Exact Path Synthesis of RCCC linkages for a Maximum of Nine Prescribed Positions

2021 ◽  
pp. 1-14
Author(s):  
Shaoping Bai ◽  
Zhongyi Li ◽  
Jorge Angeles
Keyword(s):  
Exact Solutions ◽  
Coordinate System ◽  
Simple Form ◽  
Design Parameters ◽  
Not Given ◽  
Algebraic Equations ◽  
Complex Formulation ◽  
Synthesis Procedure ◽  
New Formulation ◽  
Path Synthesis

Abstract This paper addresses the path synthesis of RCCC linkages, a problem that has not given due attention in the literature. Compared with planar and spherical four-bar linkages, a RCCC linkage has many more design parameters, which leads to a complex formulation of the path-synthesis problem and, consequently, to a quite challenging system of algebraic equations. In this paper, the problem is solved with a novel formulation of path synthesis for visiting a number of prescribed positions. This is achieved by means of an alternative coordinate system, with which point coordinates are expressed with the aid of two vectors fixed to the same body. By this means, the rotation matrix used to represent the coupler-link attitude is obviated. The synthesis equations are then formulated in a simple form. The new formulation confirms that path synthesis admits exact solutions for up to nine prescribed positions, which proves a landmark claim submitted by Burmester. Examples are included to demonstrate the path-synthesis procedure with the method thus developed.

Sensitivity Analysis for the Operating Efficiency of an Axial Piston Pump

2015 ◽  
Author(s):  
Noah D. Manring ◽  
Viral S. Mehta ◽  
Jeff L. Kuehn ◽  
Bryan E. Nelson
Keyword(s):  
Power Efficiency ◽  
Design Parameters ◽  
Operating Efficiency ◽  
Parameter Study ◽  
Total Efficiency ◽  
Pump Efficiency ◽  
Large Set ◽  
Algebraic Equations ◽  
Pump Design ◽  
Axial Piston

Axial piston pumps of swash-plate type are extensively used in off-highway machines to convert rotating mechanical power into hydraulic power. Efficiency of such pumps is of considerable importance to hydraulic design engineers. Many researchers have tried to create mathematical models for describing pump efficiency. These models are typically a system of nonlinear algebraic equations dependent upon a total of four variables (pressure, speed, temperature, displacement) and a set of experimentally determined coefficients. Since these models are not of the a-priori type, they are not of much value to a design engineer who is trying to design an efficient pump. Others have tried to use physics based models and numerical programs to accurately predict the influence of component design on efficiency. Such programs are considerably slow to run and of not much use to a design engineer who needs to make quick decisions. Hence the objective of this paper is to understand the sensitivity of various design parameters on the total efficiency of the pump by conducting a dimensionless parameter study of a large set of pump design parameters. Using this method it will be shown that a small group of design parameters have the highest influence on the efficiency of these pumps.

Nonlinear Transient Response and its Sensitivity Using Finite Elements in Time

1995 ◽  
Author(s):  
Rakesh K. Kapania ◽  
Sungho Park
Keyword(s):  
Finite Elements ◽  
Transient Response ◽  
Legendre Polynomials ◽  
Design Parameters ◽  
Algebraic Equations ◽  
System Parameters ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
Bilinear Formulation ◽  
The One

Abstract The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, the Hermite, the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various system parameters can be obtained.

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

2016 ◽  
Vol 693 ◽  
pp. 458-462
Author(s):  
D.G. Chang ◽  
F. Shu ◽  
X.B. Chen ◽  
Y.J. Zou
Keyword(s):  
Experimental Data ◽  
Coordinate System ◽  
Theoretical Basis ◽  
Integral Method ◽  
Helical Gear ◽  
Design Parameters ◽  
Double Integral ◽  
Rectangular Coordinate System ◽  
Helical Gears ◽  
Theoretical Results

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

scholarly journals XXIII.—On Systems of Solutions of Homogeneous and Central Equations of the nth Degree and of two or more Variables; with a Discussion of the Loci of such Equations

1890 ◽  
Vol 35 (4) ◽  
pp. 1043-1098
Author(s):  
M'Laren
Keyword(s):  
Exact Solutions ◽  
Plane Curves ◽  
Algebraic Equations ◽  
Linear Variation ◽  
Approximate Methods ◽  
Contour Lines

The purpose of the present paper is to ascertain how far it is possible to find exact solutions or values of x, y, &c., in equations between variables, so that the forms of plane curves and contour-lines of surfaces may be exactly determined. No approximate methods have been admitted, and only those methods have been used which are applicable to algebraic equations of every degree and any number of variables. In the examples given I have generally selected equations of even degree and even powers of the variables. But every such solution evidently includes the solution of the non-central equation of half the degree having corresponding terms and equal coefficients. The methods of solution employed are founded on the following introductory theorem or principle, which may be described as that of Homogeneous or Linear Variation of the quantities.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

Modeling of the Stress–Birefringence–Stretch Behavior in Rubbers Using the Gent Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
A. K. Mossi Idrissa ◽  
S. Ahzi ◽  
Y. Rémond ◽  
J. Gracio
Keyword(s):  
Constitutive Model ◽  
Network Theory ◽  
Elastic Behavior ◽  
Large Strains ◽  
Chain Model ◽  
Complex Formulation ◽  
Gent Model ◽  
New Formulation ◽  
Gaussian Network ◽  
Stretch Response

In this paper, we discuss the application of different stress–optic laws for rubbers to predict the birefringence evolution and the stress–stretch relationship. The main focus of this work is to propose a new formulation for the stress–birefringence relationship using the Gent theory for rubber elasticity. The Gent constitutive model for the stress–stretch response has been shown to provide a nearly equivalent rubber elastic behavior as that of the widely used eight-chain model. By combining the simpler stress–stretch relationship from the Gent model with a Gaussian network theory for birefringence, we propose a simplified stress–optic relationship. We show that our obtained results are in accord with the existing experimental results at large strains. Our proposed simplified formulation and results allow us to conclude that the Gent theory can be extended to predict optical anisotropy evolution under large strains and that these predictions are nearly equivalent to the more complex formulation based on the eight-chain model.

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