Curvature Analysis of Surfaces in Higher Pair Contact—Part 2: Application to Spatial Cam Mechanisms

1976 ◽  
Vol 98 (2) ◽  
pp. 403-409 ◽  
Author(s):  
S. G. Dhande ◽  
J. Chakraborty
Keyword(s):  
Three Dimensional ◽  
Principal Curvatures ◽  
Numerical Example ◽  
Curvature Analysis ◽  
Contact Part

In this paper curvature analysis is performed for different three-dimensional cam mechanisms. In every case the expressions for principal curvatures of the cam surface are given in closed forms for ready use. A numerical example is given to show the usefulness of the proposed procedure.

Curvature Analysis of Surfaces in Higher Pair Contact—Part 1: An Analytical Investigation

1976 ◽  
Vol 98 (2) ◽  
pp. 397-402 ◽  
Author(s):  
S. G. Dhande ◽  
J. Chakraborty
Keyword(s):  
Velocity Ratio ◽  
Analytical Investigation ◽  
Principal Curvatures ◽  
Curvature Analysis ◽  
Contact Surfaces ◽  
Contact Part

In this paper, the analytical investigation is done to evaluate the normal and principal curvatures of contacting surfaces in higher pair contact. The velocity ratio of the members connected with the higher-pair-contact surfaces is assumed to be variable. The principal curvatures of the generated or driven surface are expressed in terms of those of the generating or driving surface.

Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2

2020 ◽  
Vol 17 (05) ◽  
pp. 2050073
Author(s):  
Yaning Wang
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Geodesic Sphere ◽  
Principal Curvatures ◽  
Space Forms ◽  
Complex Dimension

Let [Formula: see text] be a three-dimensional real hypersurface in a nonflat complex space form of complex dimension two. In this paper, we prove that [Formula: see text] is [Formula: see text]-parallel with two distinct principal curvatures at each point if and only if it is locally congruent to a geodesic sphere in [Formula: see text] or a horosphere, a geodesic sphere or a tube over totally geodesic complex hyperbolic plane in [Formula: see text]. Moreover, [Formula: see text]-parallel real hypersurfaces in [Formula: see text] and [Formula: see text] under some other conditions are classified and these results extend Suh’s in [Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map, Nihonkai Math. J. 6 (1995) 63–79] and Kon–Loo’s in [On characterizations of real hypersurfaces in a complex space form with [Formula: see text]-parallel shape operator, Canad. Math. Bull. 55 (2012) 114–126].

scholarly journals Multiscale 3D Curvature Analysis of Processed Surface Textures of Aluminum Alloy 6061 T6

Materials ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 257 ◽  
Author(s):  
Tomasz Bartkowiak ◽  
Christopher A. Brown
Keyword(s):  
Principal Curvatures ◽  
Surface Textures ◽  
Curvature Analysis ◽  
Mass Finishing ◽  
Dependent Behavior ◽  
Surface Topographies ◽  
Laser Confocal Microscope ◽  
Curvature Tensors ◽  
Alloy 6061

The objectives of this paper are to demonstrate the viability, and to validate, in part, a multiscale method for calculating curvature tensors on measured surface topographies with two different methods of specifying the scale. The curvature tensors are calculated as functions of scale, i.e., size, and position from a regular, orthogonal array of measured heights. Multiscale characterization of curvature is important because, like slope and area, it changes with the scale of observation, or calculation, on irregular surfaces. Curvatures can be indicative of the topographically dependent behavior of a surface and, in turn, curvatures are influenced by the processing and use of the surface. Curvatures of surface topographies have not been well- characterized yet. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. Manufactured surfaces are studied for further validation of the calculation method because they provide certain expectations for curvatures, which depend on scale and the degree of curvature. To study a range of curvatures on manufactured surfaces, square edges are machined and honed, then rounded progressively by mass finishing; additionally, a set of surfaces was made by turning with different feeds. Topographic measurements are made with a scanning laser confocal microscope. The calculations use vectors, normal to the measured surface, which are calculated first, then the eigenvalue problem is solved for the curvature tensor. Plots of principal curvatures as a function of position and scale are presented. Statistical analyses show expected interactions between curvature and these manufacturing processes.

A fast procedure for computing incremental growth distances

Robotica ◽  
2000 ◽  
Vol 18 (4) ◽  
pp. 429-441 ◽  
Author(s):  
Sun-Mog Hong ◽  
Joon-Hyuek Yeo ◽  
Hae-Wook Park
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Computation Time ◽  
Interference Detection ◽  
Geometric Complexity ◽  
Numerical Example ◽  
Incremental Growth ◽  
Fast Procedure ◽  
Three Dimensional Space

A fast numerical procedure is presented for computing growth distances between a pair of polytopes in three dimensional space that move incrementally along specified smooth paths. The procedure carrys out the growth distance evaluations efficiently by predicting and verifying contact configurations between a pair of grown polytopes. In the prediction and verification the procedure uses vertex and facial characterizations of polytopes and exploits their geometric adjacency information. The computation time, in average, is very small and does not depend significantly on the geometric complexity of two polytopes. A numerical example is presented to demonstrate the applicability of the procedure to interference detection in robotic simulations.

Some Implications of Dundurs' Theorem for Thermoelastic Contact and Crack Problems

1980 ◽  
Vol 22 (5) ◽  
pp. 229-232 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Steady State ◽  
Thick Plate ◽  
Line Element ◽  
Three Dimensional ◽  
Contact Problems ◽  
Free Boundaries ◽  
Principal Curvatures ◽  
State Heat ◽  
Crack Problems ◽  
Steady State Heat

It is well known that a simply-connected isotropic elastic body in a state of plane strain and with traction-free boundaries remains free of stress if it is subject to steady-state heat conduction. A recent theorem due to Dundurs shows that in this state the curvature of any initially straight line element is proportional to the heat flux across the line element. A closely related three dimensional result is proved for the sum of the principal curvatures of planes parallel to the faces of an infinite thick plate. These results have certain implications for thermoelastic crack and contact problems. For example: (i) thermal distortion has no effect on the contact pressure distribution at an insulated interface or at an interface between two similar materials, (ii) the thermal stress in a cracked solid depends on the temperature field only through the value of a certain constant related to the average temperature difference across the crack, (iii) steady-state heat flow induces no stresses in an axisymmetric thick plate containing an external crack.

EDMA: a computer program for topological analysis of discrete electron densities

2012 ◽  
Vol 45 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Lukáš Palatinus ◽  
Siriyara Jagannatha Prathapa ◽  
Sander van Smaalen
Keyword(s):  
Computer Program ◽  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Real Space ◽  
Principal Curvatures ◽  
Electron Densities ◽  
Structure Solution ◽  
Aperiodic Crystals

EDMAis a computer program for topological analysis of discrete electron densities according to Bader's theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins.EDMAcan also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation ofab initioelectron densities obtained in the process of structure solution. A particular feature ofEDMAis that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions.EDMAfirst generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications ofEDMAto model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4or better.

Non-Iterative Finite Element Scheme for Combined Annular-Thrust Porous Aerostatic Bearings Analysis

2012 ◽  
Author(s):  
Polina V. Khan ◽  
Pyung Hwang
Keyword(s):  
Finite Element ◽  
Air Flow ◽  
Three Dimensional ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Numerical Example ◽  
Key Points ◽  
Aerostatic Bearings

The key points of method derivation and a numerical example for bearing with three dimensional air flow are presented.

scholarly journals Surface model of the human red blood cell simulating changes in membrane curvature under strain

2021 ◽  
Author(s):  
Philip W. Kuchel ◽  
Charles D. Cox ◽  
Daniel Daners ◽  
Dmitry Shishmarev ◽  
Petrik Galvosas
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Morphological Changes ◽  
Three Dimensional ◽  
Membrane Curvature ◽  
Glycolytic Flux ◽  
Surface Model ◽  
Principal Curvatures ◽  
Quartic Equation ◽  
Shape Changes

Abstract The highly deformable red blood cell (erythrocyte; RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a special apparatus inside an NMR spectrometer. However, direct mathematical predictions of the shapes of the morphed cells have not been reported before. We used recently available functions in Mathematica to triangularize and then compute four types of curvature. The RBCs were described by a previously presented quartic equation in three dimensional (3D) Cartesian space. A key finding was the extent to which the maximum and minimum Principal Curvatures were localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. The simulations, on the nano-metre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions that persist for many hours. This view is consistent with a recent proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. On the other hand, if the curvature that gates Piezo1 is at a much finer length scale, then membrane tension will determine local curvature and micron scale curvature as described here will be less likely to influence Piezo1 activity. The geometrical reorganization of the simulated cytoskeleton helps understanding of the concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.

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