On the dead-centre position analysis of Stephenson six-link linkages

2006 ◽  
Vol 220 (9) ◽  
pp. 1393-1404 ◽  
Author(s):  
C-C Tsai ◽  
L T Wang
Keyword(s):  
Input Parameter ◽  
Polynomial Equation ◽  
Necessary Condition ◽  
Input Output ◽  
Single Degree Of Freedom ◽  
Real Solutions ◽  
Geometric Conditions ◽  
Condition Equation ◽  
The Dead ◽  
Dead Centre

A new method for analysing the dead-centre positions of Stephenson type six-bar linkages is presented in this article. This method uses the input-output polynomial equation of the linkage and the corresponding Sturm functions to formulate the necessary condition of the dead-centre configurations as a polynomial equation in terms of the input parameter only. A simple analytical method for identifying the true dead-centre positions among the real solutions to the condition equation is also developed. The proposed method is conceptually straightforward and does not rely on any structure-related geometric conditions; therefore, it can be systematically applied to all types of Stephenson linkages and other multiple-loop, single degree-of-freedom linkages regardless of the selections of the input-output pair and the type of the joints.

On the Dead-Center Positions of Stephenson Six-Bar Linkage

2011 ◽  
Vol 52-54 ◽  
pp. 915-919
Author(s):  
Yan Huo Zou ◽  
Xiao Ning Guo ◽  
Jin Kui Chu
Keyword(s):  
Analytical Method ◽  
Input Parameter ◽  
Polynomial Equation ◽  
New Method ◽  
Necessary Condition ◽  
Input Output ◽  
Simple Analytical Method ◽  
Condition Equation ◽  
The Dead

A new method for identifying the dead-center positions of the Stephenson six-bar linkage is presented by this article. This method uses the input-output polynomial equation of the linkage and the corresponding Sylvester's resultant to formulate the necessary condition of the dead-center configurations as a polynomial equation in terms of the input parameter; then through a simple analytical method to obtain all the truly dead-center positions among the double roots to the condition equation. An example is given to demonstrate the validity of this method.

Branch identification and motion domain analysis of Stephenson type six-bar linkages

2007 ◽  
Vol 221 (5) ◽  
pp. 589-604 ◽  
Author(s):  
C-C Tsai ◽  
L-C T Wang
Keyword(s):  
Lower Bounds ◽  
Polynomial Equation ◽  
Domain Analysis ◽  
Upper And Lower Bounds ◽  
Computer Implementation ◽  
Input Output ◽  
Complicated Case ◽  
Sturm Theorem ◽  
The Dead ◽  
Selection Of

A general approach for branch identification and motion domain analysis of Stephenson type six-bar linkages is presented. By applying the Sturm theorem to the input-output polynomial equation, the dead-centre positions of the linkage are first evaluated and classified into two groups in order to discriminate the upper and lower bounds of the motion domains. The circuits of the linkage are then identified by matching the dead centres to the branches, which are attributed in accordance with the case where the input is assigned to a joint within the four-bar chain. Finally, the branches and motion domains of the more complicated case where the input is given through one of the uncoupled joints within the five-bar chain, are identified by mapping the circuits onto the domain of the specified input joint. This approach does not rely on the coupler curve of the constituent four-link mechanism. This is also suitable for computer implementation and can be systematically applied to all types of Stephenson linkages, regardless of the types of joints and the selection of input-output pair.

scholarly journals Experimental Study on Dynamic Combustion Characteristics in Swirl-Stabilized Combustors

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1609
Author(s):  
Donghyun Hwang ◽  
Kyubok Ahn
Keyword(s):  
Experimental Study ◽  
Heat Release ◽  
Dynamic Pressure ◽  
Combustion Instability ◽  
Flame Structure ◽  
Pressure Sensors ◽  
Necessary Condition ◽  
Rayleigh Criterion ◽  
Pressure Oscillations ◽  
Geometric Conditions

An experimental study was performed to investigate the combustion instability characteristics of swirl-stabilized combustors. A premixed gas composed of ethylene and air was burned under various flow and geometric conditions. Experiments were conducted by changing the inlet mean velocity, equivalence ratio, swirler vane angle, and combustor length. Two dynamic pressure sensors, a hot-wire anemometer, and a photomultiplier tube were installed to detect the pressure oscillations, velocity perturbations, and heat release fluctuations in the inlet and combustion chambers, respectively. An ICCD camera was used to capture the time-averaged flame structure. The objective was to understand the relationship between combustion instability and the Rayleigh criterion/the flame structure. When combustion instability occurred, the pressure oscillations were in-phase with the heat release oscillations. Even if the Rayleigh criterion between the pressure and heat release oscillations was satisfied, stable combustion with low pressure fluctuations was possible. This was explained by analyzing the dynamic flow and combustion data. The root-mean-square value of the heat release fluctuations was observed to predict the combustion instability region better than that of the inlet velocity fluctuations. The bifurcation of the flame structure was a necessary condition for combustion instability in this combustor. The results shed new insight into combustion instability in swirl-stabilized combustors.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Formalizing Cross-Parameter Conditions for Geoprocessing Service Chain Validation

2011 ◽  
Vol 2 (1) ◽  
pp. 18-35
Author(s):  
Daniel Fitzner
Keyword(s):  
Web Services ◽  
Service Composition ◽  
Reference System ◽  
Input Parameter ◽  
Input Output ◽  
Web Based ◽  
Rule Based ◽  
Service Chain ◽  
Spatial Reference ◽  
Automated Handling

Geoprocessing operations offered via web services provide the means for building complex web-based geospatial applications. Often, certain postconditions such as the spatial reference system, bounding box, schema or quality that hold on the output dataset after the execution of a geoprocessing service are determined and derived from the properties of the inputs passed to the service. Further, geoprocesses often hold preconditions that relate to more than one input, such as the requirement that all inputs must have the same schema. Within current process descriptions for geoprocessing operations, such conditions which we call cross-parameter conditions, can not be explicitly specified. In this paper, the author gives an approach to formalize such cross input-output and cross input parameter conditions in a rule-based language. Further, the author proposes an algorithm for deriving pre- and postconditions for a service composition or workflow out of the pre- and postconditions of the services involved, allowing a more automated handling of workflows in general.

Polynomial Solution to the Five-Position Synthesis of Spatial CC Dyads via Dialytic Elimination

2000 ◽  
Author(s):  
Chintien Huang ◽  
Yu-Jui Chang
Keyword(s):  
Polynomial Solution ◽  
Polynomial Equation ◽  
Elimination Method ◽  
Real Solutions ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
Position Synthesis

Abstract This paper presents a polynomial solution to the five-position synthesis of spatial cylindrical-cylindrical dyads. The solution procedures start with the simplification of the synthesis equations derived by Tsai and Roth. The simplified equations are solved by Sylvester’s dialytic elimination method to obtain a univariate polynomial equation of degree six, which gives at most 6 CC dyads for the five-position synthesis. A numerical example with six real solutions is provided.

The onset of multi-valued solutions of a prescribed mean curvature equation with singular non-linearity

2013 ◽  
Vol 24 (5) ◽  
pp. 631-656 ◽  
Author(s):  
N. D. BRUBAKER ◽  
A. E. LINDSAY
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Blow Up ◽  
Elliptic Partial Differential Equation ◽  
Classical Solutions ◽  
Necessary Condition ◽  
Partial Differential ◽  
End Point ◽  
Dead End ◽  
The Dead

The existence and multiplicity of solutions to a quasilinear, elliptic partial differential equation with singular non-linearity is analysed. The partial differential equation is a recently derived variant of a canonical model used in the modelling of micro-electromechanical systems. It is observed that the bifurcation curve of solutions terminates at single dead-end point, beyond which no classical solutions exist. A necessary condition for the existence of solutions is developed, revealing that this dead-end point corresponds to a blow-up in the solution's gradient at a point internal to the domain. By employing a novel asymptotic analysis in terms of two small parameters, an accurate characterization of this dead-end point is obtained. An arc length parameterization of the solution curve can be employed to continue solutions beyond the dead-end point; however, all extra solutions are found to be multi-valued. This analysis therefore suggests that the dead-end is a bifurcation point associated with the onset of multi-valued solutions for the system.

Forward Positional Analysis for the General 4–6 In-Parallel Platform

1995 ◽  
Vol 209 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Q Liao ◽  
L D Seneviratne ◽  
S W E Earles
Keyword(s):  
Polynomial Equation ◽  
Unknown Variable ◽  
Real Solutions ◽  
Positional Analysis ◽  
Order Polynomial ◽  
Parallel Platform ◽  
New Equation ◽  
Published Paper ◽  
Special Case ◽  
Kinematic Solution

Presented is the forward positional (kinematic) solution for the general case of the 4–6 in-parallel platform mechanism; in particular, the spherical joints of the moving and base platforms are not restricted to lie in planes, but can be freely chosen. The forward positional analysis consists of 13 equations which are reduced to a single thirty-second order polynomial equation in one unknown variable. This new equation is numerically solved and validated by substituting the 32 roots into the 13 forward positional equations. The new analysis is also used to solve an example, with a set of known results from a previously published paper, in which a special case of the 4–6 in-parallel platform is considered; the results are in exact agreement. For a number of general platform and actuator inputs a maximum of 24 real solutions have been found. One example is illustrated.

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