Datum Planes Based on a Constrained L1 Norm

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Reference Frame ◽  
Convex Surface ◽  
Constrained Minimization ◽  
International Organization ◽  
New Method ◽  
Sampled Data ◽  
L1 Norm ◽  
Original Surface ◽  
Data Points ◽  
American Society

This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the L1 (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a simple minimization search between the convex surface and its centroid. The data points in the discrete case do not need to have any corresponding weights provided with them, as appropriate weighting is part of the algorithm itself, thereby making the algorithm largely insensitive to nonuniformly sampled data points. Terse mathematica code is included for the reader. The code is sufficient for primary and secondary planar datum fitting as well as a 3-2-1 datum reference frame generation. The second goal of this paper is to compare this new method with several other possible means for establishing datum planes, ultimately showing several appealing characteristics of the proposed algorithm. Since both the International Organization for Standardization (ISO) and American Society of Mechanical Engineers (ASME) standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.

An Improved L1 Based Algorithm for Standardized Planar Datum Establishment

2014 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Reference Frame ◽  
Convex Surface ◽  
Constrained Minimization ◽  
New Method ◽  
Discrete Case ◽  
Sampled Data ◽  
L1 Norm ◽  
Original Surface ◽  
Data Points

This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the L1 (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a simple minimization search between the convex surface and its centroid. The data points in the discrete case do not need to have any corresponding weights provided with them, as appropriate weighting is part of the algorithm itself, thereby making the algorithm largely insensitive to nonuniformly sampled data points. Terse Mathematica code is included for the reader. The code is sufficient for constrained and unconstrained planar fitting as well as a 3-2-1 datum reference frame generation. The second goal of this paper is to compare this new method with several other possible means for establishing datum planes, ultimately showing several appealing characteristics of the proposed algorithm. Since both the ISO and ASME standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.

A Synthesis Method for Placing Workpieces in RPR Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece

1996 ◽  
Author(s):  
K. D. Chaney ◽  
J. K. Davidson
Keyword(s):  
Reference Frame ◽  
Synthesis Method ◽  
Analytical Representation ◽  
New Method ◽  
Two Dimensional ◽  
End Effector ◽  
Radial Location ◽  
Practical Applications ◽  
Full Turn ◽  
Large Rotations

Abstract A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. The method is an analytical representation of the geometry of the robot and the task, and is particularly well suited to applications in which the task requires large rotations of the end-effector. It is determined that, when the task requires that the end-effector rotate a full turn at just two locations and when the first or third joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates tasks in which the tool must rotate a full turn at three locations on the workpiece. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.

scholarly journals More faithfulness graph embedding

2015 ◽  
Vol 4 (2) ◽  
pp. 336
Author(s):  
Alaa Najim
Keyword(s):  
Dimensionality Reduction ◽  
Graph Embedding ◽  
New Method ◽  
Graph Representation ◽  
Data Sets ◽  
Graph Visualization ◽  
Graph Data ◽  
Original Space ◽  
Data Points ◽  
Effectiveness And Efficiency

<p><span lang="EN-GB">Using dimensionality reduction idea to visualize graph data sets can preserve the properties of the original space and reveal the underlying information shared among data points. Continuity Trustworthy Graph Embedding (CTGE) is new method we have introduced in this paper to improve the faithfulness of the graph visualization. We will use CTGE in graph field to find new understandable representation to be more easy to analyze and study. Several experiments on real graph data sets are applied to test the effectiveness and efficiency of the proposed method, which showed CTGE generates highly faithfulness graph representation when compared its representation with other methods.</span></p>

scholarly journals Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Dong Liang ◽  
Chen Qiao ◽  
Zongben Xu
Keyword(s):  
Manifold Learning ◽  
Computational Efficiency ◽  
New Method ◽  
Data Sets ◽  
Learning Approaches ◽  
Real World Data ◽  
Efficiency Property ◽  
Data Points ◽  
Low Dimensional ◽  
High Computational Efficiency

The problems of improving computational efficiency and extending representational capability are the two hottest topics in approaches of global manifold learning. In this paper, a new method called extensive landmark Isomap (EL-Isomap) is presented, addressing both topics simultaneously. On one hand, originated from landmark Isomap (L-Isomap), which is known for its high computational efficiency property, EL-Isomap also possesses high computational efficiency through utilizing a small set of landmarks to embed all data points. On the other hand, EL-Isomap significantly extends the representational capability of L-Isomap and other global manifold learning approaches by utilizing only an available subset from the whole landmark set instead of all to embed each point. Particularly, compared with other manifold learning approaches, the data manifolds with intrinsic low-dimensional concave topologies and essential loops can be unwrapped by the new method more successfully, which are shown by simulation results on a series of synthetic and real-world data sets. Moreover, the accuracy, robustness, and computational complexity of EL-Isomap are analyzed in this paper, and the relation between EL-Isomap and L-Isomap is also discussed theoretically.

scholarly journals On Manipulation of Objects in Three-Fingered Grasp

1995 ◽  
Vol 117 (4) ◽  
pp. 561-565 ◽  
Author(s):  
D. P. Chevallier ◽  
S. Payandeh
Keyword(s):  
Reference Frame ◽  
New Method ◽  
Inner Product ◽  
Product Spaces ◽  
End Effector ◽  
Inner Product Spaces ◽  
Contact Points ◽  
Fixed Reference ◽  
Fine Manipulation

Manipulation of the grasped object is defined as the ability of the mechanical end-effector to create an instantaneous motion of the object with respect to a fixed reference frame (e.g., palm reference frame). This class of manipulation is usually referred to as the fine manipulation whereas a collection of all these instantaneous motions of the object is referred to as the gross manipulation. This paper presents a new method where for a given desired twist of the grasped object, the instantaneous motions of the fingertips can be determined. The results of the paper are divided into two parts. First, for the case where the motion of the object is created through motions of the fingertip in off-tangent planes to the object at the contact points. Second, where a class of motion of the grasped object is achieved through motions of the fingertips which are restricted to the tangent planes. The method of this paper utilizes screw geometry, inner product spaces and information regarding grasp configuration. The method is also illustrated through examples.

Relation between oxygen consumption and pressure-volume area of in situ dog heart

1987 ◽  
Vol 253 (1) ◽  
pp. 1-1 ◽  
Author(s):  
T. Nozawa ◽  
Y. Yasumura ◽  
S. Futaki ◽  
N. Tanaka ◽  
Y. Igarashi ◽  
...  
Keyword(s):  
Oxygen Consumption ◽  
Standard Deviation ◽  
Degrees Of Freedom ◽  
Regression Line ◽  
Computer Software ◽  
Confidence Limits ◽  
Sampled Data ◽  
Dog Heart ◽  
Data Points

Page H31: T. Nozawa, Y. Yasumura, S. Futaki, N. Tanaka, Y. Igarashi, Y. Goto, and H. Suga. “Relation between oxygen consumption and pressure-volume area of in situ dog heart.” Page H37: Fig. 6: Although the last sentence of the legend states “Solid lines are linear regression lines, and inner and outer pairs of dashed curves around them are 95% confidence limits of regression lines and data points, respectively,” these dashed lines show one standard deviation of both the slope of the regression line and the sampled data from the regression line. The authors forgot to multiply these standard deviation values by t value (2.069 for degrees of freedom = 23) for P le 0.05 in the computer software to obtain the 95% confidence limits. The other statistical results in Fig. 6 are correct.

MOAA and Topology Judgment for Mesh Construction

2004 ◽  
Author(s):  
Wen-Jie Cheng ◽  
Arzu Gonenc Sorguc ◽  
Junichi Shinoda ◽  
Ichiro Hagiwara
Keyword(s):  
Topology Optimization ◽  
Data Set ◽  
Basic Principles ◽  
Intersection Problem ◽  
Line Segments ◽  
Original Surface ◽  
Aspect Ratios ◽  
And Topology ◽  
Maximum Angle ◽  
Data Points

In this paper, the Maximum Opposite Angulation Approach (MOAA) for 3-D including the topology optimization is discussed. The MOAA algorithm is developed to generate meshes in 2-D and 3-D. The basic principles of the algorithm both in 2-D applications and in 3-D applications, is to pre-set uniformity to the initial data set to form point pairs yielding possible shortest line segments. These line segments are connected with the points providing the maximum angle for the vertex of the triangular mesh to be constructed. Thus, the algorithm provides triangular meshes having well balanced interior angles and good aspect ratios. The MOAA algorithm can be proved similar to the Delaunay’s approach in 2-D from the principle and with the quickest speed. In 3-D, it was also shown that it is much more efficient than many Delaunay class algorithms with mesh architectures preserving the topology, for uniformly organized data points. In this study, the topology optimization together with the MOAA algorithm is presented to improve the precision of reconstruction of the original surface. In this context, topology judgment for intersection problem in 3-D, distortion phenomenon, the possibility of loosing some characteristics of the original surface is thoroughly investigated.

scholarly journals A New Method of Relative Coordinate-and-Time Determination

1993 ◽  
Vol 156 ◽  
pp. 427-431
Author(s):  
V.S. Gubanov ◽  
Z.M. Malkin ◽  
N.I. Solina
Keyword(s):  
Reference Frame ◽  
New Method ◽  
Radio Interferometry ◽  
Relative Coordinate ◽  
Time Determination ◽  
Clock Comparison

The paper deals with the relative coordinate-and-time determination in a ground based reference frame by using the NAVSTAR/GLONASS radio interferometry and duplex clock comparison techniques.

International Standardization of Boilers and Pressure Vessels

1974 ◽  
Vol 96 (2) ◽  
pp. 137-139
Author(s):  
Bernard Fishman
Keyword(s):  
Materials Design ◽  
Technical Committee ◽  
Pressure Vessels ◽  
National Standards ◽  
International Organization ◽  
International Organization For Standardization ◽  
Working Groups ◽  
International Standardization ◽  
American Society ◽  
Tc 11

International standardization in the field of boilers and pressure vessels is being carried out within the International Organization for Standardization (ISO) by Technical Committee No. 11. The American Society of Mechanical Engineers (ASME) is responsible for coordinating this activity on behalf of the American National Standards Institute (ANSI). Forty-two countries are involved in the work of TC 11 which is organized into 4 subcommittees and 16 working groups covering major areas such as materials, design, welded construction, and serially made pressure vessels.

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