Synthesis of spherical four-bar path generator satisfying the prescribed tangents at two cusps

1997 ◽  
Vol 211 (3) ◽  
pp. 211-216 ◽  
Author(s):  
C-F Chang ◽  
D-M Lu ◽  
W-M Hwang
Keyword(s):  
Analytical Method ◽  
Cross Ratio ◽  
Numerical Examples ◽  
Special Case

Design equations for spherical four-bar linkages to trace a coupler curve with two prescribed cusps are derived in this study by using a special case of spherical Burmester curves. For the case in which the tangents at two cusps are also prescribed, an analytical method is proposed with the aid of the foregoing design equations associated with the concept of the spherical cross ratio and spherical Bobillier theorem. The proposed method is straightforward and quite useful for those cases in which the tangents at two cusps are neither on the same plane nor on parallel planes. Numerical examples are also provided for illustrating the entire technique.

Acceleration Analysis of Platform-Type Manipulators

1996 ◽  
Author(s):  
Maher G. Mohamed
Keyword(s):  
Stewart Platform ◽  
Algebraic Manipulation ◽  
Analysis Procedure ◽  
Compact Form ◽  
Numerical Examples ◽  
Acceleration Field ◽  
Center Point ◽  
Planar Manipulators ◽  
Acceleration Analysis ◽  
Special Case

Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.

scholarly journals Optical axes of catadioptric systems including visual, Purkinje and other nonvisual systems of a heterocentric astigmatic eye

2010 ◽  
Vol 69 (3) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Visual System ◽  
Optical Axis ◽  
The Other ◽  
Optical Systems ◽  
Numerical Examples ◽  
Straight Line ◽  
Optical Axes ◽  
Catadioptric Systems ◽  
Reflecting Surfaces ◽  
Special Case

For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system.  Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique.  Formulae were derived for the locations of any optical axes.  The purpose of this paper is to extend those results to allow for reflecting surfaces in the system in addition to refracting elements.  Thus the paper locates any optical axes in catadioptric systems (including dioptric systems as a special case).  The reflecting surfaces may be astigmatic and decentred or tilted.  The theory is illustrated by means of numerical examples.  The locations of the optical axes are calculated for seven optical systems associated with a particular heterocentric astigmatic model eye.  The optical systems are the visual system, the four Purkinje systems and two other nonvisual systems of the eye.  The Purkinje systems each have an infinity of optical axes whereas the other nonvisual systems, and the visual system, each have a unique optical axis. (S Afr Optom 2010 69(3) 152-160)

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

Analysis of Half-Pipe Heating Channels on Pressure Vessel Shells

1986 ◽  
Vol 108 (4) ◽  
pp. 526-529
Author(s):  
A. E. Blach
Keyword(s):  
Pressure Vessel ◽  
Analytical Method ◽  
External Pressure ◽  
Pressure Vessels ◽  
Numerical Examples ◽  
Asme Code

Half-pipe heating channels are used on the outside of pressure vessels such as agitators, mixers, reactors, etc., to avoid the high external pressure associated with heating jackets. No applicable method of analysis is contained in the ASME Code and proof tests are normally required for registration with governing authorities. An analytical method is presented which permits the evaluation of stresses in shell and half pipe; numerical examples are included.

Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

scholarly journals Coordinating Three-Level Supply Chain under Disruptions Using Revenue-Sharing Contract with Effort Dependent Demand

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Qinghua Pang ◽  
Yanli Hou ◽  
Yifei Lv
Keyword(s):  
Supply Chain ◽  
Revenue Sharing ◽  
Optimal Contract ◽  
Market Demand ◽  
Numerical Examples ◽  
Revenue Sharing Contract ◽  
Special Case ◽  
Additive Form ◽  
Dependent Demand

Considering that the market demand is stochastic and dependent on effort, this essay shows that the benchmark revenue-sharing contract could not coordinate a three-level supply chain consisting of one manufacturer, one distributor, and one retailer. By assuming that the retailer himself bears the effort cost, coordination is achieved by implementing revenue-sharing contract based on rebate and penalty policy in one transaction or two transactions of three-level supply chain, and the former is a special case of the latter. When the disruptions induce the changes of the market demand, the revenue-sharing contract could not coordinate the supply chain. To deal with the problem, this essay introduces two forms of improved revenue-sharing contracts which have antidisruption ability. The model of improved revenue-sharing contract is optimized when the market demand is in the additive form with effort dependent demand. Formulas are given to calculate the optimal contract parameters. Finally, this essay demonstrates the accuracy of the model of improved revenue-sharing contract with the help of numerical examples.

Periodic strong ergodicity in non-homogeneous Markov systems

1991 ◽  
Vol 28 (1) ◽  
pp. 58-73 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
State Space ◽  
Manpower Planning ◽  
Practical Aspect ◽  
Periodic Case ◽  
Convergence Properties ◽  
Markov Systems ◽  
Numerical Examples ◽  
The Individual ◽  
Special Case ◽  
Theoretical Results

This paper presents a unified treatment of the convergence properties of nonhomogeneous Markov systems under different sets of assumptions. First the periodic case is studied and the limiting evolution of the individual cyclically moving subclasses of the state space of the associated Markov replacement chain is completely determined. A special case of the above result is the aperiodic or strongly ergodic convergence. Two numerical examples from the literature on manpower planning highlight the practical aspect of the theoretical results.

A theoretical evaluation of population growth after removing individuals from some age groups

1967 ◽  
Vol 57 (3) ◽  
pp. 437-445 ◽  
Author(s):  
L. P. Lefkovitch
Keyword(s):  
Life History ◽  
Matrix Algebra ◽  
Population Control ◽  
Age Groups ◽  
Mathematical Treatment ◽  
Lasioderma Serricorne ◽  
Theoretical Evaluation ◽  
Numerical Examples ◽  
Special Case ◽  
Growing Population

A mathematical treatment is proposed, utilising the methods and notation of matrix algebra, for evaluating the theroetical effects on the growth and structure of a population of the removal of individuals in particular age groups or stages in the life history. Formulae are derived to establish what proportions of given age groups or stages, individually or in combination, can be withdraw from the population whilst permitting its maintenance at a constant level. It is pointed out that these methods, appropriate to the situtation in which the population is exploited by a cropping procedure, can be extened to the special case of population control, in which it is desired to minimise or eliminate the population. The methods are illustated by numerical examples based on census observations on a growing population of Lasioderma serricorne (F.).

scholarly journals CKV-type $ B $-matrices and error bounds for linear complementarity problems

2021 ◽  
Vol 6 (10) ◽  
pp. 10846-10860
Author(s):  
Xinnian Song ◽  
◽  
Lei Gao
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Type B ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Norm Bound ◽  
Special Case ◽  
Better Than

<abstract><p>In this paper, we introduce a new subclass of $ P $-matrices called Cvetković-Kostić-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. <sup>[<xref ref-type="bibr" rid="b24">24</xref>]</sup> for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña <sup>[<xref ref-type="bibr" rid="b10">10</xref>]</sup> for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.</p></abstract>

Band Gap Formation by Cylinder Arrays in an Acoustic Waveguide

2007 ◽  
Author(s):  
Liang-Wu Cai ◽  
David C. Calvo ◽  
Dalcio K. Dacol ◽  
Gregory J. Orris
Keyword(s):  
Acoustic Waves ◽  
Stop Band ◽  
Three Dimensional ◽  
Wave Number ◽  
Pass Band ◽  
Gap Formation ◽  
Numerical Examples ◽  
Cylinder Arrays ◽  
Horizontal Wave ◽  
Special Case

Scattering of acoustic waves by arrays of identical circular cylindrical scatterers in a horizontal waveguide is studied. Although three-dimensional in its geometry, the waveguide permits only a finite number of modes of acoustic wave propagating in different directions with respect to horizontal, and the number of these propagating modes increases as the frequency increases. The horizontal wave numbers of these modes span a range of frequency limited by the total wave number. Numerical examples are used to explore a special case in which the cylinder height equals the depth of the waveguide and in which the cylinders and the waveguide have pressure-release boundaries at both top and bottom surfaces. In such a special case, there is no coupling among the modes permitted by the waveguide and hence is the simplest case for such problems. It is observed that the combination of the modes generally decreases the wave-blocking effects of a stop band; and it is likely that a stop band in one waveguide mode might correspond to a pass band in a different mode. However, numerical examples also show that the main characteristics of a stop band are maintained, despite the multiple modes; and it is possible to extend the stop band by cascading cylinders arrays of different arrangement.

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