scholarly journals A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Robotics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 6
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez ◽  
Ricardo García-García
Keyword(s):  
Screw Theory ◽  
Bilinear Forms ◽  
Theory Approach ◽  
Algebraic Equations ◽  
Euclidean Group ◽  
Planar Mechanisms ◽  
New Approach ◽  
Planar Linkages ◽  
The 19Th Century

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, se(3), of the Euclidean group, SE(3), and the invariant symmetric bilinear forms defined on se(3).

A New Approach for Locating the Instantaneous Centers of Zero Velocity for 1-DOF Planar Linkages

2018 ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
New Approach ◽  
Zero Velocity ◽  
Graphical Technique ◽  
Instantaneous Center ◽  
Planar Linkages ◽  
Consistent Approach

This paper presents a new graphical technique to locate the secondary instantaneous centers of zero velocity (ICs) for one-degree-of-freedom (1-DOF) kinematically indeterminate planar mechanisms. The proposed approach is based on transforming the 1-DOF mechanism into a 2-DOF counterpart by converting any ground-pivoted ternary link into two ground-pivoted binary links. Fixing each of these two new binary links, one at a time, results in two different 1-DOF mechanisms where the intersection of the loci of their instantaneous centers will determine the location of the desired instantaneous center for the original 1-DOF mechanism. This single and consistent approach proved to be successful in locating the ICs of various mechanisms reported in the literature that required different techniques to reach the same results obtained herein.

New Synthesis Approach for Expandable Polyhedral Linkages

2014 ◽  
Author(s):  
Ying Zhang ◽  
Hai-Jun Su ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Weiqing Li
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
New Approach ◽  
And Topology ◽  
New Synthesis ◽  
The One ◽  
Planar Linkages ◽  
Synthesis Approach ◽  
Topology Graph

This paper presents a new synthesis approach for expandable polyhedral linkages, which are synthesized by inserting appropriate link groups into the faces of polyhedron and interconnecting them by a special composite hinges (called gusset by K. Wohlhart). The overconstrained expandable polyhedral linkages are movable with one degree of freedom (DOF).The link groups are single DOF scaling planar linkages. The gussets are multiple rotary joints whose axes converge at the corresponding vertices of the polyhedron and the number of the rotary joints equals the one of the faces which meet at the vertices. This new approach is suitable for any polyhedron whatever is regular or irregular polyhedron. To verify this new approach, the expandable regular hexahedral linkage is modeled in the SolidWorks and its mobility are studied based on screw theory and topology graph.

Displacement Analysis of Multi-Loop Mechanisms Using Gröbner Bases

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
A. N. Almadi ◽  
D. Kohli
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Algebraic Equations ◽  
Multivariate Polynomial ◽  
Planar Mechanisms ◽  
Analysis Problem ◽  
Displacement Analysis ◽  
Comprehensive Information ◽  
Curve Equation

Abstract The displacement analysis problem for planar mechanisms can be written as a system of algebraic equations, in particular as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper explores an alternate approach, based on Gröbner bases, to solve the displacement analysis problem for planar mechanisms. It is shown that the reduced set of generators obtained using the Buchberger’s algorithm for Gröbner bases not only yields the input-output polynomial for the mechanism, but also provides comprehensive information on the number of closures and the relationships between various links of the mechanism. Numerical examples illustrating the applicability of Gröbner bases to displacement analysis of 10 and 12-link mechanisms and determination of coupler curve equation for 8-link mechanisms are presented.

The Dudley Lee Case: A new approach to factual causation and its implications for transformative jurisprudence

2017 ◽  
Vol 30 (1) ◽  
pp. 273-289
Author(s):  
Anmari Meerkotter
Keyword(s):  
Case Note ◽  
Constitutional Court ◽  
Recent Contribution ◽  
New Approach ◽  
State Accountability ◽  
The Law ◽  
Transformative Impact ◽  
Constitutional Jurisprudence ◽  
Law Of Delict

The Constitutional Court (CC) judgment of Lee v Minister of Correction Services 2013 2SA 144 (CC) is a recent contribution to transformative constitutional jurisprudence in the field of the law of delict. This matter turned on the issue of factual causation in the context of wrongful and negligent systemic omissions by the state. In this case note, I explore the law relating to this element of delictual liability with specific regard to the traditional test for factual causation – the conditio sine qua non (‘but-for’) test. In particular, I note the problems occasioned by formalistic adherence to this test in the context of systemic state omissions as evidenced by the SCA judgment in the same matter. I also consider the manner in which English courts have addressed this problem. Thereafter, I analyse the CC’s broader approach to the determination of factual causation as one based on common sense and justice. I argue that this approach endorses a break from a formalistic application of the test and constitutes a step towards an approach which resonates with the foundational constitutional values of freedom, dignity and equality. Furthermore, it presents an appropriate solution to the problems associated with factual causation where systemic omissions are concerned. I then consider the transformative impact of the Lee judgment. In particular, I argue that the broader enquiry favoured by the CC facilitates the realisation of constitutionally guaranteed state accountability, and amounts to an extension of the existing norm of accountability jurisprudence. Hence, I contend that the judgment presents a further effort by the Constitutional Court to effect wholesale the constitutionalisation of the law of delict, as well as a vindicatory tool to be used by litigants who have been adversely affected by systemic state omissions.

Automatic Determination of Optimal FIB Operations for Improved Circuit Probing and Fast Reconfiguration

2000 ◽  
Author(s):  
Romain Desplats ◽  
Timothee Dargnies ◽  
Jean-Christophe Courrege ◽  
Philippe Perdu ◽  
Jean-Louis Noullet
Keyword(s):  
Integrated Circuit ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Semiconductor Devices ◽  
Front Side ◽  
Automatic Determination ◽  
Metal Line ◽  
New Approach ◽  
Metal Layers

Abstract Focused Ion Beam (FIB) tools are widely used for Integrated Circuit (IC) debug and repair. With the increasing density of recent semiconductor devices, FIB operations are increasingly challenged, requiring access through 4 or more metal layers to reach a metal line of interest. In some cases, accessibility from the front side, through these metal layers, is so limited that backside FIB operations appear to be the most appropriate approach. The questions to be resolved before starting frontside or backside FIB operations on a device are: 1. Is it do-able, are the metal lines accessible? 2. What is the optimal positioning (e.g. accessing a metal 2 line is much faster and easier than digging down to a metal 6 line)? (for the backside) 3. What risk, time and cost are involved in FIB operations? In this paper, we will present a new approach, which allows the FIB user or designer to calculate the optimal FIB operation for debug and IC repair. It automatically selects the fastest and easiest milling and deposition FIB operations.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

scholarly journals New Method for Analysis of the Temporomandibular Joint Using Cone Beam Computed Tomography

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3070
Author(s):  
Sebastian Iwaszenko ◽  
Jakub Munk ◽  
Stefan Baron ◽  
Adam Smoliński
Keyword(s):  
Computed Tomography ◽  
Temporomandibular Joint ◽  
Cross Section ◽  
Cone Beam Computed Tomography ◽  
Cone Beam ◽  
Section Plane ◽  
New Approach ◽  
Volume Of Interest ◽  
Gap Width

Modern dentistry commonly uses a variety of imaging methods to support diagnosis and treatment. Among them, cone beam computed tomography (CBCT) is particularly useful in presenting head structures, such as the temporomandibular joint (TMJ). The determination of the morphology of the joint is an important part of the diagnosis as well as the monitoring of the treatment results. It can be accomplished by measurement of the TMJ gap width at three selected places, taken at a specific cross-section. This study presents a new approach to these measurements. First, the CBCT images are denoised using curvilinear methods, and the volume of interest is determined. Then, the orientation of the vertical cross-section plane is computed based on segmented axial sections of the TMJ head. Finally, the cross-section plane is used to determine the standardized locations, at which the width of the gap between condyle and fossa is measured. The elaborated method was tested on selected TMJ CBCT scans with satisfactory results. The proposed solution lays the basis for the development of an autonomous method of TMJ index identification.

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