scholarly journals Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

Micromachines ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 597
Author(s):  
Lucía Díaz Pérez ◽  
Beatriz Rubio Serrano ◽  
José A. Albajez García ◽  
José A. Yagu¨e Fabra ◽  
Esmeralda Mainar Maza ◽  
...  
Keyword(s):  
Curve Fitting ◽  
Control Strategies ◽  
Parametric Representation ◽  
Relative Accuracy ◽  
Positioning Control ◽  
Positioning Systems ◽  
High Relative Accuracy ◽  
Cad Cam ◽  
Data Points ◽  
Novel Algorithms

Nanotechnology applications demand high accuracy positioning systems. Therefore, in order to achieve sub-micrometer accuracy, positioning uncertainty contributions must be minimized by implementing precision positioning control strategies. The positioning control system accuracy must be analyzed and optimized, especially when the system is required to follow a predefined trajectory. In this line of research, this work studies the contribution of the trajectory definition errors to the final positioning uncertainty of a large-range 2D nanopositioning stage. The curve trajectory is defined by curve fitting using two methods: traditional CAD/CAM systems and novel algorithms for accurate curve fitting. This novel method has an interest in computer-aided geometric design and approximation theory, and allows high relative accuracy (HRA) in the computation of the representations of parametric curves while minimizing the numerical errors. It is verified that the HRA method offers better positioning accuracy than commonly used CAD/CAM methods when defining a trajectory by curve fitting: When fitting a curve by interpolation with the HRA method, fewer data points are required to achieve the precision requirements. Similarly, when fitting a curve by a least-squares approximation, for the same set of given data points, the HRA method is capable of obtaining an accurate approximation curve with fewer control points.

Parametric Description of Vibration Using the Autocorrelation Function

2009 ◽  
Vol 147-149 ◽  
pp. 606-611
Author(s):  
Adam Kotowski
Keyword(s):  
Autocorrelation Function ◽  
Curve Fitting ◽  
Vibration Signal ◽  
Analytic Form ◽  
Parametric Representation ◽  
Rotating Machine ◽  
Fitting Procedure ◽  
Power Spectral ◽  
Parametric Description ◽  
Harmonic Components

The paper presents the use of the autocorrelation function for the description of vibrations and the problems connected with. The proposed method is based on the analysis of vibration signal recorded for machine during its operations using an analytic form of the autocorrelation function. The parameters are obtained using a curve fitting procedure. To keep a quality of parametric representation of considered vibration, only the curve fitting causes a determination coefficient over 0.90 is taken into consideration. Therefore, the autocorrelation functions are submitted for the fast Fourier transform to be helped, in determination of number of the dominant harmonic components. Also, the analytic form and parameters of power spectral density has been also calculated. Finally, the set of parameters has been collected to describe the selected fragment of vibration of the simple rotating machine. The influence of duration of analyzed vibration on the parameters values is also examined in this work.

Globoidal Indexing Cam’s CAD/CAM Development on Pro/E

2011 ◽  
Vol 86 ◽  
pp. 496-499 ◽  
Author(s):  
Nian Fu Xu ◽  
Feng Xu ◽  
Wei He
Keyword(s):  
Main Idea ◽  
Cam Mechanism ◽  
Cad Cam ◽  
Data Points ◽  
Design And Manufacture ◽  
Further Development

Because of the design and manufacture of the globoidal indexing cam mechanism is very difficult, this paper developed a globoidal indexing cam CAD/CAM system by using Pro/ Engineer’s further development module Pro/Toolkit, which can simplify the process of designing the globoidal indexing cam. The main idea is that designing cam by parameters and generating the data points of the indexing cam automatically by the computer.

Design and Manufacturing Analyses for Integrated CAD/CAM of Cams

1989 ◽  
Vol 111 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Z. Gal-Tzur ◽  
M. Shpitalni ◽  
S. Malkin
Keyword(s):  
Thermal Damage ◽  
Spline Interpolation ◽  
Analytical Form ◽  
Design Stage ◽  
Cubic Spline Interpolation ◽  
Analytical Functions ◽  
Cnc Grinding ◽  
Design And Manufacturing ◽  
Cad Cam ◽  
Data Points

Design and manufacturing analyses are presented which are the basis for an integrated CAD/CAM system for cams. The design analysis begins with the lift schedule specified either by analytical functions or by discrete data points which are transformed to an analytical form by cubic spline interpolation. The required cam contour and its curvature at each point on the cam periphery are then derived. Machining of the required cam shape is analyzed for NC jig grinding, CNC grinding, and rocker grinding. For NC jig grinding only the geometrical aspects of the process are analyzed, but for CNC and rocker grinding both the geometrical and physical aspects of the process are considered for control of cam geometry and thermal damage. Integration of design and maufacturing tasks in this way allows for manufacturing characteristics and limitations to be taken into account in the design stage.

Parametric Design of Tractor Configuration Using API Based on CATIA

2010 ◽  
Vol 455 ◽  
pp. 411-416
Author(s):  
Ji Shun Li ◽  
L.H. Chen ◽  
L. Li
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Three Dimensional ◽  
Parametric Representation ◽  
Material Object ◽  
Chain Reactions ◽  
Development Cycle ◽  
Cad Cam ◽  
Key Issues ◽  
Small Change

The traditional shape design method of tractor is mainly completed based on the manual design. Messages are transmited mainly through material object, model, blueprint and template. The material object and model even have a small change that will cause massive chain-reactions such as tedious blueprint revision. And there will be a great many of problem, such as the development cycle of tractor to be long, the accumulative error of design to be big, the development cost to be high and product universalization and serialized degree to be low. This problem is key problem to be solved for shape designer. Advanced design method such as CAD/CAM provid solutions for us, and especially the concept of parametric design was applied. In this paper an appfoach for the parametric design of tractor configuration will be presented. To this end, there are two key issues to be solved: First, the parametric representation of the tractor configuration, second，how to generate a three—dimesional shape of the tractor automatically based on the parametric representation. The parametric design of the tractor configuration is implemented by making use of the API technique of the CAD software，namely automation in CATIA．The test example shows that the approach presented is able to generate a three dimensional shape of the tractor automatically and meet the need of the parametric design of tractor configuration.

Machine Learning Techniques on Multidimensional Curve Fitting Data Based on R- Square and Chi-Square Methods

2016 ◽  
Vol 6 (3) ◽  
pp. 974 ◽  
Author(s):  
Vidyullatha P ◽  
D. Rajeswara Rao
Keyword(s):  
Machine Learning ◽  
Linear Model ◽  
Curve Fitting ◽  
Linear Models ◽  
Machine Learning Techniques ◽  
Chi Square ◽  
Curve Fit ◽  
Learning Techniques ◽  
Non Linear ◽  
Data Points

<p>Curve fitting is one of the procedures in data analysis and is helpful for prediction analysis showing graphically how the data points are related to one another whether it is in linear or non-linear model. Usually, the curve fit will find the concentrates along the curve or it will just use to smooth the data and upgrade the presence of the plot. Curve fitting checks the relationship between independent variables and dependent variables with the objective of characterizing a good fit model. Curve fitting finds mathematical equation that best fits given information. In this paper, 150 unorganized data points of environmental variables are used to develop Linear and non-linear data modelling which are evaluated by utilizing 3 dimensional ‘Sftool’ and ‘Labfit’ machine learning techniques. In Linear model, the best estimations of the coefficients are realized by the estimation of R- square turns in to one and in Non-Linear models with least Chi-square are the criteria. </p>

Cleaving optical fibre lengths to high relative accuracy

1998 ◽  
Vol 157 (1-6) ◽  
pp. 282-290 ◽  
Author(s):  
Mark P.J.L Chang ◽  
David F Buscher
Keyword(s):  
Optical Fibre ◽  
Relative Accuracy ◽  
High Relative Accuracy
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