Displacement Analysis of Spatial 7R Mechanisms Suitable for Constant-Velocity Transmission Between Parallel Shafts

1979 ◽  
Vol 101 (4) ◽  
pp. 604-613 ◽  
Author(s):  
M. J. Gilmartin ◽  
J. Duffy
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Numerical Results ◽  
Theory Method ◽  
Unified Theory ◽  
Displacement Analysis ◽  
Loop Method ◽  
Joint Coupling ◽  
Velocity Transmission ◽  
Special Case

Three types of spatial 7R mechanisms are identified as being suitable for transmitting motion with a constant velocity ratio between two parallel shafts. A displacement analysis of each type is made using a vector loop method in conjunction with the Unified Theory method. Numerical results are presented for an example of each type. It is also shown how the double Hooke joint coupling for parallel shafts is a special case of one of these three types.

The Displacement Analysis of the Generalized Tracta Coupling

1970 ◽  
Vol 37 (3) ◽  
pp. 713-719 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Constant Velocity ◽  
General Mechanism ◽  
Universal Joint ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Previous Solution ◽  
The Subject ◽  
Algebraic Solutions ◽  
Special Case

The displacement analysis of spatial linkages has been the subject of a number of recent investigations, using a variety of mathematical approaches. Algebraic solutions have been developed principally, in cases in which the number of links, n, is less than or equal to 4. When n > 4, the complexity of the displacement analysis appears to increase by one or more orders of magnitude. In this paper we describe a method, which we call the geometric-configuration method, which we have used when n > 4. The method is illustrated with respect to the algebraic displacement analysis of a five-link spatial mechanism, which includes the Tracta joint as a special case. The Tracta joint is a spatial linkage of symmetrical proportions functioning as a constant-velocity universal joint for nonparallel, intersecting shafts (Myard, 1933). It has four turning or revolute pairs (R) and one plane pair (E), which is located symmetrically with respect to the input and output shafts. The generalization of this linkage, which we call the generalized Tracta coupling, is the R-R-E-R-R spatial linkage with general proportions. The displacement analysis of the general mechanism, for which we know of no previous solution, has been derived. An analysis of the effect of tolerances in the Tracta joint has been included.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

The Unified Theory of Tubesheet Design - Part III: Comparison with ASME Method and Case Study

2021 ◽  
Author(s):  
Hong-Song Zhu ◽  
Jinguo Zhai ◽  
Guo-Yan Zhou
Keyword(s):  
Heat Exchangers ◽  
Numerical Comparison ◽  
Unified Theory ◽  
Element Analysis ◽  
Theoretical Comparison ◽  
Comparison Results ◽  
Different Types ◽  
Special Case ◽  
Simplified Mechanical Model

Abstract Based on the unified theory of tubesheet (TS) design for fixed TS heat exchangers (HEX), floating head and U-tube HEX presented in Part I and Part II, theoretical and numerical comparisons with ASME method are performed in this paper as Part III. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the unified theory. Numerical Comparison results indicate that predictions given by the unified theory agree well with finite element analysis (FEA), while ASME results are not accurate or not correct. Therefore, it is concluded that the unified theory deals with different types of HEX in equal detail with confidence to predict design stresses.

Characteristics of a co-flowing jet with varying lip thickness and constant velocity ratio

2020 ◽  
Vol 92 (4) ◽  
pp. 633-644
Author(s):  
Naren Shankar R. ◽  
Kevin Bennett S. ◽  
Dilip Raja N. ◽  
Sathish Kumar K.
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Critical Limit ◽  
Potential Core ◽  
Content Type ◽  
Free Jet ◽  
Current Scenario ◽  
Wake Zone ◽  
Bypass Ratio ◽  
Practical Implications

Purpose This study aims to analyze co-flowing jets (CFJs) with constant velocity ratio (VR) and varying primary nozzle lip thickness (LT) to find a critical LT in CFJs below which mixing enhances and beyond which mixing inhibits. Design/methodology/approach CFJs were characterized with a constant VR and varying LTs. A single free jet with a diameter equal to that of a primary nozzle of the CFJ was used for characteristic comparison. Numerical simulation is carried out and is validated with the experimental results. Findings The results show that within a critical limit, the mixing enhanced with an increase in LT. This was signified by a reduction in potential core length (PCL). Beyond this limit, mixing inhibited leading to the elongation of PCL. This limit was controlled by parameters such as LT and constant VR. A new region termed as influential wake zone is identified. Practical implications In this study, the VR is maintained constant and bypass ratio (BR) was varied from low value to very high values. Presently, subsonic commercial turbo fan operates under low to ultra-high BR. Hence the present study becomes vital to the current scenario. Originality/value To the best of the authors’ knowledge, this is the first effort to find the critical value of LT for a constant VR for compressible co-flow jets. The CFJs with constant VR and varying LT have not been studied in the past. The present study focuses on finding a critical LT below which mixing enhances and above which mixing inhibits.

scholarly journals Optimal Design of Inlet Passage for Waterjet Propulsion System Based on Flow and Geometric Parameters

2019 ◽  
Vol 2019 ◽  
pp. 1-21 ◽  
Author(s):  
Weixuan Jiao ◽  
Li Cheng ◽  
Di Zhang ◽  
Bowen Zhang ◽  
Yeping Su ◽  
...  
Keyword(s):  
Velocity Ratio ◽  
Optimization Method ◽  
Hydraulic Performance ◽  
Numerical Results ◽  
Propulsion System ◽  
Operating Conditions ◽  
Geometric Parameters ◽  
Hydraulic Characteristics ◽  
Design And Optimization ◽  
Ship Speed

As an important overcurrent component in a waterjet propulsion system, the inlet passage is used to connect the propulsion pump and the bottom of the propulsion ship. The anticavitation, vibration, and noise performance of the waterjet propulsion pump are significantly affected by the hydraulic performance of the inlet passage. The hydraulic performance of the inlet passage directly affects the overall performance of the waterjet propulsion system, thus the design and optimization method of the inlet passage is an important part of the hydraulic optimization of the waterjet propulsion system. In this study, the hydraulic characteristics of the inlet passage in the waterjet propulsion system with different flow parameters and geometric parameters were studied by a combination of numerical simulation and experimental verification. The model test was used to verify the hydraulic characteristics of the waterjet propulsion system, and the results show that the numerical results are in good agreement with the test results. The numerical results are reliable. The hydraulic performance of the inlet passage is significantly affected by the inlet velocity ratio. There is a certain correlation between the hydraulic performance of the inlet passage and ship speed, and the hydraulic performance of the inlet passage is limited by ship speed. The geometric parameters of the best optimization case are as follows: the inflow dip angle α is 35°, the length L is 6.38D0, and the upper lip angle is 4°. The optimal operating conditions are the conditions of IVR 0.69–0.87.

Displacement Analysis of a Special Case of the 7R, Single-Loop, Spatial Mechanism

1983 ◽  
Vol 105 (1) ◽  
pp. 78-87
Author(s):  
Hiram Albala ◽  
David Pessen
Keyword(s):  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Single Loop ◽  
Spatial Mechanism ◽  
Rotation Axes ◽  
Successive Rotation ◽  
Special Case ◽  
Output Equation

Based on the displacement equations for the general n-bar, single-loop spatial linkage, obtained elsewhere, the displacement analysis for a special case of the 7R spatial mechanism is carried out. In this mechanism the successive rotation axes are perpendicular to each other, the distances between axes 3-4, 4-5, 5-6, are equal and the offsets along axes 4 and 5 are zero, when input axis is labeled axis 1. In this fashion, there still remain nine free linkage parameters. Input-output equation is of the eighth-degree in the tangent of half the output angle. A particular case of this one, where all the distances between axes are equal and all the offsets along axes are zero, leads to an input-output equation of the fourth-degree in the same quantity, with a maximum of four closures. This mechanism resulted to be a double-rocker.

A New Constant Velocity Coupling

1977 ◽  
Vol 99 (2) ◽  
pp. 367-372 ◽  
Author(s):  
V. Milenkovic
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Kinematic Model ◽  
Formal Proof

A constant velocity coupling has been developed that does not resemble any coupling built before. It was intended for a specialized application, with specifications that are outside the range of any existing designs. A kinematic model as well as a subscale prototype have been constructed, and the latter was successfully tested. The principles of the coupling are discussed in some detail, with emphasis on their kinematic aspects. The formal proof for the constancy of the velocity ratio of this coupling is presented.

Stresses Around a Reinforced Circular Hole Near a Reinforced Straight Edge

1963 ◽  
Vol 14 (4) ◽  
pp. 374-386 ◽  
Author(s):  
G. A. O. Davies
Keyword(s):  
Circular Hole ◽  
Half Plane ◽  
Numerical Results ◽  
Straight Edge ◽  
Special Case

SummaryA solution is presented for the stresses in a half plane compactly reinforced along its straight edge and pierced by a reinforced circular hole in the vicinity of the edge. Numerical results are given for two cases of uniform applied tractions at infinity. In the special case of both boundaries unreinforced, the results obtained are in agreement with an existing solution by Mindlin.

scholarly journals Towards a unified theory of fractional and nonlocal vector calculus

2021 ◽  
Vol 24 (5) ◽  
pp. 1301-1355
Author(s):  
Marta D’Elia ◽  
Mamikon Gulian ◽  
Hayley Olson ◽  
George Em Karniadakis
Keyword(s):  
Ad Hoc ◽  
Broad Class ◽  
Anomalous Behavior ◽  
Unified Theory ◽  
Constrained Problems ◽  
Vector Calculus ◽  
Weighted Laplacian ◽  
Classical Vector ◽  
Laplacian Operators ◽  
Special Case

Abstract Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

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