New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

scholarly journals A New Approach in Analytical Dynamics of Mechanical Systems

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 95 ◽  
Author(s):  
Iuliu Negrean ◽  
Adina-Veronica Crișan ◽  
Sorin Vlase
Keyword(s):  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Matrix Form ◽  
Final Part ◽  
Analytical Dynamics ◽  
Research Papers ◽  
New Approach ◽  
D’Alembert Principle ◽  
Matrix Exponentials

This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

New Formulations on Motion Equations in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 49-54 ◽  
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Analytical Dynamics ◽  
Lagrange Principle ◽  
Motion Equations ◽  
Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

Identification of Modal Parameters of an Elastic Rotor With Oil Film Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Rainer Nordmann
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
Design Process ◽  
Mechanical Engineering ◽  
Mechanical Systems ◽  
Rotating Machinery ◽  
Modal Parameters ◽  
Powerful Method ◽  
Oil Film ◽  
Engineering Problems

Investigations of the dynamic behavior of structures have become increasingly important in the design process of mechanical systems. To have a better understanding of the dynamic behavior of a structure, the knowledge of the modal parameters is very important. The powerful method of experimental modal analysis has been used to measure modal parameters in many mechanical engineering problems. But the method was mainly applied to nonrotating structures. This presentation shows improvements of the classical modal analysis for a successful application in rotating machinery with nonconservative effects. An example is given, investigating the modal parameters of an elastic rotor with oil film bearings.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

Inertia Matrix Singularity of Series-Chain Spatial Manipulators With Point Masses

1993 ◽  
Vol 115 (4) ◽  
pp. 723-725 ◽  
Author(s):  
Sunil K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Dynamic Behavior ◽  
Mechanical Systems ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Numerical Errors ◽  
Singular Configurations ◽  
Spatial Series ◽  
Inertia Matrix ◽  
Incomplete Models

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation. An important step in this simulation is the inversion of inertia matrix of the system. In singular configurations of the inertia matrix, the simulation is prone to large numerical errors. Usually, it is believed that an inertia matrix is always positive definite. In this paper, it is shown that for spatial series-chain manipulators, when the links are modeled as point masses, a multitude of configurations exists when the inertia matrix becomes singular. These singularities arise because point masses lead to incomplete models of the system.

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