Tolerance-Maps Applied to a Point-Line Cluster of Features

2006 ◽  
Vol 129 (8) ◽  
pp. 782-792 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Dimensional Space ◽  
Local Level ◽  
Two Dimensional ◽  
Relative Location ◽  
Global Level ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Cluster A ◽  
Point Line ◽  
Picture Frame

In this paper, groups of individual features, i.e., a point, a line, and a plane, are called clusters and are used to constrain sufficiently the relative location of adjacent parts. A new mathematical model for representing size and geometric tolerances is applied to a point-line cluster of features that is used to align adjacent parts in two-dimensional space. First, tolerance-zones are described for the point-line cluster. A Tolerance-Map® (Patent no. 69638242), a hypothetical volume of points, is then established which is the range of a mapping from all possible locations for the features in the cluster. A picture frame assembly of four parts is used to illustrate the accumulations of manufacturing variations, and the T-Maps® provide stackup relations that can be used to allocate size and orientational tolerances. This model is one part of a bilevel model that we are developing for size and geometric tolerances. At the local level the model deals with the permitted variations in a tolerance zone, while at the global level it interrelates all the frames of reference on a part or assembly.

Tolerance-Maps Applied to a Point-Line Cluster of Features

2005 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Dimensional Space ◽  
Local Level ◽  
Relative Location ◽  
Global Level ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Level Model ◽  
Cluster A ◽  
Point Line ◽  
Picture Frame

In this paper, groups of individual features, i.e. a point, a line, and a plane, are called clusters and are used to constrain sufficiently the relative location of adjacent parts. A new mathematical model for representing geometric tolerances is applied to a point-line cluster of features that is used to align adjacent parts in two-dimensional space. First, tolerance-zones are described for the point-line cluster. Then, a Tolerance-Map®, a hypothetical volume of points, is established which is the range of a mapping from all possible locations for the features in the cluster. A picture frame assembly of four parts is used to illustrate the accumulations of manufacturing variations, and the T-Maps provide stackup relations that can be used to allocate size and orientational tolerances. This model is one part of a bi-level model that we are developing for geometric tolerances. At the local level the model deals with the permitted variations in a tolerance zone, while at the global level it interrelates all the frames of reference on a part or assembly.

Modeling of Geometric Variations for Line-Profiles

2011 ◽  
Author(s):  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Two Dimensional ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
True Profile ◽  
Profile Tolerance ◽  
On Line ◽  
Model Features ◽  
Tolerance Accumulation ◽  
First Time

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e. an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variation of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or non-symmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

Modeling of Geometric Variations for Line-Profiles

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Two Dimensional ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
True Profile ◽  
Profile Tolerance ◽  
On Line ◽  
Model Features ◽  
Tolerance Accumulation ◽  
First Time

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e., an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

Do You Want to See the Tree? Ignore the Forest

2014 ◽  
Vol 61 (3) ◽  
pp. 205-214 ◽  
Author(s):  
Nicolas Poirel ◽  
Claire Sara Krakowski ◽  
Sabrina Sayah ◽  
Arlette Pineau ◽  
Olivier Houdé ◽  
...  
Keyword(s):  
Visual Recognition ◽  
Local Level ◽  
Local Information ◽  
Visual Environment ◽  
Global Information ◽  
Focus Attention ◽  
Global Level ◽  
Hierarchical Stimuli ◽  
Priming Paradigm ◽  
The One

The visual environment consists of global structures (e.g., a forest) made up of local parts (e.g., trees). When compound stimuli are presented (e.g., large global letters composed of arrangements of small local letters), the global unattended information slows responses to local targets. Using a negative priming paradigm, we investigated whether inhibition is required to process hierarchical stimuli when information at the local level is in conflict with the one at the global level. The results show that when local and global information is in conflict, global information must be inhibited to process local information, but that the reverse is not true. This finding has potential direct implications for brain models of visual recognition, by suggesting that when local information is conflicting with global information, inhibitory control reduces feedback activity from global information (e.g., inhibits the forest) which allows the visual system to process local information (e.g., to focus attention on a particular tree).

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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