POLYNOMIAL INTERPOLATION FUNCTIONS IN ADVANCED DYNAMICS
The present paper is devoted to the research of the main author, in what concerns the use of polynomial interpolation functions in generating the motion trajectory of an industrial robot. In this purpose are presented some classical formulations on polynomial interpolation functions of third order with restrictions. Unlike the third order polynomials, the higher order polynomials have the advantage of ensuring the continuity in accelerations of higher order. Are also presented, in explicit form, the expressions for the acceleration energy of first, second and third order, corresponding to the current and sudden motions multi body systems and which are further use to define the motion equations. In the final part of the paper, the formulations are applied to describe the dynamic behavior of a 2TR robot structure. So, are determined the expressions for the acceleration energies of first, second and third order, compulsory in defining the dynamic equations. The time variation laws for generalized coordinates, velocities, accelerations, energy of accelerations and generalized forces of first, second and third order will be also defined.
Key words: polynomial interpolation functions, advanced dynamics, acceleration energy, robotics.
R.P. Paul and H. Zhong, 1984, Robot Motion Trajectory Specification and Generation, Second International Symposium on Robotics Research, Kyoto, Japan, August.
R.E. Parkin, 1991, Applied Robotic Analysis, Prentice Hall, Englewood Cliffs, NJ.
L.Sciavicco and B. Siciliano, 2008, Robotics: Modeling, Planning, and Control, McGraw-Hill, New York.
Negrean I., Vușcan I., Haiduc N., Robotics. Kinematic and Dynamic Modeling, Editura Didactică și Pedagogică, R.A. București, 1998
J.J. Craig, 2005, Introduction to Robotics: Mechanics and Control, 3rd edition, Pearson Prentice Hall, Upper Saddle River, NJ.
Appell, P., Sur une forme générale des equations de la dynamique, Paris, 1899.
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., 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
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,
Negrean I., New Formulations on Motion Equations in Analytical Dynamics, Applied Mechanics and Materials, vol. 823 (2016),
pp 49-54 © (2016) TransTech Publications.
Negrean I., Advanced Notions in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, November. 2017, pg. 491-502.
Negrean I., Advanced Equations in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, November 2017, pg. 503-514.
Negrean I., New Approaches on Notions from Advanced Mechanics, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue II, June 2018, pg. 149-158.
Negrean I., Generalized Forces in Analytical Dynamic of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue II, June 2018, pg. 357-368.
Fu K., Gonzales R., Lee C., Control, Sensing, Vision and Intelligence, McGraw-Hill Book Co., International Edition, 1987
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