Optimal Placement of Fixture Clamps: Maintaining Form Closure and Independent Regions of Form Closure

2002 ◽  
Vol 124 (3) ◽  
pp. 676-685 ◽  
Author(s):  
Rodrigo A. Marin ◽  
Placid M. Ferreira
Keyword(s):  
Screw Theory ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Optimal Placement ◽  
Surface Type ◽  
Form Closure ◽  
Linear Programming Formulation ◽  
Precise Relationship ◽  
External Loads ◽  
Linear Algebraic Method

This paper addresses the problem of computing frictionless optimal clamping schemes with form closure on three-dimensional parts with planar and cylindrical faces. Given a work part with a pre-defined 3-2-1 locator scheme, a set of polygonal convex regions on the clamping faces are defined as the admissible positions of the clamps. The work part-fixture contact is assumed to be of the point-surface type. Using extended screw theory, we present a linear algebraic method that computes the sub-regions of the clamping faces such that clamps located within them are guaranteed to achieve form closure. These are termed dependent regions of form closure, since the clamps must be placed according to a precise relationship. We develop methods to compute these regions on work parts with planar and cylindrical faces. This result is incorporated into a new linear programming formulation to compute frictionless optimal clamping schemes. Clamping schemes with form closure are robust when uncertainty in knowledge of the external loads acting on the work part is present. Next, we extend the method to compute maximal independent regions of form closure. These are sub-regions of the dependent regions of form closure where the clamps can be placed completely independent of each other while maintaining form closure. When the clamps are placed within the independent regions of form closure, the clamping scheme is made robust against errors in their positions.

Comprehensive design analysis of a 3D printed sensor for readiness assessment applications

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tanushree Agarwal ◽  
Fatemeh Rahmani ◽  
Ishtique Zaman ◽  
Federico Gasbarri ◽  
Keivan Davami ◽  
...  
Keyword(s):  
Sensor Array ◽  
Short Circuit ◽  
Three Dimensional ◽  
Low Frequency ◽  
Optimal Placement ◽  
Chemical Plants ◽  
Readiness Assessment ◽  
Element Analysis ◽  
Content Type ◽  
Flexible Antenna

Purpose This paper aims to develop a comprehensive model of a magnetic sensor array that will be operational for a multitude of electric components in continuous and nonintrusive condition monitoring (CM) or in readiness assessment (RA) applications. Design/methodology/approach A universal nonintrusive model of a flexible antenna array is introduced to monitor and identify failures in electric machine drives. An adjustable sensor is designed to serve as a RA for a vast range of electrical elements in a typical power system by capturing the low-frequency radiated magnetic fields. Findings The optimal placement of the most sensitive radiated fields from several components has been discovered in this case study, enabling the detection of healthy current flow throughout. Thereafter, the short-circuit investigation, representing faulty situations, is implemented and compared with healthy cases. Practical implications This sensing technique can be used for nonintrusive CM of components that are out of reach and cannot have the sensor to be held around it such as components in offshore winds, wind energy generation and power and chemical plants. Originality/value The results are provided for three commonly used machines with a single sensor array with numerous settings. The three dimensional (3 D) finite element analysis is applied in the structuring of the sensor, detection of the optimum location and recognition of faults in the machines. Finally, based on the setup design, 3 D printing is used for the construction of the sensor array. Thus, the sensor array with fault detection avoids major component failures and increases system reliability/resiliency.

Kinematics of Meshing Surfaces Using Geometric Algebra

2003 ◽  
Author(s):  
Scott M. Miller
Keyword(s):  
Geometric Algebra ◽  
Screw Theory ◽  
Three Dimensional ◽  
Normal Vector ◽  
The Past ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
The Common ◽  
Two Bodies ◽  
Theoretical Developments

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

scholarly journals Three-Dimensional Assembly Synthesis for Robust Dimensional Integrity Based on Screw Theory

2004 ◽  
Vol 128 (1) ◽  
pp. 243-251 ◽  
Author(s):  
Byungwoo Lee ◽  
Kazuhiro Saitou
Keyword(s):  
Screw Theory ◽  
Three Dimensional ◽  
Proper Part ◽  
Space Frame ◽  
Reverse Sequence ◽  
3D Representation

This paper presents a three-dimensional (3D) extension of our previous work on the synthesis of assemblies whose dimensional integrity is insensitive to the dimensional variations of individual parts. Assuming that assemblies can be built in the reverse sequence of decomposition, the method recursively decomposes a given product geometry into two subassemblies until parts become manufacturable. At each recursion, joints are assigned to the interfaces between two subassemblies to ensure the two criteria for robust dimensional integrity, in-process dimensional adjustability, and proper part constraints. Screw theory is utilized as a unified 3D representation of the two criteria. A case study on an automotive space frame is presented to demonstrate the method.

Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

3D Digital Measurement of Large Scale Objects Based on Viscous Target

2005 ◽  
Vol 295-296 ◽  
pp. 687-692 ◽  
Author(s):  
B. Wu ◽  
Ji Gui Zhu ◽  
Xue You Yang ◽  
T. Xue ◽  
S.H. Ye
Keyword(s):  
Large Scale ◽  
Screw Theory ◽  
Three Dimensional ◽  
Automatic Identification ◽  
Digital Measurement ◽  
Image Mosaic ◽  
Space Length ◽  
Dimensional Image ◽  
Spatial Image ◽  
Measuring Field

For 3D digital measurement of large scale objects, image mosaic is the key technology to achieve whole measurement for a small measuring field of the sensor unit. A viscous-target-based three-dimensional image mosaic technology is proposed. The screw theory is introduced to realize the spatial image mosaic. The method permits an automatic identification of targets and a better matching for the feature coded technology. In experiments, the method was proved to be valid, with a relatively high precision on three-dimensional image mosaic. The relative error of the space length measurement is less than 0.6%.

scholarly journals Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 300 ◽  
Author(s):  
Artur Karimov ◽  
Erivelton G. Nepomuceno ◽  
Aleksandra Tutueva ◽  
Denis Butusov
Keyword(s):  
Dynamical System ◽  
Nonlinear Systems ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Data Series ◽  
Lorenz Attractor ◽  
State Variables ◽  
Laurent Polynomials ◽  
Actual Problem ◽  
Partially Observed

The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one should reconstruct the entire phase space to restore unobserved state variables. For this purpose, the integration or differentiation of the observed data series can be performed. Then, a fast-algebraic method can be used to obtain a nonlinear system in the form of a polynomial dynamical system. In this paper, we extend the algebraic method proposed by Kera and Hasegawa to Laurent polynomials which contain negative powers of variables, unlike ordinary polynomials. We provide a theoretical basis and experimental evidence that the integration of a data series can give more accurate results than the widely used differentiation. With this technique, we reconstruct Lorenz attractor from a one-dimensional data series and B. Muthuswamy’s circuit equations from a three-dimensional data series.

A simple approach for optimal allocation of dampers in nonsymmetrical 3D multi-storey structures

2014 ◽  
Vol 14 (03) ◽  
pp. 1350074 ◽  
Author(s):  
L. J. Leu ◽  
J. T. Chang
Keyword(s):  
Optimal Allocation ◽  
Seismic Analysis ◽  
Search Algorithm ◽  
Three Dimensional ◽  
Time History ◽  
Simple Approach ◽  
Optimal Placement ◽  
Drift Ratio ◽  
History Analysis ◽  
Stop Criterion

A new simple approach is proposed to search for the optimal placement of dampers in nonsymmetrical three-dimensional (3D) structures. Dampers are placed uniformly and initially at each storey of two selected bays of the bare structures and the time-history seismic analysis is performed. The maximal inter-storey drift ratio is chosen as the performance index. Then the inter-storey drift ratio is checked for the locations where dampers were added. The damper in the location with the minimal inter-storey drift ratio is moved to the location having the maximal inter-storey drift ratio. This process is repeated until the prescribed stop criterion is met. Both linear and nonlinear viscous dampers are used in this study. The damping coefficient of added dampers for the initial damper placement is determined by setting the maximal inter-storey drift ratio of the whole structure equal to a certain value when a ground motion is applied. In the proposed relocation process, the maximal inter-storey drift ratio will be reduced significantly. Three examples, including two 10-storey and one 20-storey 3D nonsymmetrical structures, are used to demonstrate the efficiency and accuracy of the proposed approach. The results are compared with those obtained using the simplified sequential search algorithm (SSSA). It is found that the proposed approach requires fewer number of time-history analysis than that using the SSSA while their accuracy is comparable.

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