Solving the Forward Kinematic Problem of 4-DOF Parallel Mechanisms (3T1R) With Identical Limb Structures and Revolute Actuators Using the Linear Implicitization Algorithm

2011 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Dominic R. Walter ◽  
Manfred Husty ◽  
Cle´ment Gosselin
Keyword(s):  
Linear Equations ◽  
Linear Constraint ◽  
Mathematical Framework ◽  
Parallel Mechanisms ◽  
Novel Approach ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Rotation Motion ◽  
Forward Kinematic ◽  
General Architecture

This paper investigates the forward kinematic problem of 4-DOF parallel mechanisms with revolute actuators and identical limb structures and performing a three translations and one rotation motion pattern. The general architecture of all the mechanisms under study in this paper originates from the type synthesis performed for 4-DOF parallel mechanisms with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematics and constraint expressions are explored in a seven-dimensional kinematic space by means of the so-called Study parameters (dual quaternions). In this paper, the algorithm applied for obtaining the forward kinematic and constraint expressions is based on a recent and novel approach, called linear implicitization algorithm, which is based on solving systematically a system of linear equations to determine the coefficients of the non-linear constraint equations. This paper presents also an example of a 4-DOF parallel mechanism.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Manfred Husty ◽  
Cle´ment Gosselin
Keyword(s):  
Dimensional Space ◽  
Large Set ◽  
Parallel Mechanisms ◽  
General Methodology ◽  
Higher Dimensional ◽  
Kinematic Mapping ◽  
Rigid Body Displacement ◽  
Forward Kinematic Problem ◽  
Dimensional Projective Space ◽  
Forward Kinematic

In this paper, a general methodology is introduced in order to formulate the FKP of symmetrical parallel mechanisms in a 7-dimensional projective space by the means of the so-called Study’s parameters. The main objective is to consider rigid-body displacement, and consequently the FKP, based on algebraic geometry, rather than rely on classical recipes, such as Euler angles, to assist in problem-solving. The state of the art presented in this paper is general and can be extended to other types of symmetrical mechanisms. In this paper, we limit the concept of kinematic mapping to topologically symmetrical mechanisms, i.e., mechanisms with limbs having identical kinematic arrangement. Exploring the FKP in a higher dimensional space is more challenging since it requires the use of a larger number of coordinates. There are, however, advantages in adopting a large set of coordinates, since this approach leads to expressions with lower degree that do not involve trigonometric functions.

Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures

2011 ◽  
Vol 46 (7) ◽  
pp. 945-959 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin ◽  
Manfred Husty ◽  
Dominic R. Walter
Keyword(s):  
Parallel Mechanisms ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2257-2277 ◽  
Author(s):  
Mohammad H. Abedinnasab ◽  
Farzam Farahmand ◽  
Bahram Tarvirdizadeh ◽  
Hassan Zohoor ◽  
Jaime Gallardo-Alvarado
Keyword(s):  
Parallel Manipulators ◽  
Optimum Number ◽  
Parallel Mechanisms ◽  
Performance Indices ◽  
Singular Configurations ◽  
Redundantly Actuated ◽  
Forward Kinematic Problem ◽  
Kinematic Measures ◽  
Forward Kinematic ◽  
Legged Mechanism

SUMMARYIn this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough–Stewart (3–3) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough–Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.

scholarly journals Estimation of hepatitis B virus cccDNA persistence in chronic infection using within-host evolutionary rates

2020 ◽  
Author(s):  
Katrina A. Lythgoe ◽  
Sheila F. Lumley ◽  
Jane A. McKeating ◽  
Philippa C. Matthews
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Chronic Infection ◽  
Standard Of Care ◽  
Evolutionary Rates ◽  
Mathematical Framework ◽  
Novel Approach ◽  
B Virus ◽  
Order Of Magnitude ◽  
Progressive Liver Disease

AbstractHepatitis B virus (HBV) infection is a major global health problem with over 240 million infected individuals at risk of developing progressive liver disease and hepatocellular carcinoma. HBV is an enveloped DNA virus that establishes its genome as an episomal, covalently closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Currently available standard-of-care treatments for chronic hepatitis B (CHB) include nucleos(t)ide analogues (NA) that suppress HBV replication but do not target the cccDNA and hence rarely cure infection. There is considerable interest in determining the lifespan of cccDNA molecules to design and evaluate new curative treatments. We took a novel approach to this problem by developing a new mathematical framework to model changes in evolutionary rates during infection which, combined with previously determined within-host evolutionary rates of HBV, we used to determine the lifespan of cccDNA. We estimate that during HBe-antigen positive (HBeAgPOS) infection the cccDNA lifespan is 61 (36-236) days, whereas during the HBeAgNEG phase of infection it is only 26 (16-81) days. We found that cccDNA replicative capacity declined by an order of magnitude between HBeAgPOS and HBeAgNEG phases of infection. Our estimated lifespan of cccDNA is too short to explain the long durations of chronic infection observed in patients on NA treatment, suggesting that either a sub-population of long-lived hepatocytes harbouring cccDNA molecules persists during therapy, or that NA therapy does not suppress all viral replication. These results provide a greater understanding of the biology of the cccDNA reservoir and can aid the development of new curative therapeutic strategies for treating CHB.

scholarly journals Evaluating the Performance of Novel JWT Revocation Strategy

2021 ◽  
Author(s):  
László Viktor Jánoky ◽  
Péter Ekler ◽  
János Levendovszky
Keyword(s):  
Access Control ◽  
Real World ◽  
Mathematical Framework ◽  
Web Based ◽  
Novel Approach ◽  
User Access ◽  
Digital Signing

JSON Web Tokens (JWT) provide a scalable, distributed way of user access control for modern web-based systems. The main advantage of the scheme is that the tokens are valid by themselves – through the use of digital signing – also imply its greatest weakness. Once issued, there is no trivial way to revoke a JWT token. In our work, we present a novel approach for this revocation problem, overcoming some of the problems of currently used solutions. To compare our solution to the established solutions, we also introduce the mathematical framework of comparison, which we ultimately test using real-world measurements.

Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

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