Virtual Locator Trimming in Pre-Production: Rigid and Non-Rigid Analysis

2005 ◽  
Author(s):  
Lars Lindkvist ◽  
Johan S. Carlson ◽  
Rikard So¨derberg
Keyword(s):  
Least Square ◽  
Computer Tool ◽  
Number Of Components ◽  
Form Errors ◽  
Influence Coefficients ◽  
Least Square Problem ◽  
Inspection Data ◽  
Linear Least Square

In pre-production, during assembly of newly produced components geometrical deviations, caused by form errors of the parts, are discovered that can cause either functional or esthetical problems. One commonly used way of solving this is to reposition the components by adjusting their locators, also known as trimming. Traditionally this is done by assembling a number of components, measuring the deviations to surrounding parts, adjusting the locator points, reassembling the components and measuring the result. This is repeated until the result is satisfactory, and is a quite time and effort consuming activity. This paper presents a method and a tool that simplifies this process. Based on inspection data from the initial components all trimming activities are performed in the computer tool presented. After the locators are adjusted, the result is presented directly, which eliminates the need for physical inspection in order to verify the result of the trimming. The presented tool also includes optimization of the trimming. By formulating the problem of minimizing the geometrical deviations as a linear least square problem a general optimization package can be used. The optimization handles both boundaries on the allowed trimming and weighting of the different inspection features. By using the method of influence coefficients, also compliant (non-rigid) components can be handled.

A novel method to identify DH parameters of the rigid serial-link robot based on a geometry model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tao Zhang ◽  
Yuntao Song ◽  
Huapeng Wu ◽  
Qi Wang
Keyword(s):  
Geometric Model ◽  
Least Square ◽  
Geometric Features ◽  
Serial Link ◽  
Redundant Robot ◽  
Content Type ◽  
Redundant Robots ◽  
Geometry Model ◽  
Least Square Problem ◽  
Linear Least Square

Purpose Every geometric model corresponding to a unique feature whose errors of parameters uncorrelated, so the linearization technique can be successfully applied. The solution of a linear least square problem can be applied straightforwardly. This method has advantages especially in calibrate the redundant robot because it’s relatively small. The parameters of kinematics are unique and determined by this algorithm. Design/methodology/approach In this paper, a geometric identification method has been studied to estimate the parameters in the Denavit–Hartenberg (DH) model of the robot. Through studying the robot’s geometric features, specific trajectories are designed for calibrating the DH parameters. On the basis of these geometric features, several fitting methods have been deduced so that the important geometric parameters of robots, such as the actual rotation centers and rotate axes, can be found. Findings By measuring the corresponding motion trajectory at the end-effector, the trajectory feature can be identified by using curve fitting methods, and the trajectory feature will reflect back to the actual value of the DH parameters. Originality/value This method is especially suitable for rigid serial-link robots especially for redundant robots because of its specific calibration trajectory and geometric features. Besides, this method uses geometric features to calibrate the robot which is relatively small especially for the redundant robot comparing to the numerical algorithm.

GPS-DERIVED SECULAR VELOCITY FIELD AROUND SANGIHE ISLAND AND ITS IMPLICATION TO THE MOLUCCA SEA SEISMICITY

GEOMATIKA ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 107
Author(s):  
Leni Sophia Heliani ◽  
Cecep Pratama ◽  
Parseno Parseno ◽  
Nurrohmat Widjajanti ◽  
Dwi Lestari
Keyword(s):  
Surface Displacement ◽  
Active Regions ◽  
Least Square ◽  
The Other ◽  
Gps Data ◽  
West Side ◽  
Active Deformation ◽  
Secular Motion ◽  
Small Change ◽  
Linear Least Square

<p><em>Sangihe-Moluccas region is the most active seismicity in Indonesia. Between 2015 to 2018 there is four M6 class earthquake occurred close to the Sangihe-Moluccas region. These seismic active regions representing active deformation which is recorded on installed GPS for both campaign and continuous station. However, the origin of those frequent earthquakes has not been well understood especially related to GPS-derived secular motion. Therefore, we intend to estimate the secular motion inside and around Sangihe island. On the other hand, we also evaluate the effect of seismicity on GPS sites. Since our GPS data were conducted on yearly basis, we used an empirical global model of surface displacement due to coseismic activity. We calculate the offset that may be contained in the GPS site during its period</em><em>. </em><em>We remove the offset and estimate again the secular motion using linear least square. Hence, in comparison with the secular motion without considering the seismicity, we observe small change but systematically shifting the motion. We concluded the seismicity in the Molucca sea from 2015 to 2018 systematically change the secular motion around Sangihe Island at the sub-mm level. Finally, we obtained the secular motion toward each other between the east and west side within 1 to 5.5 cm/year displacement. </em></p>

scholarly journals An Indoor Visible Light Positioning System Using Tilted LEDs with High Accuracy

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 920
Author(s):  
Neha Chaudhary ◽  
Othman Isam Younus ◽  
Luis Nero Alves ◽  
Zabih Ghassemlooy ◽  
Stanislav Zvanovec ◽  
...  
Keyword(s):  
Visible Light ◽  
Polynomial Regression ◽  
Power Level ◽  
Least Square ◽  
Line Of Sight ◽  
Received Power ◽  
Strength Based ◽  
Complex Linear ◽  
Linear Least Square ◽  
First Time

The accuracy of the received signal strength-based visible light positioning (VLP) system in indoor applications is constrained by the tilt angles of transmitters (Txs) and receivers as well as multipath reflections. In this paper, for the first time, we show that tilting the Tx can be beneficial in VLP systems considering both line of sight (LoS) and non-line of sight transmission paths. With the Txs oriented towards the center of the receiving plane (i.e., the pointing center F), the received power level is maximized due to the LoS components on F. We also show that the proposed scheme offers a significant accuracy improvement of up to ~66% compared with a typical non-tilted Tx VLP at a dedicated location within a room using a low complex linear least square algorithm with polynomial regression. The effect of tilting the Tx on the lighting uniformity is also investigated and results proved that the uniformity achieved complies with the European Standard EN 12464-1. Furthermore, we show that the accuracy of VLP can be further enhanced with a minimum positioning error of 8 mm by changing the height of F.

scholarly journals Numerical method to a class of boundary value problems

2018 ◽  
Vol 22 (4) ◽  
pp. 1877-1883 ◽  
Author(s):  
Yu-Yang Qiu
Keyword(s):  
Boundary Value Problems ◽  
Numerical Method ◽  
Conjugate Gradient ◽  
Iteration Method ◽  
Boundary Value ◽  
Solution Process ◽  
Least Square ◽  
Least Square Problem ◽  
Matrix Iteration

A class of boundary value problems can be transformed uniformly to a least square problem with Toeplitz constraint. Conjugate gradient least square, a matrix iteration method, is adopted to solve this problem, and the solution process is elucidated step by step so that the example can be used as a paradigm for other applications.

scholarly journals Characteristics and Application of the NHPP Log-Logistic Reliability Model

2018 ◽  
Vol 8 (1) ◽  
pp. 44
Author(s):  
Lutfiah Ismail Al turk
Keyword(s):  
Evaluation Criteria ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Reliability Model ◽  
Reliability Engineering ◽  
Reliability Models ◽  
Time Domain Data ◽  
Linear Least Square

In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model&rsquo;s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.

scholarly journals An Optimum Balance Weight Search Algorithm

1993 ◽  
Author(s):  
James C. Austrow
Keyword(s):  
Search Algorithm ◽  
Least Square ◽  
Test Case ◽  
Influence Coefficient ◽  
Residual Vibration ◽  
Single Plane ◽  
Vibration Data ◽  
Influence Coefficients ◽  
Balance Weight ◽  
Optimum Balance

A mathematical description for an optimum balance weight search algorithm for single plane multipoint balance is presented. The algorithm uses influence coefficients, either measured or known beforehand, and measured complex vibration data to determine an optimum balance correction weight. The solution minimizes the maximum residual vibration. The algorithm allows user defined balance weights to be analyzed and evaluated. A test case is presented showing actual results and comparison with a least square solution algorithm. An efficient multiplane influence coefficient calculation scheme is also presented.

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