Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
József Kövecses
Keyword(s):  
Configuration Space ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Constrained Systems ◽  
Dynamic Equations ◽  
Analytical Mechanics ◽  
Constrained Motion ◽  
Equilibrium Equations ◽  
Free Body Diagram ◽  
Free Body

In this paper, we generalize the idea of the free-body diagram for analytical mechanics for representations of mechanical systems in configuration space. The configuration space is characterized locally by an Euclidean tangent space. A key element in this work relies on the relaxation of constraint conditions. A new set of steps is proposed to treat constrained systems. According to this, the analysis should be broken down to two levels: (1) the specification of a transformation via the relaxation of the constraints; this defines a subspace, the space of constrained motion; and (2) specification of conditions on the motion in the space of constrained motion. The formulation and analysis associated with the first step can be seen as the generalization of the idea of the free-body diagram. This formulation is worked out in detail in this paper. The complement of the space of constrained motion is the space of admissible motion. The parametrization of this second subspace is generally the task of the analyst. If the two subspaces are orthogonal then useful decoupling can be achieved in the dynamics formulation. Conditions are developed for this orthogonality. Based on this, the dynamic equations are developed for constrained and admissible motions. These are the dynamic equilibrium equations associated with the generalized free-body diagram. They are valid for a broad range of constrained systems, which can include, for example, bilaterally constrained systems, redundantly constrained systems, unilaterally constrained systems, and nonideal constraint realization.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part II: Imposition of Constraints

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
József Kövecses
Keyword(s):  
Mechanical System ◽  
Configuration Space ◽  
Mechanical Systems ◽  
Constrained Systems ◽  
Simulation Design ◽  
Free Body Diagram ◽  
Free Body ◽  
Dynamics Models ◽  
And Control

In this part of the work we present some applications of the formulation developed in Part I (Kövecses, 2008, “Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation,” ASME J. Appl. Mech., 75(6), p. 061012) for the generalized free-body diagram in configuration space. This involves the specification and imposition of constraint conditions, which were identified as Step 2 of the analysis of a mechanical system in Part I. We will particularly consider bilaterally and unilaterally constrained systems, where constraints are realized via ideal or nonideal interfaces. We also look at the general case where the constraint configuration is possibly redundant. The results represent novel forms of dynamics models for mechanical systems, and can offer the possibility to gain more insight for simulation, design, and control.

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

Two Basic Features of Instantaneous Conjugate Motion and Their Importance in Facilitating Motion Analysis

2004 ◽  
Vol 126 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Chih-Hsin Chen ◽  
Janet Hong-Jian Chen
Keyword(s):  
Motion Analysis ◽  
Mechanical Systems ◽  
Body Motion ◽  
Geometrical Constraints ◽  
Free Body ◽  
Basic Features

Two basic features of instantaneous conjugate motion, which distinguishes it from instantaneous free body motion, are pointed out. Their influences on the geometrical constraints requisite for surface/line conjugation are discussed. Their importance in facilitating motion analysis of mechanical systems through linearization of relevant equations is clarified. Two illustrative examples are cited.

scholarly journals System Dynamics Model Application for Ergonomic Assessment of Manual Material Handling Tasks

2016 ◽  
Author(s):  
Hossein Abaeian ◽  
Osama Moselhi ◽  
Mohamad Al-Hussein
Keyword(s):  
System Dynamics ◽  
Material Handling ◽  
Dynamic Equilibrium ◽  
Project Managers ◽  
Dynamics Modeling ◽  
Work Related ◽  
Manual Material Handling ◽  
Compressive Loads ◽  
Levels Of Automation ◽  
Free Body

Despite increased levels of automation in manufacturing occupations in recent years, many activities are still performed through human intervention and involve Manual Material Handling (MMH), thus exposing workers to stress due to over-exertion and potential Work-Related Musculoskeletal Disorders (WRMSDs). An early ergonomic and physical demand assessment of work activities is critical to reducing exposure to risk and to maintaining desired levels of productivity. Biomechanics consists of applying concepts of static and dynamic equilibrium to different parts of the human musculoskeletal system using free-body diagrams to estimate muscle force and loads generated across the joints and tissues. System dynamics is a powerful tool applied in resolving complex problems with different influencing variables. This technique can help designers and managers to understand, evaluate and simulate the factors causing problems in the system. This paper presents the application of System Dynamics modeling to assess the biomechanical risks associated with manual material handling tasks. The case study presents predicted cumulative biomechanical compressive loads from material handling task and can assist project managers to understand and reduce exposure to ergonomic risks in the workplace.

Dynamics Redesign of Marine Structures

1985 ◽  
Vol 29 (04) ◽  
pp. 285-295 ◽  
Author(s):  
Curtis J. Hoff ◽  
Michael M. Bernitsas
Keyword(s):  
Large Scale ◽  
Structural Changes ◽  
Dynamic Equilibrium ◽  
Degree Of Freedom ◽  
Attractive Alternative ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Solution Methods ◽  
Tower Model ◽  
Energy Equations

The dynamic response of a marine structure depends upon the exciting forces and the modal characteristics of the structure. Excessive vibratory response requires reduction of the exciting loads or redesign of the structure or both. In this paper the general redesign problem is formulated. It applies to large-scale structures and allows for large structural changes. Solution of the redesign problem is achieved through perturbation methods which are an attractive alternative to traditional trial-and-error methods. Perturbation solution methods are based on dynamic equilibrium equations or energy equations or both. A new method based on the energy equations which enforces the mode orthogonality conditions is developed and evaluated against all existing methods. Two test cases, a 191-degree-of-freedom two-dimensional ship model and a 810-degree-of-freedom offshore light tower model are used to compare the methods numerically. It is shown that the method developed in this paper can produce, with a single finite element analysis of the baseline system, a structure which satisfies within acceptable limits all nonconflicting design objectives.

Method for solving dynamic equilibrium equations based on displacement excitation

2020 ◽  
Vol 19 (2) ◽  
pp. 423-433
Author(s):  
Xu Guolin ◽  
Zhang Lingxin ◽  
Bai Yashuang ◽  
Sun Hao
Keyword(s):  
Dynamic Equilibrium ◽  
Equilibrium Equations
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