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1

The Jacobians of non-maximal degree

Lara-Dziembek S., Biernat G., Pawlak E.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 4

99--104

EN

In the article the leading forms of the polynomial mapping having the Jacobians of non-maximal degree are considered. In particular, the mappings having two zeros at infinity are discussed.

2

Density not realizable as the Jacobian determinant of a bilipschitz map

Kaluza V.

Journal of Applied Analysis

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2016

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Vol. 22, nr 1

37--47

EN

Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen's construction is simpler than the Burago–Kleiner one, and we provide a full proof of its nonrealizability, which has not been available in the literature.

3

Analiza kinematyki manipulatora o pięciu stopniach swobody

Gierlak P.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2014

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z. 86 [290], nr 4

491--500

PL

W artykule przestawiono analizę kinematyki manipulatora o pięciu stopniach swobody na przykładzie jednostki kinematycznej robota manipulacyjnego Scorbot-ER 4pc. Do opisu kinematyki układu zastosowano notację Denavita-Hartenberga. Przyjęto schemat kinematyki manipulatora i podano parametry opisujące układ. Zapisano odpowiednie macierze transformacji, które zastosowano w dalszej analizie. Wyznaczono jakobian analityczny manipulatora oraz jakobian geometryczny w ciele i przeprowadzono analizę osobliwości. Są to takie konfiguracje manipulatora, w których wyznaczenie rozwiązania zadania odwrotnego kinematyki jest znacznie utrudnione, a przy zastosowaniu klasycznych metod – niemożliwe. Dlatego znajomość konfiguracji osobliwych jest niezbędna w celu poprawnego planowania i generowania trajektorii manipulatora. Zaprezentowana metodyka jest uniwersalna i może być stosowana do analizy kinematyki manipulatorów o innej strukturze kinematycznej niż zaprezentowana w niniejszej pracy.

EN

In the paper the kinematics analysis of 5 degrees of freedom manipulator is presented. The analysis was realised for the Scorbot-ER 4pc robotic manipulator. To describe the kinematics of the manipulator the Denavit-Hartenberg notation is used. The kinematics scheme and parameters of the manipulator as well as appropriate transformation matrices, that were used in the further analysis, are given. The analytical Jacobian of the manipulator and the geometrical Jacobian in the body are determined and the analysis of singularities is realised. In singular manipulator’s configurations the solution of the inverse kinematics problem is very difficult, and using classical methods – impossible. Therefore, knowledge of the singular configurations is necessary for the proper planning and generating the trajectory of the manipulator. The presented methodology is universal and can be used to analyze the kinematics of manipulators with a other kinematic structure that is not presented in this paper.

4

Stiffness Matrix Analysis of Six-Revolute Serial Manipulator

Knapczyk J., Ryska M.

Acta Mechanica et Automatica

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2012

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Vol. 6, no. 2

62-65

EN

This paper presents a simple procedure that can be used to determine the stiffness matrix of 6R serial manipulator in selected points of the work space with joint stiffness coefficients taking into account. Elastokinematical model for the robot manipulator FANUC S-420F was considered as spatial and serial kinematical chain composed of six rigid links, connected by ideal revolute joint (without clearances and deformable elements), with torsion elasticity of the joint drive system (relative torsion deformations are proportional to acted torques) taking into account. Assumed model is used for displacement analysis of the end-effector for a given applied force in quasi-static condition. The analysis results are presented as Cartesian stiffness matrix of studied manipulator.

5

Loads of Lower Limb Joints During Bicycle Ride

Stępniewski A.

Acta Mechanica et Automatica

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2012

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Vol. 6, no. 2

84-87

EN

This work features a geometric and static analysis of the lower limb during bicycle ride. Basic dimensions are indicated, which are necessary for the description of movement geometry. The simplified flat model was adopted for the analysis. Using the transformation of Denavit-Hartenberg frames, vectors were developed for the position of the rotation axis of the joints in immovable frame. The inverse kinematics problem was solved. The course of displacement changes in the ankle joint was adopted as an angle function for crankset position, based on experimental research results, published in professional literature. The course was approximated with fifth grade polynomial. Joint displacements and loads were established. A sample calculation is presented, illustrating the subject computational algorithm.

6

Estimation of platform spatial pose and displacement of parallel mechanism using wire-based sensors

Góra M., Knapczyk J., Maniowski M.

Archive of Mechanical Engineering

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2007

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Vol. LIV, nr 4

365-389

EN

This paper presents an estimation method for the spatial pose and displacement parameters of multi-rod suspension mechanism, based on measurement results by using wire sensors. Some changes of position and orientation of the platform fixed to wheel knuckle cause corresponding changes of sensors' cable lengths. The fixation points of the cable sensors are selected with the collision-free conditions taken into account. Numerical example deals with platform poses and positioning of the sensors that satisfy the measurement conditions.

PL

W artykule przedstawiono metodę estymacji parametrów przestrzennego położenia i przemieszczenia mechanizmu wielo-wahaczowego zawieszenia koła samochodu na podstawie wyników pomiarów za pomocą czujników linkowych. Pewne zmiany pozycji i orientacji platformy zamocowanej do zwrotnicy koła powodują odpowiednie zmiany długości linek czujników. Punkty zaczepienia czujników linkowych dobrano uwzględniając warunki uniknięcia kolizji. Przykład liczbowy dotyczy analizy położeń i przemieszczeń platformy oraz usytuowania czujników dające dobre uwarunkowania pomiarów.