ADVANCED EQUATIONS 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 on the advanced notions, such as: generalized forces, 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 advanced equations of dynamics contain on the one hand advanced notions from kinematics and their differential transformations, typically to absolute motions, and on the other hand mass properties and generalized forces.

By means of the especially researches of the author, within of this paper will be presented reformulations and new formulations concerning the advanced kinematics parameters, as well as polynomial interpolating functions of higher order. In the following of the paper a few reformulations on fundamental theorems of dynamics and differential generalized principle of analytical dynamics will be presented. But, the fundamental aspect of this paper will consist in the fact that the author of the paper will propose generalized differential equations of higher order for any sudden and transitory motion. These equations contain acceleration energies of higher orders in generalized mathematical form.

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


Full Text:

PDF

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.

Negrean I., Advanced Notions in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics, and Engineering, Vol.60, Issue IV, October 2017, pp.

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.


Refbacks

  • There are currently no refbacks.


JOURNAL INDEXED IN :