A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the Set of Configurations of Certain Rank of Lower Pair Linkages

2018 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Configuration Space ◽  
Global Analysis ◽  
Polynomial System ◽  
Past Research ◽  
Local Approximation ◽  
Higher Order ◽  
Local Analysis ◽  
Local Geometry ◽  
Universal Method ◽  
Set Of Points

The determination of the finite mobility of a linkage boils down to the analysis of its configuration space (c-space). Since a global analysis is not feasible in general (but only for particular cases), the research focused on methods for a local analysis. Past research has in particular addressed the approximation of finite curves in c-space (i.e. finite motions). No universal method for the approximation of the c-space itself has been reported. In this paper a generally applicable formulation of the equations defining the higher-order local approximation of the c-space as well as the set of points where the Jacobian has a certain rank are presented. To this end, algebraic formulations of the higher-order differential of the constraint mapping (defining the loop closure) and of the Jacobian minors of arbitrary order are introduced. The respective local approximation is therewith given in terms of a low-order polynomial system. Results are shown for a simple planar 4-bar linkage and a planar three-loop linkage. Since the latter exhibits a cusp singularity it cannot be treated by the local analysis methods proposed thus far, which are based on approximating finite curves.

A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the Set of Configurations of Certain Rank of Lower Pair Linkages

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Configuration Space ◽  
Taylor Series Expansion ◽  
Past Research ◽  
Local Approximation ◽  
Higher Order ◽  
Local Analysis ◽  
Algebraic Expression ◽  
Local Geometry ◽  
Mobility Analysis ◽  
Lower Pair

A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space geometry at a given configuration. A higher-order analysis is necessary to determine the finite mobility. To this end, past research leads to approaches using higher-order time derivatives of loop closure constraints assuming (implicitly) that all possible motions are smooth. This continuity assumption limits the generality of these methods. In this paper, an approach to the higher-order local mobility analysis of lower pair multiloop linkages is presented. This is based on a higher-order Taylor series expansion of the geometric constraint mapping, for which a recursive algebraic expression in terms of joint screws is presented. An exhaustive local analysis includes analysis of the set of constraint singularities (configurations where the constraint Jacobian has certain corank). A local approximation of the set of configurations with certain rank is presented, along with an explicit expression for the differentials of Jacobian minors in terms of instantaneous joint screws. The c-space and the set of points of certain corank are therewith locally approximated by an algebraic variety determined algebraically from the mechanism's screw system. The results are shown for a simple planar 4-bar linkage, which exhibits a bifurcation singularity and for a planar three-loop linkage exhibiting a cusp in c-space. The latter cannot be treated by the higher-order local analysis methods proposed in the literature.

Higher-Order Analysis of Kinematic Singularities of Lower Pair Linkages and Serial Manipulators

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Critical Points ◽  
Tangent Cone ◽  
Polynomial System ◽  
Higher Order ◽  
Computational Method ◽  
Local Geometry ◽  
Serial Manipulators ◽  
Order Analysis ◽  
Forward Kinematic ◽  
Kinematic Singularities

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical and can neither be distinguished nor identified by simply investigating the rank deficiency of the constraint Jacobian (linear dependence of joint screws). C-space singularities are reflected by the c-space geometry. In a previous work, a kinematic tangent cone was introduced as an approximation of the c-space, defined as the set of tangents to smooth curves in c-space. Identification of kinematic singularities amounts to analyze the local geometry of the set of critical points. As a computational means, a kinematic tangent cone to the set of critical points is introduced in terms of Jacobian minors. Closed form expressions for the derivatives of the minors in terms of Lie brackets of joint screws are presented. A computational method is introduced to determine a polynomial system defining the kinematic tangent cone. The paper complements the recently proposed mobility analysis using the tangent cone to the c-space. This allows for identifying c-space and kinematic singularities as long as the solution set of the constraints is a real variety. The introduced approach is directly applicable to the higher-order analysis of forward kinematic singularities of serial manipulators. This is briefly addressed in the paper.

Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages

2017 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Critical Points ◽  
Tangent Cone ◽  
Polynomial System ◽  
Computational Method ◽  
Local Analysis ◽  
Closed Form Expression ◽  
Local Geometry ◽  
Lower Pair ◽  
Kinematic Singularities ◽  
Derivatives Of

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical. C-space singularities are reflected by the c-space geometry. Identifying kinematic singularities amounts to locally analyze the set of critical points. The local geometry of the set of critical points is best approximated by its tangent cone (an algebraic variety). The latter is defined in this paper in a form that allows for its computational determination using the Jacobian minors. An explicit closed form expression for the derivatives of the minors is presented in terms of Lie brackets of joint screws. A computational method is proposed to determine a polynomial system defining the tangent cone. This finally allows for identifying c-space and kinematic singularities.

scholarly journals An Integrated Geometric and Material Survey for the Conservation of Heritage Masonry Structures

Heritage ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 585-611
Author(s):  
Michele Betti ◽  
Valentina Bonora ◽  
Luciano Galano ◽  
Eugenio Pellis ◽  
Grazia Tucci ◽  
...  
Keyword(s):  
Seismic Behavior ◽  
Laser Scanning ◽  
Global Analysis ◽  
Interdisciplinary Approach ◽  
Local Analysis ◽  
Masonry Building ◽  
In Situ Tests ◽  
Knowledge Process ◽  
Giorgio Vasari ◽  
House Museum

This paper reports the knowledge process and the analyses performed to assess the seismic behavior of a heritage masonry building. The case study is a three-story masonry building that was the house of the Renaissance architect and painter Giorgio Vasari (the Vasari’s House museum). An interdisciplinary approach was adopted, following the Italian “Guidelines for the assessment and mitigation of the seismic risk of the cultural heritage”. This document proposes a methodology of investigation and analysis based on three evaluation levels (EL1, analysis at territorial level; EL2, local analysis and EL3, global analysis), according to an increasing level of knowledge on the building. A comprehensive knowledge process, composed by a 3D survey by Terrestrial Laser Scanning (TLS) and experimental in situ tests, allowed us to identify the basic structural geometry and to assess the value of mechanical parameters subsequently needed to perform a reliable structural assessment. The museum represents a typology of masonry building extremely diffused in the Italian territory, and the assessment of its seismic behavior was performed by investigating its global behavior through the EL1 and the EL3 analyses.

scholarly journals DETERMINANTS OF LATENT PROFILES IN HIGHER-ORDER THINKING SKILLS OF KOREAN UNIVERSITY STUDENTS

2018 ◽  
Vol 76 (4) ◽  
pp. 483-498
Author(s):  
Soo Eun Chae ◽  
Mi-Suk Lee
Keyword(s):  
University Students ◽  
Lower Order ◽  
Latent Profile Analysis ◽  
Profile Analysis ◽  
Past Research ◽  
Higher Order Thinking ◽  
Thinking Skills ◽  
Higher Order ◽  
Logistic Analysis ◽  
Latent Profile

Past research on higher-order thinking (HOT) was mainly conducted on the bases of educational context in U.S. or western countries. This research aimed to see what kinds of HOT styles actually appear in universtiy students in South Korea. The use of HOT skills were explored in Korean universtiy students and the factors influencing the classification were examined. 1,138 Korean university students were called to respond to Lee’s (2016) Higher-Order-Thinking-Scale for Korean University Students (HOTUS). Then, a latent profile analysis and the multinomial logistic analysis were conducted. The latent profile analysis revealed that the use of HOT skills could be classified into four classes (i.e., a lower-order thinking class, a creative-argumentative class, an analytical-caring class, and a higher-order thinking class). Gender, year, and instructional approach were the determinants of latent profile types. However, there were no differences when measured by academic fields. Students with lower years were likely to fall under lower-order thinking class. The probability that men was classified as a caring class was statistically significantly lower than that of women. Students who received lecturer-centered learning were more likely to fall under the analytical and caring class. Keywords: higher-order thinking skill, latent profile analysis, multinomial logistic analysis.

GLOBAL ANALYSIS OF THE AIRCRAFT STRUCTURE AND ITS APPLICATION TO THE PRELIMINARY DESIGN STAGE

Aviation ◽  
2005 ◽  
Vol 9 (3) ◽  
pp. 29-35
Author(s):  
Jerzy Bakunowicz ◽  
Tomasz Kopecki
Keyword(s):  
Numerical Model ◽  
Global Analysis ◽  
Economic Factor ◽  
Computer Application ◽  
Local Analysis ◽  
Design Stage ◽  
Preliminary Design ◽  
Preliminary Design Stage ◽  
Sufficient Strength ◽  
Made In

Modern aircraft safety depends on sufficient strength and rigidity of the structure. This must sustain with lightest possible weight, because any excess mass has not only detrimental effect upon the performance but also is significant economic factor. The most rational way to achieve the proper structure seems to be global analysis commenced in the preliminary design stage already. The analysis outcomes provide base for local analysis of the details led parallel. Any revisions more or less relevant can be made in the numerical model with very expensive prototype changes avoiding. The paper illustrates efficiency of the airframe structure global analysis. As examples the aircrafts still in service but designed without computer application were chosen. The finite elements numerical model of each was created and some critical in-flight load cases were simulated.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

Multi-Scale Overlapping Domain Decomposition to Consider Local Deformations in the Analysis of Thin-Walled Members

2014 ◽  
Vol 553 ◽  
pp. 667-672
Author(s):  
R. Emre Erkmen
Keyword(s):  
Numerical Technique ◽  
Global Analysis ◽  
Local Deformation ◽  
Local Analysis ◽  
Type Model ◽  
Cross Sectional ◽  
Multi Scale ◽  
Shell Type ◽  
Thin Walled ◽  
The Cross

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-column type finite element formulations. Beam-column elements however, are based on the assumption of rigid cross-section, thus they cannot consider the cross-sectional deformations such as local buckling and only allows considerations of the beam axis behaviour such as flexural or lateral-torsional buckling. Shell-type finite elements can be used to model the structure in order to consider these local deformation effects. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member.

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