Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators

1995 ◽  
Vol 117 (B) ◽  
pp. 71-79 ◽  
Author(s):  
M. Raghavan ◽  
B. Roth
Keyword(s):  
Kinematic Analysis ◽  
State Of The Art ◽  
Polynomial Systems ◽  
The State ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Systems Of Polynomial Equations ◽  
And Robotics

Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators

1995 ◽  
Vol 117 (B) ◽  
pp. 71-79 ◽  
Author(s):  
M. Raghavan ◽  
B. Roth
Keyword(s):  
Kinematic Analysis ◽  
State Of The Art ◽  
Polynomial Systems ◽  
The State ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Systems Of Polynomial Equations ◽  
And Robotics

Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

scholarly journals Digi-HTA: Health technology assessment framework for digital healthcare services

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Jari Haverinen ◽  
Niina Keränen ◽  
Petra Falkenbach ◽  
Anna Maijala ◽  
Timo Kolehmainen ◽  
...  
Keyword(s):  
Health Technology Assessment ◽  
Technology Assessment ◽  
State Of The Art ◽  
Health Technology ◽  
Healthcare Services ◽  
The State ◽  
Systematic Evaluation ◽  
Health Technologies ◽  
Digital Healthcare ◽  
And Robotics

Health technology assessment (HTA) refers to the systematic evaluation of the properties, effects, and/or impacts of health technology. The main purpose of the assessment is to inform decisionmakers in order to better support the introduction of new health technologies. New digital healthcare solutions like mHealth, artificial intelligence (AI), and robotics have brought with them a great potential to further develop healthcare services, but their introduction should follow the same criteria as that of other healthcare methods. They must provide evidence-based benefits and be safe to use, and their impacts on patients and organizations need to be clarified. The first objective of this study was to describe the state-of-the-art HTA methods for mHealth, AI, and robotics. The second objective of this study was to evaluate the domains needed in the assessment. The final aim was to develop an HTA framework for digital healthcare services to support the introduction of novel technologies into Finnish healthcare. In this study, the state-of-the-art HTA methods were evaluated using a literature review and interviews. It was noted that some good practices already existed, but the overall picture showed that further development is still needed, especially in the AI and robotics fields. With the cooperation of professionals, key aspects and domains that should be taken into account to make fast but comprehensive assessments were identified. Based on this information, we created a new framework which supports the HTA process for digital healthcare services. The framework was named Digi-HTA.

scholarly journals Galois theory for general systems of polynomial equations

2019 ◽  
Vol 155 (2) ◽  
pp. 229-245 ◽  
Author(s):  
A. Esterov
Keyword(s):  
Galois Theory ◽  
General System ◽  
Mixed Volume ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Change Of Variables ◽  
General Polynomial ◽  
General Systems ◽  
Systems Of Polynomial Equations

We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because arbitrary systems split into reduced irreducible ones upon monomial changes of variables. In particular, our result proves the multivariate version of the Abel–Ruffini theorem: the classification of general systems of equations solvable by radicals reduces to the classification of lattice polytopes of mixed volume 4 (which we prove to be finite in every dimension). We also notice that the monodromy of every general system of equations is either symmetric or imprimitive. The proof is based on a new result of independent importance regarding dual defectiveness of systems of equations: the discriminant of a reduced irreducible square system of general polynomial equations is a hypersurface unless the system is linear up to a monomial change of variables.

scholarly journals Kinematic Analysis and Synthesis of Mechanisms

2021 ◽  
Author(s):  
Asok Kumar Mallik ◽  
Amitabha Ghosh ◽  
Günter Dittrich
Keyword(s):  
Kinematic Analysis ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis

scholarly journals Solving a fixed number of equations over finite groups

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Philipp Nuspl
Keyword(s):  
Abelian Group ◽  
Finite Groups ◽  
Abelian Groups ◽  
Single Equation ◽  
Fixed Number ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Semidirect Products ◽  
Equations Over Groups ◽  
Systems Of Polynomial Equations

AbstractWe investigate the complexity of solving systems of polynomial equations over finite groups. In 1999 Goldmann and Russell showed $$\mathrm {NP}$$ NP -completeness of this problem for non-Abelian groups. We show that the problem can become tractable for some non-Abelian groups if we fix the number of equations. Recently, Földvári and Horváth showed that a single equation over groups which are semidirect products of a p-group with an Abelian group can be solved in polynomial time. We generalize this result and show that the same is true for systems with a fixed number of equations. This shows that for all groups for which the complexity of solving one equation has been proved to be in $$\mathrm {P}$$ P so far, solving a fixed number of equations is also in $$\mathrm {P}$$ P . Using the collecting procedure presented by Horváth and Szabó in 2006, we furthermore present a faster algorithm to solve systems of equations over groups of order pq.

Bangla Speech Analysis, Synthesis, and Vowel Nasality

2013 ◽  
pp. 209-245
Author(s):  
Shahina Haque
Keyword(s):  
Speech Production ◽  
Distinctive Feature ◽  
Speech Processing ◽  
State Of The Art ◽  
The State ◽  
Speech Analysis ◽  
Speech Synthesizer ◽  
Language Perception ◽  
Analysis And Synthesis ◽  
Cross Language

The chapter provides an overview of the theory of speech production, analysis, and synthesis, and status of Bangla speech processing. As nasality is a distinctive feature of Bangla and all the vowels have their nasal counterpart, both Bangla vowels and nasality are also considered. The chapter reviews the state-of-the-art of nasal vowel research, cross language perception of vowel nasality, and vowel nasality transformation to be used in a speech synthesizer.

Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics

1990 ◽  
Vol 112 (1) ◽  
pp. 59-68 ◽  
Author(s):  
C. W. Wampler ◽  
A. P. Morgan ◽  
A. J. Sommese
Keyword(s):  
Polynomial Systems ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Basic Material ◽  
Polynomial Equations ◽  
All Solutions ◽  
Recent Developments ◽  
Position Problem ◽  
Main Ideas ◽  
Systems Of Polynomial Equations

Many problems in mechanism design and theoretical kinematics can be formulated as systems of polynomial equations. Recent developments in numerical continuation have led to algorithms that compute all solutions to polynomial systems of moderate size. Despite the immediate relevance of these methods, they are unfamiliar to most kinematicians. This paper attempts to bridge that gap by presenting a tutorial on the main ideas of polynomial continuation along with a section surveying advanced techniques. A seven position Burmester problem serves to illustrate the basic material and the inverse position problem for general six-axis manipulators shows the usefulness of the advanced techniques.

scholarly journals Approximate Gröbner Bases, Overdetermined Polynomial Systems, and Approximate GCDs

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Daniel Lichtblau
Keyword(s):  
Relative Error ◽  
Gröbner Bases ◽  
Approximate Solutions ◽  
Polynomial Systems ◽  
Grobner Bases ◽  
Polynomial Equations ◽  
Secondary Feature ◽  
Approximate Polynomial ◽  
Polynomial Gcd ◽  
Systems Of Polynomial Equations

We discuss computation of Gröbner bases using approximate arithmetic for coefficients. We show how certain considerations of tolerance, corresponding roughly to absolute and relative error from numeric computation, allow us to obtain good approximate solutions to problems that are overdetermined. We provide examples of solving overdetermined systems of polynomial equations. As a secondary feature we show handling of approximate polynomial GCD computations, using benchmarks from the literature.

scholarly journals Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

2021 ◽  
Vol 24 (3) ◽  
pp. 97-103
Author(s):  
E.G. Krylov ◽  
R.F. Valiev
Keyword(s):  
Kinematic Analysis ◽  
Practical Interest ◽  
Kinematic Chains ◽  
Replacement Method ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Long Time ◽  
Shape Irregularity ◽  
Kinematic Equivalence ◽  
Higher Kinematic Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

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