Kinematics and dynamics of a mechanical system on rollers that provide nonholonomic constraints

1994 ◽  
Vol 72 (5) ◽  
pp. 3299-3305 ◽  
Author(s):  
V. P. Legeza
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraints ◽  
Kinematics And Dynamics

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.

The Design on Installation and Demolition Device for Lamps and Lanterns

2014 ◽  
Vol 494-495 ◽  
pp. 747-750
Author(s):  
Kai Bao Wang ◽  
Qiu Xiao Yang ◽  
Bo Wang ◽  
Bo Zhu ◽  
Qun Zhang ◽  
...  
Keyword(s):  
Mechanical System ◽  
Optimization Design ◽  
Simulation Analysis ◽  
Daily Life ◽  
Design Method ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Work Efficiency ◽  
Residential Areas ◽  
Related Research

A wide variety of lighting lamps and lanterns were used in various occasions in our daily life. Considering the service life, the lamps and lanterns were changeed usually. It is extremely complicated to replace the lamps and lanterns installed in high or concealed position. The installation and demolition device for lamps and lanterns based on optimization design method and dynamics analysis is introduced in the paper. The device can be used in the place of ordinary families, residential areas and fitted for different specifications of the lamps and lanterns. The work efficiency was improved greatly through the mechanisms arranged in circular. In the research, the virtual prototype technology was used to simulate the kinematics and dynamics characteristics of the mechanical system. The feasibility of the design scheme of mechanical system was proved with the simulation analysis results. The equipment has advantages of the structure is compact, safe and reliable, easy to use. The research of the installation and demolition device for lamps and lanterns can be regarded as the reference of the related research.

Design and Research on Automatic Opening Device for the Medical Ampoule

2013 ◽  
Vol 765-767 ◽  
pp. 1912-1915
Author(s):  
Kai Bao Wang ◽  
Qiu Xiao Yang ◽  
Guang Hao Song ◽  
Bo Wang ◽  
Wen Kai Ma
Keyword(s):  
Mechanical System ◽  
Optimization Design ◽  
Simulation Analysis ◽  
Design Method ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Work Efficiency ◽  
Related Research ◽  
Medical Institutions ◽  
Intermittent Motion

In various medical institutions, the ampoule is an essential container in daily medical operations. The automatic opening device for medical ampoule based on optimization design method and dynamics analysis is introduced in the paper. The automatic opening device can be used in the place of hospitals and clinics and fitted for different specifications of the ampoule. The necessary operational process that included nick, disinfection and break in the work of ampoule opening was integrated in the device. The work efficiency was improved greatly through the mechanisms arranged in circular. In the process of using, all ampoules kept an intermittent motion in a circulation under the control of transmission unit. The process of automatic opening will be completed in its cyclical-intermittent motion in about 30 seconds. In the research, the virtual prototype technology was used to simulate the kinematics and dynamics characteristics of the mechanical system. The feasibility of the design scheme of mechanical system was proved with the simulation analysis results. The equipment has advantages of the structure is compact, safe and reliable, easy to use. The research of the automatic opening device for the medical ampoule can be regarded as the reference of the related research.

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.

A New Method of Integrate Simulation Based on ADAMS and Pro/ENGINEER

2012 ◽  
Vol 229-231 ◽  
pp. 2065-2068
Author(s):  
Gang Lian Zhao ◽  
Yi Jiang ◽  
Yu Jun Chen ◽  
Yan Li Ma
Keyword(s):  
Dynamic Analysis ◽  
Mechanical System ◽  
Experimental Model ◽  
New Method ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Manual Method ◽  
Complex Mechanical System ◽  
Simulation Based ◽  
Crank Mechanism

A new method of integrate simulation for the kinematics and dynamics analysis of complex mechanical system is presented in this paper. This platform of the method is based on Visual Studio 2005, MD ADAMS( Automatic Dynamic Analysis of Mechanical System) R3 and Pro/Engineer Wildfire 4.0. The experimental model is built with Pro/E, and then some functions of Pro/Toolkit are used to export file of parasolid format and coordinates of some specified Datum Points. Finally, the coordinates of these Datum Points are written into a CMD file (Commands file of ADAMS). A slider-crank mechanism is used as a numerical example to demonstrate the application of the method. It is shown that this approach is a much easier, faster than usual manual method especially for complex mechanical system which has a lot of Marker Points and constraints.

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