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Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky

Konoplev, V., Cheremensky, A. (2002)

Serdica Mathematical Journal

The Union of Bulgarian Mathematicians starts a new series of publica- tions: Mathematics and Its Applications. The first issue of the series is “Multi- body System Mechanics: Modelling, Stability, Control and Robustness”. The authors are well known mathematicians with various published books and articles. Professor Vladimir Konoplev works in the Institute of Problems of Mechanical Engineering, Russian Academy of Sciences (St. Petersburg, Russia), while Professor Alexander Cheremensky works...

Neutral wrenches of 3-parametric robot-manipulators of the spherical rank 1

Marta Bakšová (2011)

Applications of Mathematics

Let S E ( 3 ) be the Lie group of all Euclidean motions in the Euclidean space E 3 , let s e ( 3 ) be its Lie algebra and s e * ( 3 ) the space dual to s e ( 3 ) . This paper deals with structures of the subspaces of s e * ( 3 ) which are formed by all the forces whose power exerted on the robot effector is zero.

Non-cooperative game approach to multi-robot planning

Adam Gałuszka, Andrzej Świerniak (2005)

International Journal of Applied Mathematics and Computer Science

A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm...

Numerical simulation of suspension induced rheology

Rodolphe Prignitz, Eberhard Bänsch (2010)

Kybernetika

Flow of particles suspended in a fluid can be found in numerous industrial processes utilizing sedimentation, fluidization and lubricated transport such as food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. The ability to understand rheology effects of particulate flows is elementary for the design, operation and efficiency of the underlying processes. Despite the fact that particle technology is widely used, it is still...

On asymptotic motions of robot-manipulator in homogeneous space

Anton Dekrét, Ján Bakša (2008)

Applications of Mathematics

In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group G of motions. Some kinematic subspaces of the Lie algebra 𝒢 (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.

On the analytic non-integrability of the Rattleback problem

H. R. Dullin, A.V. Tsygvintsev (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.

On the KAM - Theory Conditions for the Kirchhoff Top

Christov, Ognyan (1997)

Serdica Mathematical Journal

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.

Parameter influence on passive dynamic walking of a robot with flat feet

Xiangze Lin, Haibo Du, Shihua Li (2013)

Kybernetika

The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...

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