A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

2018 ◽  
Vol 123 ◽  
pp. 495-506 ◽  
Author(s):  
Soufiane Haddout
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraints ◽  
Geometrical Theory ◽  
Practical Application ◽  
Fibered Manifolds

scholarly journals A Kinematical Analysis of the Flap and Wing Mechanism of a Light Sport Aircraft Using Topological Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1243
Author(s):  
Sorin Vlase ◽  
Ion-Marius Ghiţescu ◽  
Marius Paun
Keyword(s):  
Graph Theory ◽  
Mechanical System ◽  
Linear Systems ◽  
Kinematic Analysis ◽  
Control Mechanism ◽  
Practical Application ◽  
Dynamic Level ◽  
New Formulation ◽  
Topological Models ◽  
Independent Loops

In this, paper, we propose a method of kinematic analysis of a planar mechanism with application to the flap and wing mechanism of a light sport aircraft. A topological model is used to describe a mechanical system, which is a model that allows the study of the maneuverability of the system. The proposed algorithm is applied to determine the velocity and acceleration field of this multibody mechanical system. The graph associated with the mechanical system is generated in a new formulation and based on it, the fundamental loops of the graph are identified (corresponding to the independent loops of the mechanism), the equations for closing vectorial contours are written, and the kinematic conditions for determining velocities and accelerations and the associated linear systems are solved, which provides the field of speeds and accelerations. Graph Theory is applied at a kinematic level and not at a dynamic level, as in previous studies. A practical application for the kinematic analysis of the control mechanism of a light aircraft illustrates the proposed method.

Signal Measurement Error Analysis of the Bayesian Network of Mechanical Fault Detection

2014 ◽  
Vol 945-949 ◽  
pp. 2183-2186
Author(s):  
Yun Xia Zhang ◽  
Ling Lan ◽  
Xiao Hui Wang
Keyword(s):  
Measurement Error ◽  
Fault Detection ◽  
Error Analysis ◽  
Bayesian Network ◽  
Mechanical System ◽  
Gibbs Sampling ◽  
Sampling Method ◽  
Practical Application ◽  
Denoising Method ◽  
Signal Measurement

Based on measurement error of observation nodes is commom in mechanical system fault detection, but the traditional denoising method has many shortcomings. This paper introduce the Gibbs sampling method, which can be used to denoise and eliminate measurement error for node discreted information. We discuss it, and expect some promotion in practical application.

An Adding Mass Method for Stiffly Mechanical System Simulation and Applications to Construction Machinery

2001 ◽  
Author(s):  
Etsujiro Imanishi ◽  
Satoshi Yonezawa ◽  
Naoki Sugano ◽  
Eiko Hirooka ◽  
Takahiro Kobayashi
Keyword(s):  
Mechanical System ◽  
Dynamic Simulation ◽  
Hydraulic System ◽  
Piecewise Linear ◽  
Hydraulic Systems ◽  
Practical Application ◽  
Construction Machinery ◽  
Linear Elements ◽  
Improvement Method ◽  
And Control

Abstract A characteristic improvement method for dynamic simulation of a stiff mechanical system by adding mass is presented. Hydraulic systems with check valves and control valves on construction machinery exhibit piecewise-linear characteristics for hydraulic flow rate and spool stroke. The proposed improvement method involves no time delay in determining the mass by considering both eigenvalue distortion of the system and time response. This paper shows a practical application to the boom derricking system of a rough terrain crane, and demonstrates that this method is useful for dynamic simulation of hydraulic system including stiff piecewise-linear elements.

Study on Vibration Transmission, with Application to the Calibration of a Measuring Stand

2013 ◽  
Vol 430 ◽  
pp. 153-157
Author(s):  
Andrei Craifaleanu ◽  
Cristian Dragomirescu ◽  
Nicolaie Orăşanu ◽  
Adrian Costache
Keyword(s):  
Mechanical System ◽  
Experimental Model ◽  
Forced Vibration ◽  
Mechanical Characteristics ◽  
Final Part ◽  
Practical Application ◽  
Vibration Transmission ◽  
Vibration Measuring ◽  
Theoretical Results

The paper studies the vibration transmitted by a mechanical oscillating system to its fixing device. The influence of the mechanical characteristics (inertial and elastic) of the device on the quantities specific to the free and forced vibration, respectively, of the principal system, is analyzed. In this context, the paper investigates the possibility to correlate the vibrations of the mechanical system with the vibrations measured on the fixing device. The conclusions of this study can be used for the calibration of vibration measuring stands. In the final part, a practical application is presented, aimed to compare the theoretical results with the data obtained by measurements performed on an experimental model built by the authors.

scholarly journals Two problems of movement of multi-link wheeled vehicles

2021 ◽  
Vol 2094 (2) ◽  
pp. 022063
Author(s):  
E A Mikishanina
Keyword(s):  
Mechanical System ◽  
Software Package ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Nonholonomic Constraints ◽  
Mechanical Parameters ◽  
Controlled Motion ◽  
The Law ◽  
Wheeled Vehicles ◽  
Derivatives Of

Abstract The paper presents the results of a study of the dynamics of multi-link wheeled vehicles with nonholonomic connections superimposed on this mechanical system. The article is of an overview nature. The mathematical formulation is a system of ordinary differential equations of motion in the form of Lagrange with undefined multipliers, solved together with derivatives of nonholonomic constraints. The results are presented in the case of controlled motion, when the law of motion of the first link is known, as well as in the case of uncontrolled motion, when the law of motion of the leading link is also the desired function of time. General equations are obtained for a mechanical system consisting of an arbitrary number of links. Numerical results are presented for the case of three coupled trolleys. The software package Maple was used to perform numerical calculations and plotting of the desired mechanical parameters.

scholarly journals A new method for determining the reactions of mechanical constraints

2006 ◽  
Vol 28 (1) ◽  
pp. 35-42
Author(s):  
Do Sanh ◽  
Do Dang Khoa
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraints ◽  
Inverse Matrix ◽  
Algebraic Equations ◽  
Closed Set ◽  
Mechanical Constraints ◽  
Large Size ◽  
Holonomic And Nonholonomic Constraints ◽  
The Matrix ◽  
Lagrange’S Multipliers

In the present paper it is introduced the method for determining the reactions of mechanical constraints (holonomic and nonholonomic constraints).As is known, for studying dynamical characters of a mechanical system it is necessary to determine the constraint reactions acting on the system. Up to now, the reactions are calculated through Lagrange's multipliers. By such a way the reactions are determined only indirectly. In the [3, 4], two methods of determining directly the reactions are discussed. However, for applying these methods, it is necessary to compute the inverse matrix of the matrix of inertia. This thing in general is not convenient, specially when the matrix of inertial is of large size and dense.In the present paper it is represented the method for determining the constraint reactions, by which it is possible to avoid inertia the computation of the inverse matrix of the matrix of inertia is avoided. For this in the paper it is used the middle variables by which we obtain a closed set of algebraic equations for directly determining reactions.

Hamiltonian formulation for mechanical systems with nonholonomic constraints

2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez
Keyword(s):  
Finite Number ◽  
Mechanical System ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Hamiltonian Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Hamilton Equations

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.

On the Lagrangian Formalism of Nonholonomic Mechanical Systems

2005 ◽  
Author(s):  
Hiroaki Yoshimura
Keyword(s):  
Mechanical System ◽  
Tangent Bundle ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Lagrangian System ◽  
Lagrangian Formalism ◽  
Nonholonomic Mechanical Systems ◽  
Points Of View ◽  
Configuration Manifold

The paper illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d’Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d’Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

scholarly journals Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system

2016 ◽  
Vol 43 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Bojan Jeremic ◽  
Radoslav Radulovic ◽  
Aleksandar Obradovic
Keyword(s):  
Differential Equations ◽  
Mechanical System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Nonholonomic Constraints ◽  
Initial Position ◽  
Mass Particle ◽  
Control Forces ◽  
And Control

The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ?pitchfork? type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin?s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.

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