scholarly journals Influence of the Trajectory Planning on the Accuracy of the Orthoglide 5-Axis

2016 ◽  
Author(s):  
R. Jha ◽  
D. Chablat ◽  
F. Rouillier ◽  
G. Moroz
Keyword(s):  
Trajectory Planning ◽  
Polynomial Equation ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
Dynamic Parameters ◽  
Cartesian Space ◽  
Order Polynomial ◽  
Joint Parameters ◽  
Fifth Order ◽  
Order Polynomial Equation

Usually, the accuracy of parallel manipulators depends on the architecture of the robot, the design parameters, the trajectory planning and the location of the path in the workspace. This paper reports the influence of static and dynamic parameters in computing the error in the pose associated with the trajectory planning made and analyzed with the Orthoglide 5-axis. An error model is proposed based on the joint parameters (velocity and acceleration) and experimental data coming from the Orthoglide 5-axis. Newton and Gröbner based elimination methods are used to project the joint error in the workspace to check the accuracy/error in the Cartesian space. For the analysis, five similar trajectories with different locations inside the workspace are defined using fifth order polynomial equation for the trajectory planning. It is shown that the accuracy of the robot depends on the location of the path as well as the starting and the ending posture of the manipulator due to the acceleration parameters.

Estimation of Optimum Braking Time for Capacitor-Excited Induction Motor

1978 ◽  
Vol 15 (3) ◽  
pp. 225-235
Author(s):  
I. K. Puri
Keyword(s):  
Detailed Analysis ◽  
Induction Motor ◽  
Polynomial Equation ◽  
Computer Programme ◽  
Order Polynomial ◽  
Experimental Values ◽  
Fifth Order ◽  
Order Polynomial Equation

The braking time of a capacitor-excited induction motor estimated from approximation of the fifth order polynomial equation does not give satisfactory results; whereas detailed analysis results, using a computer programme, are very close to experimental values. This paper explains how to obtain optimum values of braking time, resistance and capacitance for any particular motor.

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.

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”.

An algorithm for smooth trajectory planning optimization of isotropic translational parallel manipulators

2015 ◽  
Vol 230 (12) ◽  
pp. 1987-2002 ◽  
Author(s):  
Mahmood Reza Azizi ◽  
Rahmatolah Khani
Keyword(s):  
Trajectory Planning ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Nsga Ii ◽  
End Effector ◽  
B Splines ◽  
Planning Optimization ◽  
Need To Evaluate ◽  
Significant Performance ◽  
Fifth Order

This paper presents a new algorithm for smooth trajectory planning optimization of isotropic translational parallel manipulators (ITPM) that their Jacobian matrices are constant and diagonal over the whole robot workspace. The basic motivation of this work is to formulate the robot kinematic and geometric constraints in terms of optimization variables to reduce the mathematical complexity and running time of the resulting algorithm which are important issues in trajectory planning optimization. To achieve this aim, the end-effector trajectory of ITPMs in Cartesian space is defined using fifth-order B-Splines, and as a main contribution, all of the actuators limitations and robot constraints are formulated in terms of B-Spline parameters with no need of any information about the workspace geometry. Then the total required energy, total time of motion, and maximum absolute value of actuators’ jerk are defined as objective functions and non-dominated sorting genetic algorithm-II (NSGA-II) is used to solve the resulting nonlinear constrained multi-objective optimization problem. Finally, the proposed algorithm is implemented in MATLAB software for Cartesian parallel manipulator (CPM) as a case study, and the results are demonstrated and discussed. The obtained results show the significant performance of the proposed algorithm with no need to evaluate the robot’s constraints and boundaries of its workspace in each point of the end-effector trajectory.

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 Stationary values of the transmission ratio of the planar fourbar

2008 ◽  
Vol 30 (4) ◽  
Author(s):  
J. Wittenburg
Keyword(s):  
Polynomial Equation ◽  
Sixth Order ◽  
New Method ◽  
Transmission Ratio ◽  
Output Link ◽  
Order Polynomial ◽  
Angular Velocities ◽  
Order Polynomial Equation

The transmission ratio of the planar fourbar, i.e. the ratio of the angular velocities of input link and output link, is a function of the input angle. Freudenstein [1] showed how to calculate stationary values of the transmission ratio. In the present paper a new method is described. Like Freudenstein’s method it results in a sixth-order polynomial equation.

Forward Position Analysis of Nearly General Stewart Platforms

1992 ◽  
Author(s):  
Change-de Zhang ◽  
Shin-Min Song
Keyword(s):  
Closed Form Solution ◽  
Polynomial Equation ◽  
Stewart Platform ◽  
Form Solution ◽  
Constraint Equations ◽  
Position Analysis ◽  
Order Polynomial ◽  
Moving Platform ◽  
Order Polynomial Equation ◽  
Simultaneous Elimination

Abstract This paper presents the closed-form solution of forward position analysis of the nearly general stewart platform, which consists of a base and a moving planar platforms connected by six extensible limbs through spherical joints in the two planar platforms. It becomes a general stewart platform if the centers are not constrained to those two planes. In this study, transformation matrix is used to represent the position of the moving platform. Based on the six dependency equations of the rotation matrix and the six constraint equations related to the six link lengths, a set of six 4-th degree equations in three unknowns are derived. Further derivations produce twenty-one dependent constraint equations. By simultaneous elimination of two unknowns a 20-th order polynomial equation in one unknown is obtained. Due to dual solutions of other unknowns, this indicates a maximum of forty possible solutions. The roots of this polynomial are solved numerically and the realistic solutions are constructed using computer graphics.

Formulation and optimization of biological removal of flue gas pretreatment wastewater and sulfur recycling process by Box–Behnken design

2013 ◽  
Vol 67 (12) ◽  
pp. 2706-2711 ◽  
Author(s):  
Juan Wang ◽  
Yuan Cao ◽  
Qin Zhong
Keyword(s):  
Flue Gas ◽  
Elemental Sulfur ◽  
Polynomial Equation ◽  
Box Behnken Design ◽  
Independent Variables ◽  
Biological Removal ◽  
Order Polynomial ◽  
Contour Plots ◽  
Order Polynomial Equation ◽  
Sulfur Yield

The aim of this study was to investigate optimum conditions for biological removal of flue gas pretreatment wastewater and achieve maximum elemental sulfur yield. A three-factor, three-level Box–Behnken design was used to derive a second-order polynomial equation and construct contour plots to predict responses. The independent variables selected were hydraulic retention time (X1), inlet sulfate concentration (X2), and air flow (X3). Fifteen batches were done in a biological united system and evaluated for elemental sulfur yield (Y1). The transformed values of the independent variables and Y1 were subjected to a full-model second-order polynomial equation. The equation was modified based on Fisher's F- and probability P-values. The computer optimization process and contour plots predicted the values of independent variables X1, X2 and X3 (16 h, 1,348 mg L−1 and 165 L h−1 respectively), for maximized response of Y1. The experimental results at predicted conditions demonstrate that the modified model equation has good applicability to the practical system.

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