Synthesis of Quasi-Constant Transmission Ratio Planar Linkages

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Giorgio Figliolini ◽  
Ettore Pennestrì
Keyword(s):  
Range Of Motion ◽  
Closed Form ◽  
Optimality Criterion ◽  
Transmission Ratio ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
First Case ◽  
Finite Displacements ◽  
Planar Linkages

The present paper deals with the formulation of novel closed-form algorithms for the kinematic synthesis of quasi-constant transmission ratio planar four-bar and slider–crank linkages. The algorithms are specific for both infinitesimal and finite displacements. In the first case, the approach is based on the use of kinematic loci, such as centrodes, inflection circle, and cubic of stationary curvature, as well as Euler–Savary equation. In the second case, the design equations follow from the application of Chebyshev min–max optimality criterion. These algorithms are aimed to obtain, within a given range of motion, a quasi-constant transmission ratio between the driving and driven links. The numerical examples discussed allow a direct comparison of structural errors for mechanisms designed with different methodologies, such as infinitesimal Burmester theory and the Chebyshev optimality criterion.

Kinematic Synthesis of Quasi-Homokinetic Four-Bar Linkages Through the Burmester and Chebyshev Theories

2014 ◽  
Author(s):  
Giorgio Figliolini ◽  
Ettore Pennestrì
Keyword(s):  
Range Of Motion ◽  
Closed Form ◽  
Optimality Criterion ◽  
Transmission Ratio ◽  
Kinematic Synthesis ◽  
Closed Form Solutions

The present paper deals with the formulation of specific algorithms for the kinematic synthesis of quasi-homokinetic four-bar linkages, slider-crank mechanisms included, which are based on the fundamentals of kinematics, as the centrodes, the inflection circle, the cubic of stationary curvature, Freudenstein’s theorem, the Euler-Savary equation and Chebyshev’s theory. These algorithms are aimed to obtain in a given range of motion, a quasi-constant transmission ratio between the driving and driven links, thus producing a quasi-homokinetic behaviour. In particular, the infinitesimal Burmester theory and the Chebyshev optimality criterion are applied to propose a compact closed-form solutions, which are validated through several significant examples.

Kinematic Synthesis of a Geared Five-Bar Function Generator

1971 ◽  
Vol 93 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Arthur G. Erdman ◽  
George N. Sandor
Keyword(s):  
Computer Program ◽  
Closed Form ◽  
Complex Numbers ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
Function Generation ◽  
Structural Error ◽  
Dependent Variables ◽  
Angular Displacements

A general closed form method of planar kinematic synthesis, using complex numbers to represent link vectors, is applied to the synthesis of a geared five-bar linkage for function generation. Equations are derived and a computer program is developed to yield several solutions. Angular displacements of the input, a cycloidal crank, and the output, a simple follower, are used as linear analogs of the independent and the dependent variables, respectively. A method is demonstrated for six precision conditions (three first, three second-order precision conditions). Numerical examples are included, and the structural error of these geared five-bars are compared to that of optimized four-bar linkages generating the same functions.

Finite-Position Theory Applied to Mechanism Synthesis

1967 ◽  
Vol 34 (3) ◽  
pp. 599-605 ◽  
Author(s):  
B. Roth
Keyword(s):  
Similarity Transformation ◽  
Companion Paper ◽  
Spatial Theory ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
Planar Linkages

The well-known finite-position planar theory of kinematic synthesis (the so-called Burmester theory) and the corresponding spherical theory are derived from the results of the general spatial theory which has been given in a companion paper [1]. Other special displacements studied are those for which the author has coined the names “similarity transformation,” “pseudoplanar,” and “pseudospherical.” These results, as well as those obtained in [1], are shown to be applicated to the synthesis of spatial, spherical, and planar linkages. Several numerical examples are presented.

scholarly journals True Symphalangism of All Bilateral Proximal Interphalangeal Joints with Multi-carpal Coalition and Hypoplasia of the Ulnar Styloid Process

2021 ◽  
Author(s):  
Hao Yu ◽  
Chongjie Li
Keyword(s):  
Case Report ◽  
Range Of Motion ◽  
Styloid Process ◽  
Genetic Condition ◽  
Ulnar Styloid ◽  
Wrist Motion ◽  
First Case ◽  
Distal Interphalangeal ◽  
Carpal Coalition ◽  
Ulnar Styloid Process

AbstractSymphalangism is a rare genetic condition characterized by ankylosis of the proximal interphalangeal (PIP) or/and distal interphalangeal (DIP) joints. The patient presented with fused bilateral PIP joints and poor flexion, and an unsatisfactory range of motion (ROM) in the metacarpophalangeal (MP) and DIP joints. Concomitantly, multi-carpal coalition, proximal carpal malalignment, and ulnar styloid process abnormality were also observed in radiographs obtained at diagnosis. Rehabilitation training of the MP and DIP joints and a wrist supporter were recommended to achieve MP and DIP functional motion and restrict dramatic wrist motion. This is the first case report of symphalangism with multi-carpal coalition and abnormality of the ulnar styloid process to the best of our knowledge.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

scholarly journals Conditional and Unconditional Deterministic Bounds on the MSE of the Non-Uniform Linear Co-centered Orthogonal Loop and Dipole Array

2021 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Tao Bao ◽  
Mohammed Nabil EL KORSO
Keyword(s):  
Theoretical Analysis ◽  
Closed Form ◽  
Mean Square Error ◽  
Source Localization ◽  
Threshold Region ◽  
Observation Model ◽  
Mean Square ◽  
Numerical Examples ◽  
Cramer Rao Bound ◽  
Deterministic Bounds

The co-centered orthogonal loop and dipole (COLD) array exhibits some interesting properties, which makes it ubiquitous in the context of polarized source localization. In the literature, one can find a plethora of estimation schemes adapted to the COLD array. Nevertheless, their ultimate performance in terms the so-called threshold region of mean square error (MSE), have not been fully investigated. In order to fill this lack, we focus, in this paper, on conditional and unconditional bounds that are tighter than the well known Cramér-Rao Bound (CRB). More precisely, we give some closed form expressions of the McAulay-Hofstetter, the Hammersley-Chapman-Robbins, the McAulaySeidman bounds and the recent Todros-Tabrikian bound, for both the conditional and unconditional observation model. Finally, numerical examples are provided to corroborate the theoretical analysis and to reveal a number of insightful properties.

scholarly journals The Krylov problem in the case of a beam on Vlasov inertial foundation

2018 ◽  
Vol 19 (6) ◽  
pp. 728-736
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Closed Form ◽  
Compressive Force ◽  
Elastic Beam ◽  
Forced Vibrations ◽  
Critical Force ◽  
Winkler Foundation ◽  
Static Deflection ◽  
Numerical Examples ◽  
Moving Force ◽  
Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

Effects of the design parameters on the synthesis of Geneva mechanisms

2012 ◽  
Vol 227 (9) ◽  
pp. 2000-2009 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea
Keyword(s):  
Shock Loading ◽  
General Algorithm ◽  
Design Parameters ◽  
Kinematic Synthesis ◽  
Numerical Examples

A general algorithm for the kinematic synthesis of Geneva mechanisms with curved slots is introduced here, when a suitable displacement program is given with the aim of avoiding the typical shock-loading problems of conventional Geneva mechanisms. Moreover, the effects of the design parameters are analyzed through significant numerical examples. These parameters are: number of driving cranks; number of slots; imposed displacement program; and pin radius of the driving crank for the Geneva mechanism.

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