A Novel Approach to Algebraic Fitting of a Pencil of Quadrics for Planar 4R Motion Synthesis

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar ◽  
Xiangyun Li
Keyword(s):  
Fast Algorithm ◽  
Nonlinear Least Squares ◽  
Linear Formulation ◽  
Image Space ◽  
Kinematic Synthesis ◽  
Novel Approach ◽  
Motion Approximation ◽  
New Formulation ◽  
Algebraic Manifolds ◽  
Fitting Problem

The use of the image space of planar displacements for planar motion approximation is a well studied subject. While the constraint manifolds associated with planar four-bar linkages are algebraic, geometric (or normal) distances have been used as default metric for nonlinear least squares fitting of these algebraic manifolds. This paper presents a new formulation for the manifold fitting problem using algebraic distance and shows that the problem can be solved by fitting a pencil of quadrics with linear coefficients to a set of image points of a given set of displacements. This linear formulation leads to a simple and fast algorithm for kinematic synthesis in the image space.

A Novel Approach to Algebraic Fitting of a Pencil of Quadrics for Planar 4R Motion Synthesis

2012 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar ◽  
Xiangyun Li
Keyword(s):  
Least Squares ◽  
Fast Algorithm ◽  
Linear Formulation ◽  
Image Space ◽  
Kinematic Synthesis ◽  
One Dimensional ◽  
Least Squares Fitting ◽  
Novel Approach ◽  
Motion Approximation ◽  
Algebraic Manifolds

The use of the image space of planar displacements for planar motion approximation is a well studied subject. While the constraint manifolds associated with planar four-bar linkages are algebraic, geometric (or normal) distances have been used as default metric for least-squares fitting of these algebraic manifolds. This paper studies the problem of using algebraic distance for least-squares fitting of quadrics defining the constraint manifolds associated with Planar 4R mechanisms. It shows that the problem can be solved by fitting a pencil of quadrics with linear coefficients to a set of image points of a given one dimensional set of displacements. This linear formulation leads to a simple and fast algorithm for kinematic synthesis in the image space.

scholarly journals Enhanced Resorption of Liposomal Packed Vitamin C Monitored by Ultrasound

2020 ◽  
Vol 9 (6) ◽  
pp. 1616 ◽  
Author(s):  
Lukas Prantl ◽  
Andreas Eigenberger ◽  
Sebastian Gehmert ◽  
Silke Haerteis ◽  
Thiha Aung ◽  
...  
Keyword(s):  
Vitamin C ◽  
Oral Intake ◽  
The Body ◽  
Post Processing ◽  
Novel Approach ◽  
Health Related ◽  
Essential Nutrient ◽  
Freeze Etching ◽  
New Formulation ◽  
First Time

Vitamin C is an essential nutrient for humans and is involved in a plethora of health-related functions. Several studies have shown a connection between vitamin C intake and an improved resistance to infections that involves the immune system. However, the body cannot store vitamin C and both the elevated oral intake, and the intravenous application have certain disadvantages. In this study, we wanted to show a new formulation for the liposomal packaging of vitamin C. Using freeze etching electron microscopy, we show the formed liposomes. With a novel approach of post-processing procedures of real-time sonography that combines enhancement effects by contrast-like ultrasound with a transducer, we wanted to demonstrate the elevated intestinal vitamin C resorption on four participants. With the method presented in this study, it is possible to make use of the liposomal packaging of vitamin C with simple household materials and equipment for intake elevation. For the first time, we show the enhanced resorption of ingested liposomes using microbubble enhanced ultrasound imaging.

New Formulation of Bolted Joint Stiffness

2008 ◽  
Author(s):  
Sayed A. Nassar ◽  
Antoine Abboud
Keyword(s):  
Joint Stiffness ◽  
Effective Area ◽  
Accurate Estimate ◽  
Diameter Ratio ◽  
Bolted Joint ◽  
Reliable Prediction ◽  
Novel Approach ◽  
Fea Modeling ◽  
New Formulation ◽  
External Loads

New formulation is proposed for a more accurate estimate of bolted joint stiffness. In this study, a novel approach is used to obtain an expression for an effective area to be used for determining the clamped parts stiffness. A more accurate estimate of the joint stiffness would naturally provide a more reliable prediction of the bolted assembly response to external loads. The effects of the grip length-to-diameter ratio, joint dimensions, and the contact radii ratio of the joint plates are investigated and analyzed. Experimental data and finite element (FEA) modeling are provided to evaluate the accuracy of the proposed formulation of joint stiffness.

scholarly journals Tensor Decomposition for Multilayer Networks Clustering

2019 ◽  
Vol 33 ◽  
pp. 3371-3378 ◽  
Author(s):  
Zitai Chen ◽  
Chuan Chen ◽  
Zibin Zheng ◽  
Yi Zhu
Keyword(s):  
Clustering Algorithms ◽  
Cluster Structure ◽  
Real Life ◽  
Nonlinear Least Squares ◽  
Tensor Decomposition ◽  
Underlying Structure ◽  
Network Clustering ◽  
Multilayer Networks ◽  
Novel Approach ◽  
Real World Datasets

Clustering on multilayer networks has been shown to be a promising approach to enhance the accuracy. Various multilayer networks clustering algorithms assume all networks derive from a latent clustering structure, and jointly learn the compatible and complementary information from different networks to excavate one shared underlying structure. However, such an assumption is in conflict with many emerging real-life applications due to the existence of noisy/irrelevant networks. To address this issue, we propose Centroid-based Multilayer Network Clustering (CMNC), a novel approach which can divide irrelevant relationships into different network groups and uncover the cluster structure in each group simultaneously. The multilayer networks is represented within a unified tensor framework for simultaneously capturing multiple types of relationships between a set of entities. By imposing the rank-(Lr,Lr,1) block term decomposition with nonnegativity, we are able to have well interpretations on the multiple clustering results based on graph cut theory. Numerically, we transform this tensor decomposition problem to an unconstrained optimization, thus can solve it efficiently under the nonlinear least squares (NLS) framework. Extensive experimental results on synthetic and real-world datasets show the effectiveness and robustness of our method against noise and irrelevant data.

Planar Linkage Synthesis for Mixed Exact and Approximated Motion Realization Via Kinematic Mapping

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Ping Zhao ◽  
Xin Ge ◽  
Bin Zi ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Parallel Manipulators ◽  
Surface Fitting ◽  
Dimensional Synthesis ◽  
Constraint Equations ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
Mapping Theory ◽  
Discrete Motion ◽  
Fitting Problem

It has been well established that kinematic mapping theory could be applied to mechanism synthesis, where discrete motion approximation problem could be converted to a surface fitting problem for a group of discrete points in hyperspace. In this paper, we applied kinematic mapping theory to planar discrete motion synthesis of an arbitrary number of approximated poses as well as up to four exact poses. A simultaneous type and dimensional synthesis approach is presented, aiming at the problem of mixed exact and approximate motion realization with three types of planar dyad chains (RR, RP, and PR). A two-step unified strategy is established: first N given approximated poses are utilized to formulate a general quadratic surface fitting problem in hyperspace, then up to four exact poses could be imposed as pose-constraint equations to this surface fitting system such that they could be strictly satisfied. The former step, the surface fitting problem, is converted to a linear system with two quadratic constraint equations, which could be solved by a null-space analysis technique. On the other hand, the given exact poses in the latter step are formulated as linear pose-constraint equations and added back to the system, where both type and dimensions of the resulting optimal dyads could be determined by the solution. These optimal dyads could then be implemented as different types of four-bar linkages or parallel manipulators. The result is a novel algorithm that is simple and efficient, which allows for N-pose motion approximation of planar dyads containing both revolute and prismatic joints, as well as handling of up to four prescribed poses to be realized precisely.

Informed Latent Space Exploration for Image-Based Path Synthesis of Linkages

2021 ◽  
Author(s):  
Shrinath Deshpande ◽  
Zhijie Lyu ◽  
Anurag Purwar
Keyword(s):  
Probability Distributions ◽  
Space Exploration ◽  
Design Parameters ◽  
Concept Generation ◽  
Kinematic Synthesis ◽  
Input Coupler ◽  
Novel Approach ◽  
Latent Space ◽  
Path Synthesis ◽  
Practical Constraints

Abstract This paper brings together rigid body kinematics and machine learning to create a novel approach to path synthesis of linkage mechanisms under practical constraints, such as location of pivots. We model the coupler curve and constraints as probability distributions of image pixels and employ a Convolutional Neural Network (CNN) based Variational AutoEncoder (VAE) architecture to capture and predict the features of the mechanism. Plausible solutions are found by performing informed latent space exploration so as to minimize the changes to the input coupler curve while seeking to find user-defined pivot locations. Traditionally, kinematic synthesis problems are solved using precision point approach, wherein the input path is represented as a set of points and a set of equations in terms of design parameters are formulated. Generally, this problem is solved via optimization, wherein a measure of error between the given path and the coupler curve is minimized. A limitation of this approach is that the existing formulations depend on the type of mechanism, do not admit practical constraints in a unified way, and provide a limited number of solutions. However, in the machine design pipeline, kinematic synthesis problems are concept generation problems, where designers care more about a large number of plausible and practical solutions rather than the precision of input or the solutions. The image-based approach proposed in this paper alleviates the difficulty associated with inherently uncertain inputs and constraints.

Precipitation of Hydroxyapatite on Pure Titanium Substrate via Single Step Anodic Oxidation

2016 ◽  
Vol 694 ◽  
pp. 78-82 ◽  
Author(s):  
Te Chuan Lee ◽  
Muhammad Hanif Abd Rashid ◽  
Mohamad Ali Selimin ◽  
Hasan Zuhudi Abdullah ◽  
Maizlinda Izwana Idris
Keyword(s):  
Anodic Oxidation ◽  
Pure Titanium ◽  
Titanium Substrate ◽  
Ceramic Coatings ◽  
Single Step ◽  
X Ray ◽  
Novel Approach ◽  
Glancing Angle ◽  
New Formulation ◽  
Titanium Foils

Anodic oxidation is an electrochemical method that deposits ceramic coatings on the metal substrates to improve the bioactivity of implant. In this study, a novel approach was proposed to precipitate hydroxyapatite (HAP) directly on the surface of pure titanium through anodic oxidation approach. As part of the proposed approach, a new formulation of electrolyte was introduced, which consists of 0.04 M β-glycerophosphate (β-GP), 0.4 M calcium acetate (CA) and 1.0 M sulphuric acid (H2SO4). The approach herein only requires a single step to precipitate the HAP directly on the surface of titanium through anodisation process within the electrolyte. High purity titanium foils were anodised in 0.04 M β-GP + 0.4 M CA + 1.0 M H2SO4 at 350 V and 70 mA.cm-2 for 10 minutes at varying fractions of mixture volumes of H2SO4 (0-100 vol%). The surface properties of anodised titanium were characterised by using several methods, namely the field emission scanning electron microscopy (FESEM), glancing angle X-ray diffractometer (GAXRD) and goniometer. The outcome of the characterisation showed that the needle-like HAP was precipitated on the titanium, whereby anodising in electrolyte contains 12.5 vol% H2SO4. Combinations of anatase, rutile, titanium, tricalcium phosphate (Ca3O8P2) and calcium diphosphate (Ca2O7P2) elements were detected within the anodised titanium, whereby the anodising in electrolyte contains 50 vol% H2SO4.

scholarly journals Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Ke Wang ◽  
Guolin Liu ◽  
Qiuxiang Tao ◽  
Min Zhai
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Coefficient Matrix ◽  
Nonlinear Parameters ◽  
Nonlinear Least Squares Problem ◽  
Ill Posed ◽  
Characteristic Values ◽  
Parameter Separation ◽  
Fitting Problem

In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

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