Analytical Methods for Solution Sets of Interval Wrench

2015 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Analytical Methods ◽  
Jacobian Matrix ◽  
Parametric Method ◽  
Parallel Manipulators ◽  
Solution Set ◽  
The Other ◽  
Discrete Method ◽  
Solution Sets ◽  
Dominant Parameter

Methodologies for calculating the solution set of actuator inputs, in the presence of uncertainty/error in parameters/data, are investigated. The enclosure for the vector of actuator torques is formulated utilizing the interval forms of the Jacobian matrix and external wrench. Two analytical methods are utilized to identify the solution set; one method generates the rays that bound the solution set in each orthant, and the other one is based on parameterizing the interval entries of the Jacobian matrix and wrench. For the parametric method, the existence of dominant parameter groups to produce the whole solution set (or a subset of solution set) is examined. Implementation of these methods on example parallel manipulators are presented to identify the solution set for the actuator torques, and the results are verified with the discrete method.

Wrench Accuracy for Parallel Manipulators and Interval Dependency

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Interval Arithmetic ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Upper Bounds ◽  
Solution Set ◽  
Lower And Upper Bounds ◽  
Solution Sets ◽  
The Given

In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Constrained Systems ◽  
Solution Set ◽  
Least Squares Solution ◽  
Interval Linear ◽  
Interval Linear Systems ◽  
Parameter Dependency ◽  
Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

Investigation of Wrench Accuracy for Parallel Manipulators

2016 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Parallel Manipulators ◽  
Coefficient Matrix ◽  
Solution Set ◽  
Output Vector ◽  
Discrete Method ◽  
Interval Linear ◽  
Closed Line ◽  
Interval Linear Systems ◽  
Real Linear ◽  
The Given

In this paper, the wrench accuracy for parallel manipulators is examined and the solution sets of actuator forces/torques are investigated under variations in parameters and data. The subset of solution set that produces platform wrenches within the required lower and upper bounds are modeled using discrete and analytical methods. In addition, the formulation of the solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Moreover, the dependency among the entries of the interval linear systems and its effect on the solution set is considered. The discrete method is based on the discretization of solution set enclosure and validation at each increment, or the collection of the solutions of real linear relations for the discretized interval coefficient matrix and output vector. The analytical method for each solution set is based on the intersection of the pertinent closed half-spaces or the assembly of closed line segments that encompass the solution. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

2017 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Constrained Systems ◽  
Solution Set ◽  
Least Square ◽  
Data Problem ◽  
Interval Linear ◽  
Interval Linear Systems ◽  
Parameter Dependency ◽  
Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized and implemented to identify the solution set, as well as the minimum 2-norm least square solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least square solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

On the Solution Set for Positive Wire Tension With Uncertainty in Wire-Actuated Parallel Manipulators

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Solution Set ◽  
Design Parameters ◽  
Negative Solution ◽  
Wire Tension

The solution for positive wire tension vector in the presence of uncertainties in design parameters and error in data is investigated for parallel manipulators. The minimum 2-norm non-negative solution and enclosures for the vector of wire tensions are formulated utilizing the perturbed and the interval forms of Jacobian matrix and platform wrench. Methodologies for calculating the minimum 2-norm non-negative solution set of wire tension vector, for interval Jacobian matrix and interval external wrench, are presented. Example parallel manipulators are simulated to investigate the implementation and effectiveness of these methodologies while relating their results.

scholarly journals Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

Polymers ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 334
Author(s):  
Ekaterina Vachagina ◽  
Nikolay Dushin ◽  
Elvira Kutuzova ◽  
Aidar Kadyirov
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Analytical Methods ◽  
Experimental Validation ◽  
Parametric Method ◽  
Fluid Flows ◽  
Parametric Representation ◽  
Viscoelastic Flow ◽  
Exponential Form ◽  
Image Velocimetry

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

مكافحة الجرائم الإلكترونية وعقوباتها

2021 ◽  
pp. arabic cover-english cover
Author(s):  
أحمد المرضي ◽  
محمد النذير الزين
Keyword(s):  
Analytical Method ◽  
Analytical Methods ◽  
Comparative Research ◽  
International Standards ◽  
The Other ◽  
Legal Basis ◽  
Technological Systems ◽  
Negative Effects ◽  
Electronic Crime ◽  
Legal Measure

يتناولُ هذا البحثُ التعريفَ بتقنيةِ المعلوماتِ، وماهية الجريمة الإلكترونية، والأخطار الناجمة عنها وتصنيف المُجْرِمين الإلكترونيين، وتنويع الجرائم المُتعلقة بتقنية المعلومات، والأسباب التي تعزي إلى صعوبةِ الكشفِ عنها، وإيراد نموذجًا للجرائم التقنية وفقًا لأحكام القانون الجنائِيّ الإماراتِيّ والمصرِيّ المُتعلقين بمكافحة جرائم تقنية المعلومات. ويشيرُ البحثُ في إيجازٍ إلى: التعريف بالجريمة، وركنها المادي، وبيان شروط الركن المادي، والركن المعنوي، والعقوبة الأصيلة للجريمة، والعقوبة في صورتها المشددة، والعقوبات البديلة. وينطوي البحثُ أيضًا على الأسس الشرعية المُتضمنة حظر الجرائم الماسة بتقنيةِ المعلوماتِ تبعًا لنصوص القرآن الكريم، والسنة النبوية الشريفة، والقواعد الفقهية القاضية بحظر جرائم الانتحال الإلكتروني. ويشتملُ هذا البحثُ على مُقدمةٍ، وخمسة مباحث، وخاتمةٍ على النحو الآتـي: المبحث الأول الأصل الشرعي في تحريم الجرائم الإلكترونية، والمبحث الثاني تعريفات عامة للجرائم المعلوماتية وتصنيفها، والمبحث الثالث أنواع المجرمين المحترفين في المعلوماتية التقنية، وصعوبة اكتشافهم، والمخاطر الأمنية للإنترنت، والمبحث الرابع نماذج من أحكام القانون الجنائي الإماراتي والمصري في مكافحة الجرائم الإلكترونية، والمبحث الخامس الأدلة الرقمية لإثبات الجرائم الإلكترونية وفقًا للقضاءين الإماراتِيّ والمصرِيّ، ثمَّ جاءَت الخاتمةُ لتحتوي على أهم النتائج والتوصياتِ. By this forgoing paper which bearing the title: Combating Electronic Crimes According to Provisions of Criminal Laws of Emirates and Egypt, It Aims to, Enforcement to principals of shariah Law actualization which intents detterence commission crimes through mechanism of” Amr Bil Maroof and Nahy An Munkar”, actualization to the measures of shariah Law that prevent disobedience and electronic crimes. To explain that application of shariah legal maxims such as: "Al Ghurm Bi Al ghunm" whereby it implies whoever owns illegally as a result of committing an offense on a property of whosever should be suffered a penalty, typically to the legal maxim " La dharar wa La dirar ".(damage should be removed) The research methodology which adopted is the descriptive and analytical methods where the researcher intents to define, explains elements and punishments of the crimes. On the other hand the researcher under took the analytical method where he proceeds comparison between the provisions of the two selective criminal laws of Emirates and Egypt, for the achievement the purpose of identification of the similarity and distinctiveness. The problems that presumed to be settled by this research such as: Are there any legal basis to criminalize electronic crime with reference to shariah law? Are there any legal justifications to enforce punishment of fine on the criminal hackers? What are the dangerous consequences for committing the electronic crimes? What are the negative effects for commission electronic crime on individuals and societies at large, and what are the preventive international standards measure and strategies in this context? Concerning the expected achievements by this research, It will enrich the Islamic Library because a comparative research on this topic is so scarce and limited. It will guide the researchers by exploring a new referencing methods for application shariah law, It provides and exposes the legal measure for combating the electronic crimes by using the techniques of detection the electronic criminals by hiding cameras, intelligent phone thumb prints to enable the police investigative officer to deter, identify and arrest the electronic criminals. In the light of combating the researcher advices government officers’ bankers and others to provide top advanced sophisticated technological systems to protect their computers and account numbers against the expected threads of the electronic offences.

A Family of 3-DOF Translational Parallel Manipulators1

2003 ◽  
Vol 125 (2) ◽  
pp. 302-307 ◽  
Author(s):  
Marco Carricato ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Degrees Of Freedom ◽  
Translational Motion ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
The Other ◽  
Six Degrees Of Freedom ◽  
Revolute Joints ◽  
Rotational Degrees Of Freedom

This article addresses parallel manipulators with fewer than six degrees of freedom, whose use may prove valuable in those applications in which a higher mobility is uncalled for. In particular, a family of 3-dof manipulators containing only revolute joints or at the most revolute and prismatic ones is studied. Design and assembly conditions sufficient to provide the travelling platform with a pure translational motion are determined and two sub-families that fulfill the imposed constraint are found: one is already known in the literature, while the other is original. The new architecture does not exhibit rotation singularities, i.e., configurations in which the platform gains rotational degrees of freedom. A geometric interpretation of the translation singularities is provided.

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