◽  
V.K. Srivastava
Keyword(s):  
Fracture Strength ◽  
Composite Laminates ◽  
Polynomial Equation ◽  
Simple Relation ◽  
Tensile Fracture ◽  
Tensile Fracture Strength ◽  
Order Polynomial ◽  
Fourth Order Polynomial ◽  
Order Polynomial Equation ◽  
Made In

Modifications are made in the inherent flaw model to predict the tensile fracture strength of cracked composite laminates. A simple relation is used for the inherent flaw length to improve the accuracy while evaluating the fracture strength of laminates. A quartic (fourth-order polynomial) equation is developed for the fracture strength of an infinite width plate containing a crack. This model is successfully applied to centre crack tensile specimens of graphite/epoxy and nylon/glass polyamide.

EVALUATION OF A NATURAL RUBBER SLEEVE STOPPER AS A CONTROLLED-RELEASE SUBSTRATE FOR USE IN STUDIES OF SEX-PHEROMONE-MEDIATED MATING DISRUPTION OF THE SPOTTED TENTIFORM LEAFMINER

1999 ◽  
Vol 131 (1) ◽  
pp. 137-149 ◽  
Author(s):  
R.M. Trimble ◽  
C.A. Tyndall ◽  
B.D. McGarvey
Keyword(s):  
Sex Pheromone ◽  
Natural Rubber ◽  
Mating Disruption ◽  
Polynomial Equation ◽  
Order Polynomial ◽  
Rubber Sleeve ◽  
Rate Of Evaporation ◽  
The Relationship ◽  
Linear Decline ◽  
Order Polynomial Equation

AbstractNatural rubber sleeve stoppers were impregnated with 10 mg of (E)-10-dodecen-1-yl-acetate, the major component of spotted tentiform leafminer, Phyllonorycter blancardella (F.), pheromone. In the laboratory, there was a linear decline in the amount of pheromone remaining on stoppers during 8 weeks of exposure to 10, 15, 20, and 25 °C. At 30 and 35 °C, the relationship was curvilinear and could be described using a second-order polynomial equation. The estimated rate of evaporation ranged from 0.03 mg/day at 10 °C to 0.08 mg/day at 25 °C; the rate of evaporation at 30 and 35 °C varied with the time since first exposure. There was a linear decline in the amount of pheromone remaining on stoppers during 8 weeks of exposure to fluctuating temperature regimes with average temperatures of 10 °C (i.e., 5–15 °C) and 20 °C (i.e., 15–25 °C). At a fluctuating regime with an average temperature of 30 °C (i.e., 25–35 °C), the relationship was curvilinear and could be described using a second-order polynomial equation. The estimated rate of evaporation was 0.02 and 0.09 mg/day at 5–15 and 15–25 °C, respectively; the estimated daily rate of evaporation at 25–35 °C varied with the time since first exposure. In an orchard, the estimated average rate of evaporation of pheromone from stoppers ranged from 0.05 to 0.31 mg/day and did not vary significantly with temperature. During the first 4 weeks of exposure in an orchard, the observed rate of evaporation was up to 4.4-fold greater than the rate predicted using the relationship between evaporation rate and constant temperatures observed in the laboratory. The potential for using natural rubber sleeve stoppers as controlled-release substrates in studies of sex-pheromone-mediated mating disruption of P. blancardella is discussed.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

scholarly journals Digestibility, fermentation and microbiological characteristics of Calotropis procera silage with different quantities of grape pomace

2016 ◽  
Vol 40 (6) ◽  
pp. 698-705 ◽  
Author(s):  
Clérison dos Santos Belém ◽  
Anderson Miranda de Souza ◽  
Patrícia Rodrigues de Lima ◽  
Francisco Allan Leandro de Carvalho ◽  
Mário Adriano Ávila Queiroz ◽  
...  
Keyword(s):  
Lactic Acid ◽  
Animal Feed ◽  
Polynomial Equation ◽  
Grape Pomace ◽  
Calotropis Procera ◽  
Soluble Carbohydrate ◽  
In Vitro Digestibility ◽  
Fresh Matter ◽  
Order Polynomial ◽  
Order Polynomial Equation

ABSTRACT Preserving forage plants adapted to a semi-arid climate as silage may minimize the animal feed deficit during drought. The objective of this study was to evaluate the effects of different quantities of grape pomace added to Calotropis procera silage on its fermentation, in vitro digestibility, total digestible nutrients and microbiology. A completely randomized experimental design was used with four treatments (0, 10, 20 and 40% fresh matter) and four replicates. The silos were opened after 90 days of ensilage, and the soluble carbohydrate, ethanol, organic acid and ammoniacal nitrogen concentrations; pH; fermentation loss; dry matter (DM) recovery; DM density, and microbial populations were determined. The pH (3.96-3.87) was adequate for ensiling in all silage samples. The soluble carbohydrate concentration decreased (p<0.05), and the ethanol concentration increased with increasing quantities of grape pomace. The lactic acid concentration decreased (p<0.05) from 5.3 to 1.94% DM, and the acetic, propionic and butyric acid concentrations increased with increasing quantities of grape pomace. The lactic acid bacteria decreased linearly (p <0.05), varying from 6.43 to 5.82 log CFU/g silage. The mold and yeast population variations fit best using a third-order polynomial equation (p <0.05). Enterobacteria and Clostridium spp were not observed. Adding grape pomace to the silage increased the effluent and gas loss; the latter varied from 5.35 to 14.4%. The total digestible nutrient (TDN) variation fit best using a second-order polynomial equation, and the maximum value was estimated at 82.95% DM with 3.5% grape pomace using the regression equation. The percent digestibility decreased linearly (p<0.05) with increasing quantities of grape pomace. We show that Calotropis procera has potential as silage even without adding grape pomace.

Effects of Crystallization Degree on Rate during Isothermal Crystallization from PET Melt

2012 ◽  
Vol 174-177 ◽  
pp. 1520-1523
Author(s):  
Hong Ya Zhang ◽  
Feng Wang ◽  
Hua Cheng
Keyword(s):  
Heat Flow ◽  
Flow Rate ◽  
Crystallization Process ◽  
Crystallization Rate ◽  
Polynomial Equation ◽  
Heat Flow Rate ◽  
Order Polynomial ◽  
Coefficient Vector ◽  
Crystallization Degree ◽  
Order Polynomial Equation

In this study, one new function is defined as change of relative crystallization degree in unit time and named relative crystallization rate (1/min.). The curve of heat flow rate to time is transmitted to that of to . The produced curve was fitted using one high-order polynomial equation with a variable of and the coefficient vector （Ai ,in this paper，the values of i were from 0 to 9）was produced. It was found that, even during the accelerated stage of crystallization from PET melt，both aspects to promote and delay the relative crystallization rate existed， furthermore， both aspects of promotion and delay declined with the crystallization process and appeared “internal exhaustion”.

Soil-line vegetation indices for corn nitrogen content prediction

2012 ◽  
Vol 26 (2) ◽  
pp. 103-108 ◽  
Author(s):  
N. Bagheri ◽  
H. Ahmadi ◽  
S. Alavipanah ◽  
M. Omid
Keyword(s):  
Nitrogen Content ◽  
Vegetation Indices ◽  
Polynomial Equation ◽  
Measured Data ◽  
Second Order ◽  
Soil Line ◽  
Order Polynomial ◽  
Canopy Nitrogen ◽  
Order Polynomial Equation ◽  
Corn Canopy

Soil-line vegetation indices for corn nitrogen content prediction The soil-line vegetation indices for prediction of corn canopy nitrogen content were investigated. Results indicated that the vegetation indices applied were correlated with corn canopy nitrogen content and the wavelengths between 630-860 nm are suitable for nitrogen diagnosis. The second-order polynomial equation was the best model for nitrogen content prediction among different regression types. Analyses based on both predicted and measured data were carried out to compare the performance of existing vegetation indices.

scholarly journals Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

1997 ◽  
Vol 12 (15) ◽  
pp. 2725-2739 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Quantum Mechanics ◽  
Fourth Order ◽  
Classification Scheme ◽  
Algebraic Expression ◽  
Topological Invariants ◽  
Square Root ◽  
Fredholm Operators ◽  
Compatibility Conditions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

The general features of the degeneracy structure of (p = 2) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a fourth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.

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