ADVANCED NOTIONS IN ANALYTICAL DYNAMICS OF SYSTEMS

Iuliu NEGREAN

Abstract


The dynamical study of the current and sudden motions of the multibody systems (MBS), as example the mechanical robot structure, and in accordance with differential principles typical to analytical dynamics of systems, is based, among others, on the advanced notions, such as: kinetic energy, acceleration energies of different orders and their absolute time derivatives of higher order. Advanced notions are developed in the direct connection with the generalized variables, also named independent parameters corresponding to holonomic mechanical systems. But, mechanically, the expressions of definition of the advanced notions contain on the one hand kinematical parameters and their differential transformations, corresponding to absolute motions, on the other hand the mass properties, highlighted by mass and mass center, inertial tensors and their generalized laws, as well as pseudoinertial tensors.

By means of the especially researches of the author, in this paper will be presented reformulations and new formulations concerning the advanced kinematics parameters, as well as advanced notions such as: kinetic energy and acceleration energies of different orders in explicit and matrix form. They are corresponding to the current and sudden motions of MBS. These formulations will also contain the absolute time derivatives of higher order of the advanced notions, according to differential equations of higher order, typically to analytical dynamics of systems.

Key words: analytical dynamics, mechanics, advanced notions, dynamics equations, robotics.


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References


Appell, P., Sur une forme générale des equations de la dynamique, Paris, 1899.

Appell, P., Traité de mécanique rationnelle, Paris, 1903.

Fu, K., et al, Robotics: Control, Sensing, Vision and Intelligence, McGraw-Hill Book Co., International Edition, 1987

Negrean, I., Robotics - Kinematic and Dynamic Modelling, EDP-R.A., Bucureşti, ISBN 973-30-5958-7, 1998.

Negrean, I., Negrean, D. C., Matrix Exponentials to Robot Kinematics, 17th International Conference on CAD/CAM, Robotics and Factories of the Future, CARS&FOF 2001, Durban South Africa, 2001, Vol.2, pp. 1250-1257, 32 rel., 4 ref.

Negrean, I., Negrean, D. C., The Acceleration Energy to Robot Dynamics, International Conference on Automation, Quality and Testing, Robotics, AQTR 2002, May 23-25, Cluj-Napoca, Tome II, pp. 59-64

Negrean I., Mecanică avansată în Robotică, ISBN 978-973-662-420-9, UT Press, Cluj-Napoca, 2008.

Negrean I., Mecanică, Teorie şi Aplicaţii, Editura UT PRESS, Cluj – Napoca, ISBN 978-973-662-523-7, 2012.

Negrean, I., Formulations in Advanced Dynamics of Mechanical Systems, The 11 th IFTOMM International Symposium on Science of Mechanisms and Machines, Mechanisms and Machine Science 18, DOI:10.1007/978-3-319-01845-4-19 Springer International Publishing Switzerland, pp. 185-195.

Negrean, I., Energies of Acceleration in Advanced Robotics Dynamics, Applied Mechanics and Materials, ISSN: 1662-7482, vol 762, pp 67-73 Submitted: 2014-08-05 ©(2015)TransTech Publications Switzerland DOI:10.4028/www.scientific.net/AMM.762.67, Revised:2014-11-16.

Negrean I., New Formulations on Acceleration Energy in Analytical Dynamics, Applied Mechanics and Materials, vol. 823 pp 43-48 © (2016) TransTech Publications Switzerland Revised: 2015-09, Doi: 10.4028

/www.scientific.net/AMM.823.43.

Negrean I., New Formulations on Motion Equations in Analytical Dynamics, Applied Mechanics and Materials, vol. 823 (2016),

pp 49-54 © (2016) TransTech Publications Switzerland Revised: 2015-09-09, DOI:

4028/www.scientific.net/AMM.823.49.

Negrean I., Formulations on the Advanced Notions in analytical Dynamics of Mechanical Systems, published in IJERM, ISSN: 2349-2058, Volume-03, Issue-04,

pp 123-130, 2016.

Negrean I., Advanced Notions and Differential Principles of Motion in Analytical Dynamics, Journal of Engineering Sciences and Innovation, Technical Sciences Academy of Romania, Vol. 1/2016, Issue 1, pp. 49-72, ISSN 2537-320X.

Negrean I., New Formulations in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics, and Engineering, Vol.60, Issue I, March 2017, pp. 49 – 56.

Negrean I., Mass Distribution in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics, and Engineering, Vol.60, Issue II, June 2017, pp. 175 – 184.

Negrean I., Generalized Forces in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics, and Engineering, Vol.60, Issue III, September 2017, pp.

Park, F.C., Computational Aspects of the Product-of-Exponentials Formula for Robot Kinematics, IEEE Transaction on Automatic Control, Vol. 39, No. 3, 1994

Pars L.A., A Treatise on Analytical Dynamics, Heinemann, London, (2007), Volume I, pp. 1-122.

Ursu – Fischer, N., Elemente de Mecanică Analitică, Casa Cărții de Știință, 2015.


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